MSc, MA, & PhD defences
Organizer: Graduate Program Assistant
Upcoming defences
Title:  Advancements in Model Combination and Uncertainty Quantification with Applications in Actuarial Science 
Speaker:  Sébastien Jessup 
Date:  Monday, September 30, 2024 
Time:  9:00 AM 
Location:  Conference Room, LB 9214 
Abstract: 
In this thesis, we focus on model combination, incorporating elements of uncertainty quantification to address different actuarial science issues. We first tackle the issue of overconfidence from a single model combination approach, highlighting how different combination assumptions can lead to different conclusions about the predicted variable. This is illustrated with an extreme precipitation example for the regions of Montreal and Quebec. We then focus on Bayesian model averaging (BMA), a very popular model combination technique relying on Bayes' theorem to attribute weights to models based on the likelihood that the observed data comes from the models considered. We propose a correction to the classical expectationmaximisation algorithm to account for data uncertainty, where we assume that the observed data is in fact not the only possible observable data. We then generalise our method to include Dirichlet regression, allowing for combination weights to vary depending on risk characteristics. These BMA approaches are applied to a simulation study as well as a simulated actuarial database and are shown to be very promising, as they allow for a more formal model combination framework for combining actuarial reserving methods in a smooth way based on predictive variables. Next, we adapt Bayesian model averaging using Generalised Likelihood Uncertainty Estimation to extreme value mixture models, and show that this modification allows for identifiying the "best" extreme value threshold, although a combination of models will outperform the single best mixture model. This is illustrated using the Danish reinsurance dataset. Finally, we show that the generalised BMA algorithm can be used to identify flexible extreme value thresholds depending on predictive variables. We use this generalised mixture model combination on a recent dataset from a Canadian automobile insurer. Kindly contact Dr. Melina Mailhot at melina.mailhot@concordia.ca for more details. 
Title:  Frames For Measures On Cantor Sets 
Speaker:  René Girard 
Date:  Thursday, September 26, 2024 
Time:  10:00 AM 
Location:  Conference Room, LB 9214 
Abstract: 
In this study of frames for measures on Cantor sets, we consider four measures with support contained in a Cantor set. These are the mass distribution measure, the Hausdorff measure of the appropriate dimension restricted to the Cantor set, the unique Borel measure from Hutchinson's theorem for selfsimilar sets and the LebesgueStieltjes measure with respect to the CantorLebesgue function. For the ternary and quaternary Cantor sets, respectively, we show that these four measures give the same Borel measure μ. This allows us to study frames in L2(μ). While the theory of frames is well developed, the literature on frames on Cantor sets is recent and limited. Central in defining frames of exponentials on Cantor sets is the set of integers (hereafter called exponent set) obtained from the Fourier transform of each measure supported on the corresponding Cantor set. After giving some background on frames, we follow the work of Jorgensen and Pedersen (1998) to find the exponent set of the mass distribution measure on the quaternary Cantor set from its Fourier transform and show that we do have an orthonormal basis, which is a special case of a frame. We also present the result of Jorgensen and Pedersen (1998) for the mass distribution measure on the ternary Cantor set, that it is not possible to have an exponent set that yields an orthonormal set of more than two exponentials. However, this leads to the question: can we show the existence of a frame from the exponent set of the mass distribution measure on the ternary Cantor set? Recent work (for example, Dutkay et al. (2011), Lev (2018), Picioroaga and Weber (2017) study this question but it remains an open problem. Please contact Dr. Galia Dafni at galia.dafni@concordia.ca for more details. 
Past defences
Title:  QuasiCompactness Of FrobeniusPerron Operator For Piecewise Convex Maps With Countable Branches 
Speaker:  Aparna Rajput 
Date:  Tuesday, September 17, 2024 
Time:  10:00 AM 
Location:  Conference Room, LB 9214 
Abstract: 
In this thesis proposal, we investigate the quasicompactness of the FrobeniusPerron operator associated with a piecewise convex map 𝜏 possessing a countably infinite number of branches on the interval [0,1]. We establish that for sufficiently large 𝑛, the iterates 𝜏𝑛 are piecewise expanding. By adapting the LasotaYorke inequality to satisfy the conditions of the IonescuTulcea and Marinescu ergodic theorem, we demonstrate the existence of an absolutely continuous invariant measure (ACIM) for the map, the exactness of the dynamical system, and the quasicompactness of the FrobeniusPerron operator.
Kindly contact Dr. Pawel Gora at pawel.gora@concordia.ca for more details. 
Title:  Inference of Extreme Value Distributions Using Bayesian Neural Networks 
Speaker:  Gabriel Haeck 
Date:  Monday September 9, 2024 
Time:  13:00 PM 
Location:  Conference Room, LB 9214 
Abstract: 
Accurate prediction of extreme weather events are crucial from a societal point of view, where the consequences of said events can have major financial and demographic impacts upon society. Extreme Value Theory (EVT) provides a statistical framework for the modelling of such extreme events. On the other hand, Bayesian Neural Networks (BNNs) extend traditional neural networks by incorporating Bayesian inference, which provides a probabilistic approach to learning and prediction in any given regression task. In this thesis, we extend the methodology of a recently introduced BNN and integrate it with EVT to be able to infer the parameters of Generalised Extreme Value (GEV) distributions. We then apply our methodology to annual maximal rainfall in Eastern Canada, where we infer and interpolate GEV parameter estimates across the interpolation region. The obtained results demonstrate that our approach outperforms Polynomial Regression and Inverse Distance Weighting methods in predicting extreme rainfall events. Please contact Dr. Melina Mailhot at melina.mailhot@concordia.ca for more details. 
Title:  A Comparison of Students’ Models of Knowledge to be Learned in an Introductory Linear Algebra Course with Results from Prior Research on Such Models in College Calculus Courses 
Speaker:  Hadas Brandes 
Date:  Wednesday, August 14, 2024 
Time:  2:00 PM 
Location:  Conference Room, LB 9214 
Abstract: 
Research done from an institutional perspective has found students to develop nonmathematical practices in college calculus courses that emphasize routinization of knowledge. The knowledge students are expected to learn, as indicated by tasks determining their grade in the course, enables students to routinize techniques and use nonmathematical considerations, such as didactic and social norms from their course, to justify their techniques. Such research has mostly been done in the calculus context. We sought to calibrate the study of the effects of institutionalized routinization of knowledge by investigating these in the context of a course in a different domain of mathematics and regulated by institutional mechanisms similar to those regulating college calculus courses. To this end, we adapted, to an introductory college linear algebra course at a large urban North American university, the framework and methodology from a body of research that qualifies students’ activity by attending to institutional mechanisms that regulate it. The framework appends to the Anthropological Theory of the Didactic (ATD) (Chevallard, 1985) notions from the Institutional Analysis and Development framework (IAD) (Ostrom, 2005). The ATD provides tools through which to model activities that occur in institutions and the IAD elaborates institutional mechanisms that regulate activity that occurs in institutions. We analyzed curricular documents to develop taskbased interviews (TBI) that could draw out the nature of the knowledge students mobilize. We conducted interviews with ten students shortly after they had completed the course. Our qualitative approach included an analysis of curricular documents to model knowledge to be learned in the course that relates to each TBI task, as well as an analysis to model the knowledge students mobilized in response to each TBI task. We found students mobilized nonmathematical practices: what they activated was conditioned by and delimited to knowledge normally expected of students in the course, and their mobilization contrasted in various ways with mathematics intrinsic to the tasks they were offered. We also propose an operationalization of the institutional notion of positioning previously proposed andexamined as a mechanism regulating students’ activity in didactic institutions. Kindly contact Dr. Nadia Hardy at nadia.hardy@concordia.ca for more details. 
Title:  Some Results In The Theory Of Real Hardy Spaces And BMO 
Speaker:  Shahaboddin Shaabani 
Date:  Friday, July 5, 2024 
Time:  10:00 AM 
Location:  Conference Room, LB 9214 
Abstract: 
In this talk, we discuss three results related to the theory of Hardy spaces Hp, the space of functions of bounded mean oscillation (BMO), and several types of operators acting on them. Our first result concerns the theory of Hardy spaces on domains. Here, we discuss a geometric characterization of the extension domains for Hp when 0 < p ≤ 1. Our result describes such domains completely in terms of their geometry. Next, we discuss a new characterization of Hp(Rn), where we show that the Hp(Rn) norm of any tempered distribution is equivalent to the operator norm of the associated paraproduct operator acting between two other suitable Hardy spaces. Then, we turn our attention to BMO(Rn). Here, there are three counterexamples and two theorems to be discussed. First, we present a counterexample to the continuity of the HardyLittlewood maximal operator on BMO(Rn). The next one concerns the unboundedness of the directional and strong maximal operators on BMO(Rn), and the last one is an example of a function in BMO(R2) with the property that none of its horizontal or vertical slices are in BMO(R), disproving the Fubini property for BMO(R2). At the end of this section, we show that the HardyLittlewood maximal operator preserves the space of functions of vanishing mean oscillation, VMO(Rn), and discuss a property of the slices of BMO functions. At the end, we discuss some directions of research related to the weak characterization of function spaces and the context in which they arise, and if time allows, we discuss some open problems in multiparameter harmonic analysis. Please contact Dr. Galia Dafni at galia.dafni@concordia.ca for more information. 
Title:  Deformation Of Convex Hypersurfaces In Euclidean Spaces By Powers Of Principal Curvatures 
Speaker:  Meraj Hosseini 
Date:  Thursday June 6, 2024 
Time:  3:00 PM 
Location:  LB362 in the Webster library 
Abstract: 
The results presented in this thesis contribute to the understanding of the evolution of smooth, strictly convex, closed hypersurfaces in ℝ𝑛+1 driven by nonsymmetric speeds on the principal curvatures. The preservation of convexity, the occurrence of singularities, and the asymptotic behavior of the flows are studied. After an introduction to geometric flows, Chapter 3 focuses on the analysis of the shortterm and longterm behavior of a contraction flow governed by a nonsymmetric speed for rotationally symmetric hypersurfaces. Our investigation reveals two key findings. Firstly, we establish that the flow maintains convexity throughout the deformation process. Secondly, we observe the development of a singularity within a finite time, leading to the convergence of every such strictly convex hypersurface to a single point. To investigate the asymptotic behavior of the flow, we employ a proper rescaling technique of the solutions. Through this rescaling, we demonstrate that the rescaled solutions converge subsequentially to the boundary of a convex body. In the fourth chapter, we extend our study to the shortterm and longterm behavior of a nonsymmetric expansion flow in ℝ𝑛+1. We show that, starting with a smooth, strictly convex, rotationally symmetric, closed hypersurface, the flow preserves convexity while expanding infinitely in all directions. Depending on certain parameters within the speed function, we establish that the existence time of the flow can be either finite or infinite. We also investigate the asymptotic behavior of the flow through a suitable rescaling process and demonstrate the subsequential convergence of the solutions to the boundary of a convex body in the Hausdorff distance. In the fifth chapter, we introduce the most general version of the flow studied in the Chapter 3. We address the barriers and challenges encountered when transitioning from a symmetric speed to a nonsymmetric speed and present our strategies to tackle some of these difficulties Kindly contact Dr. Alina Stancu at alina.stancu@concordia.ca for more details. 
Title:  Triple Product padic Lfunctions For Finite Slope Families And A padic GrossZagier Formula 
Speaker:  TingHan Huang 
Date:  Friday, May 24, 2024 
Time:  10:00 AM 
Location:  LB 9214 
Abstract: 
In this thesis, we generalize the padic GrossZagier formula of DarmonRotger on triple product padic Lfunctions to finite slope families. First, we recall the construction of triple product padic Lfunctions for finite slope families developed by AndreattaIovita. Then we proceed to compute explicitly the padic AbelJacobi image of the generalized diagonal cycle. We also establish a theory of finite polynomial cohomology with coefficients for varieties with good reduction. It simplifies the computation of the padic AbelJacobi map and has the potential to be applied to more general settings. Finally, we show by qexpansion principle that the special value of the Lfunction is equal to the AbelJacobi image. Hence, we conclude the formula. Please contact Dr. Giovanni Rosso at giovanni.rosso@concordia.ca or Dr. Adrian Iovita at adrian.iovita@concordia.ca for more details. 
Title:  Certain Rational Solution Of The Fifth Painlevé Equation And Their Asymptotic Behaviour 
Speaker:  Malik Balogoun 
Date:  Wednesday May 15, 2024 
Time:  11:30 AM 
Location:  LB 9214 
Abstract: 
In this thesis, our first goal is to formulate a generating function and compute its moments alongside the corresponding Hankel determinant. When the latter is nonzero, we will prove that for Painlevé 5, we can construct a Lax pair whose solution is a combination of the solution of the Riemann Hilbert Problem (RHP) and the generating function. An ingredient of that solution, called the Hamiltonian will be used to construct the Tau function which solves the ODE Painlevé V. As such, it will be easy to show that when the Hankel determinant vanishes, the RHP is not solvable, and its zeroes correspond to the poles of the rational solution of the ODE Painlevé V i.e. the Tau function. On the other hand, an asymptotic analysis will be conducted to prove that the domain of the poles of the rational solution of the ODE Painlevé V (its domain of non analyticity) defines a well shaped region with boundaries on the complex plane as the size of the square Hankel matrix goes to infinity. Kindly contact Dr. Marco Bertola at marco.bertola@concordia.ca for more details. 
Title:  DistanceBased Approach To Independent Component Analysis 
Speaker:  Debopriya Basu 
Date:  Monday April 15, 2024 
Time:  2:00 PM 
Location:  LB 9214 
Abstract: 
Independent Component Analysis (ICA) models are wellknown models that are used to decompose multivariate signals (mixtures) into nonGaussian independent sources (Independent Components). The independent observations are modeled as 𝒀 = 𝑨𝑿, where A is a nonsingular matrix and 𝑿 contains the independent components. In this study, we propose a distancebased method for estimating the unmixing matrix 𝑩 = 𝑨−𝟏, by minimizing the "distance" between the joint and the product of marginal empirical densities using a squarederror statistic. We investigate the largesample properties of the statistic and the related empirical process. Finally, we look to develop an algorithm to compute the Independent Components based on this derived theory and conduct a simulation study to justify the approach. Please contact Dr. Arusharka Sen at arusharka.sen@concordia.ca for more information. 
Title:  RiskAverse Policy Gradient For Tail Risk Optimizing Using Extreme Value Theory 
Speaker:  Parisa Davar 
Date:  Friday April 12, 2024 
Time:  10:00 AM 
Location:  LB 9214 
Abstract: 
In this work, we develop a riskaverse Policy Gradient algorithm in a tail risk optimization problem. Our objective is to find the optimal policy that minimizes tail risk, given a risk measure such as Conditional Value at Risk (CVaR). We employed Extreme Value Theory (EVT), along with the automated threshold method to manage risks associated with extreme events. This paper is the first to integrate EVT within riskaverse policy gradient RL algorithms for sequential decision making. To evaluate our approach, we initially test it on simulated data generated from heavytailed distributions, including the Generalized Pareto distribution (GPD) and the Burr distribution. Subsequently, we applied our method to address a hedging problem, aiming to mitigate exceedingly high risks and finding optimal gamma hedging strategies within a highly volatile market where options are notably expensive. This involves identifying the optimal proportion of gamma to hedge, while minimizing costs and risk associated with gamma hedging errors. Also, we utilize the finite difference method to approximate the gradient of the estimated CVaR. The experimental results indicate convergence in the policy, CVaR estimation, and the gradient approximation of estimated CVaR. Moreover, integrating Extreme Value Theory (EVT) into riskaverse policy gradient methods significantly improves performance, especially in markets characterized by an underlying asset following a Normal Inverse Gaussian distribution (NIG), known for its purejump semiheavy tail distribution. Please contact Dr. Frédéric Godin at frederic.godin@concordia.ca or Dr. Jose Garrido at jose.garrido@concordia.ca for more details. 
Title:  A Deep FewShot Network For Protein Family Classification 
Speaker:  Saeedeh (Nasrin) Jamali 
Date:  Monday March 25, 2024 
Time:  9:30 AM 
Location:  LB 9214 
Abstract: 
Protein sequence analysis is arguably a challenging modern bioinformatics problem covering various areas and applications such as sequence annotation, metagenomics, and comparative genomics. Proteomic information is primarily obtained through highthroughput techniques such as mass spectrometry and microarrays. Manually extracting and analyzing this information can be exceedingly timeconsuming, potentially taking weeks or months. Consequently, mathematicians and computer science researchers collaborate with scholars and scientists to computationally analyze proteinrelated information. By utilizing contemporary network approaches, they can expedite their projects and enhance accuracy. Proteins are essential for biological processes, such as functionality, structure, and regulation of the body’s tissues. They play a central role in various functions derived from enzymatic catalysis, transporting molecules from one organ to another to manage cells. Understanding unknown properties of proteins, and their functions based on measurable features is crucial for disease research, precision medicine, and therapeutics. Proteins mostly are built from 20 different amino acids making a onedimension sequence, called the primary protein sequence. When a new protein is discovered, the primary sequence family classification is seeking to examine the probability of its similarity based on its properties to a prior labeled family class with similar function and general behavior. Given the emergence of sequencing technologies and the resulting largescale protein databases with unknown properties, protein family classification is an open problem in the bioinformatics research area. Recent advances in computer science and digital technologies have opened new gates to researchers in various scientific domains. Bioinformatics, as an intermediary research field, takes advantage of these advancements from conventional machine learning methods to large language models, and biostatistics. Conventional alignmentfree techniques such as Kmer are commonly used for protein family classification, but they are limited to defining parameters that are computationally expensive, or difficult to estimate. Moreover, in the classification step, they depend on heuristic methods that can lead to a rough approximation of alignment distances. The latter limitation has been offset via the training step in machine learning models. Although machine learning techniques such as Support Vector Machines have been utilized for protein family classification, they are dependent on domain experts to generate features which could be a timeconsuming and challenging task. Deep learning (DL) algorithms have shown promising results in proteomics; however, their application is limited to the availability of massive data sets for training. Since the required data comes from experiments, it can be highly complex or incomplete. Moreover, optimizing parameters in DL models can be timeconsuming and costly. As an alternative, fewshot models can learn and generalize from a few observations. To rank the similarity between inputs, these networks employ a unique ranking structure, not requiring extensive training. To address the mentioned limitations, in this research, we designed and implemented a deep fewshot learning network for protein family classification and our result showed outperformance to stateofthe art baseline models. To the best of our knowledge, this is the first deep network tailored for primary sequence family classification that can highly perform with a very limited number of observations. Please contact Dr. Yogendra Chaubey at yogen.chaubey@concordia.ca for more details 
Title:  Surrogate Models for Diffusion on Graphs: A HighDimensional Polynomial Approach 
Speaker:  Kylian Ajavon 
Date:  Tuesday March 19, 2024 
Time:  11:00 AM 
Location:  LB 9214 
Abstract: 
Graphs are an essential mathematical tool used to model reallife complex systems such as social and transportation networks. Understanding diffusion processes on graphs is crucial for modelling phenomena such as the propagation of information within a network of individuals or the flux of goods and/or people through a transportation network. Accurately simulating these diffusion processes can be, in general, computationally demanding since it requires the solution of large systems of ordinary differential equations. Motivated by this challenge, we propose to construct surrogate models able to approximate the state of a graph at a given time from the knowledge of the diffusivity parameters. Specifically, we consider recently introduced highdimensional approximation methods based on sparse polynomial expansions, which are known to produce accurate, sampleefficient approximations when the function to be approximated has holomorphic regularity. Hence, to justify our methodology, we will theoretically show that solution maps arising from a certain class of parametric graph diffusion processes are indeed holomorphic. Then, we will numerically illustrate that it is possible to efficiently compute accurate sparse polynomial surrogate models from a few random samples, hence empirically showing the validity of our approach. Please contact Dr. Simone Brugiapaglia at simone.brugiapaglia@concordia.ca or Dr. Pawel Gora at pawel.gora@concordia.ca for more details. 
Title:  A RogersShephard Type Inequality For Surface Area 
Speaker:  Fadia Ounissi 
Date:  Monday March 11, 2024 
Time:  11:30 AM 
Location:  LB 9214 
Abstract: 
The famous RogersShephard inequality states that, for any convex body 𝐾 ⊂ ℝ𝑛, we have a volumetric inequality 𝑉𝑛 (𝐾 − 𝐾) ≤ (2𝑛/𝑛) 𝑉𝑛 (𝐾) that compares the volume of the difference body of 𝐾, 𝐾 − 𝐾, with the volume of K. Using Cauchy's surface area formula, a particular case of the more general Kubota's Formulae for Quermassintegrals, we extend this classical inequality to extrapolate an upper bound 𝐶𝐾 =𝑆(𝐾−𝐾) / 𝑆(𝐾) for the surface area of the difference body within the Euclidean space ℝ𝑛. We accompany this upper bound with a lower bound that we derive from the classical BrunnMinkowski inequality, 𝑉𝑛 (𝐴 + 𝐵) 1/𝑛 ≥ 𝑉𝑛(𝐴)1/𝑛 + 𝑉𝑛(𝐵)1/𝑛. Embracing a geometric perspective, we delve into the nuanced relationships between convex bodies and their respective surface areas, scrutinizing the patterns and properties of the difference body. This includes the validation of the upper bound in ℝ3 for certain classes of convex bodies, including smooth bodies and polytopes. We then analyse and establish a pattern for the formation of the difference body of pyramidal structures in ℝ3. Finally, we draw a conclusion on the effect of symmetry on 𝐶𝐾′𝑠 proximity to either bound. More specifically, we observe how deviations from symmetry, mainly when 𝐾 is a simplex, often considered the most asymmetric convex body, draws the constant closer to the upper bound. Please contact Dr.Alina Stancu at alina.stancu@concordia.ca for more details 
Title:  A RogersShephard Type Inequality For Surface Area 
Speaker:  Fadia Ounissi 
Date:  Monday March 11, 2024 
Time:  11:30 AM 
Location:  LB 9214 
Abstract: 
The famous RogersShephard inequality states that, for any convex body 𝐾 ⊂ ℝ𝑛, we have a volumetric inequality 𝑉𝑛 (𝐾 − 𝐾) ≤ (2𝑛/𝑛) 𝑉𝑛 (𝐾) that compares the volume of the difference body of 𝐾, 𝐾 − 𝐾, with the volume of K. Using Cauchy's surface area formula, a particular case of the more general Kubota's Formulae for Quermassintegrals, we extend this classical inequality to extrapolate an upper bound 𝐶𝐾 =𝑆(𝐾−𝐾) / 𝑆(𝐾) for the surface area of the difference body within the Euclidean space ℝ𝑛. We accompany this upper bound with a lower bound that we derive from the classical BrunnMinkowski inequality, 𝑉𝑛 (𝐴 + 𝐵) 1/𝑛 ≥ 𝑉𝑛(𝐴)1/𝑛 + 𝑉𝑛(𝐵)1/𝑛. Embracing a geometric perspective, we delve into the nuanced relationships between convex bodies and their respective surface areas, scrutinizing the patterns and properties of the difference body. This includes the validation of the upper bound in ℝ3 for certain classes of convex bodies, including smooth bodies and polytopes. We then analyse and establish a pattern for the formation of the difference body of pyramidal structures in ℝ3. Finally, we draw a conclusion on the effect of symmetry on 𝐶𝐾′𝑠 proximity to either bound. More specifically, we observe how deviations from symmetry, mainly when 𝐾 is a simplex, often considered the most asymmetric convex body, draws the constant closer to the upper bound. Please contact Dr.Alina Stancu at alina.stancu@concordia.ca for more details 
Title:  Hybrid Models For Claim Frequency And Severity Thesis Proposal 
Speaker:  Abhirupa Sen 
Date:  Friday February 2, 2024 
Time:  10:00 AM 
Location:  Via Zoom 
Abstract: 
Rate making in insurance refers to the pricing of insurance premiums through calculations, by actuaries, and adjustments in various factors. Fair pricing of insurance products is of utmost importance for insurance companies to be able to face market competition and stay in business. Therefore, poor rate making, which could be the result of poor prediction of risks, would be dangerous for insurers. Insurance data is characterized by an imbalance between the number of policyholders that claim and does that do not. The majority of premium payers do not incur accidents and thus do not claim their losses, resulting in a large number of “zero–claims". However, it is very important for the company to identify the customers who are more likely in future to file a claim, because every claim incurs a cost to the enterprise. Chapter 1 proposes a sampling technique devised to improve the identification of the possible future losses by better tracking of the non–zero claims. Generalized Linear Models have long been used by actuaries to accomplish the rate making task. The method is parametric and is based on certain assumptions about the distribution of the data. Insurance data with its probability mass at zero, do not fall exactly into the framework of GLMs. However, in recent years, various new machine learning algorithms have provided improvement by being more effective predictors than GLMs. What these algorithms lack is interpretability. Chapter 2 uses simple algorithms like regression trees, in combination with GLMs, to create a pre–processed GLM that is more effective than a standalone GLM. The endeavor of improving the classical GLM continues in Chapter 3. Here another combination of trees and GLM is used to produce results with more predictive capability that anyone of these algorithms as standalones. The new results are interpretable as well as improved. Please contact Dr. Jose Garrido at jose.garrido@concordia.ca for more information. 
Title:  Outliers Detection Based On Quantiles And Depth Functions 
Speaker:  Fidence Munyamahoro 
Date:  Thursday February 8, 2024 
Time:  1:00 PM 
Location:  SGW Campus, LB 9214 
Abstract: 
Outlier detection plays a crucial role in data analysis and is employed in various domains such as finance, healthcare, and anomaly detection. This Thesis presents a novel approach for detecting outliers using quantiles and depth functions, and we apply it to an air quality dataset. Quantiles provide a statistical measure of the distribution of data, while depth functions assess the centrality of observations relative to the entire dataset. Combining these two techniques, we propose a robust and effective method to identify outliers in multidimensional datasets. Our approach is particularly useful in scenarios where traditional outlier detection methods may be inadequate or fail to capture the complex patterns present in the data. By considering multiple quantiles, we can identify outliers that deviate from different aspects of the data distribution. Additionally, we incorporate depth functions, which measure the centrality of observations within a dataset, to further refine our outlier detection process. To evaluate the effectiveness of our approach, we apply it to a realworld air quality dataset. The data is about the New York Air Quality Measurements of 1973 for five months from May to September recorded daily. It contains 153 observations of 6 variables. By applying our method, we can identify outliers representing unusual air quality patterns, potentially indicating anomalies or errors in the data collection process. Our experimental findings support the proposed approach and effectively detect outliers in the air quality dataset. Compared to traditional outlier detection techniques, our method achieves higher accuracy and provides more detailed insights into the nature of the outliers. Furthermore, we show that the identified outliers can be valuable in understanding the factors contributing to air pollution and in improving the quality of air quality monitoring systems. The findings of this research contribute to the advancement of outlier detection methodologies and provide valuable insights for practitioners in identifying and handling outliers in realworld applications. Please contact Dr. Melina Mailhot at melina.mailhot@concordia.ca for more details 
Title:  Quadratic Hedging In A NonCausal AR (1) Model 
Speaker:  Caleb Danquah 
Date:  Wednesday, December 20, 2023 
Time:  9:00 AM 
Location:  LB 9214 
Abstract: 
This thesis explores hedging strategies for Europeantype derivatives under the noncausal AR (1) Cauchy model. Recently, such noncausal models have raised much attention in the finance literature due to their ability to replicate bubbles often observed in the cryptocurrency market, as well as their tractability for pricing standard European options. However, these discretetime models are incomplete, meaning that it is impossible to perfectly replicate a derivative's payoff in such a market. This thesis explores the use of quadratic hedging approaches to manage the risk of a derivative trader. Please contact Dr. Patrice Gaillardetz at patrice.gaillardetz@concordia.ca and/or Dr. Yang Lu at yang.lu@concordia.ca for more details. 
Title:  Complex Analytic Structure of the Stationary Solutions of the Euler Equations 
Speaker:  Aleksander Danielski 
Date:  Wednesday, December 20, 2023 
Time:  2:00 PM 
Location:  LB 9214 
Abstract: 
This work is devoted to the stationary solutions of the 2D Euler equations describing the timeindependent flows of an ideal incompressible fluid. There exists an infinitedimensional set of such solutions; however, they do not form a smooth manifold in the space of all divergencefree vector fields tangent to the boundary of the flow domain. This circumstance hinders the efforts to understand the structure of the set of stationary flows, and to further study other classes of solutions such as the timeperiodic or quasiperiodic flows. The previous authors considered the solutions in the Fréchet space of smooth functions and used powerful methods such as the NashMoserHamilton implicit function theorem. However, in their approach they overlook a surprising feature of the stationary flows which make the picture much more transparent and opens the way to further progress. This is the observation that the particle trajectories in the flow described by arbitrary solutions of the Euler equations in domains with analytic boundary are analytic curves, even if the velocity field has a finite regularity (say, belongs to the Sobolev or Hölder space). In particular, for any stationary solution, the flow lines are analytic curves, despite limited regularity of the velocity field. To study the stationary flows we change the viewpoint and consider the flow field as a family of analytic flow lines nonanalytically depending on parameter. We quantify the analyticity by introducing spaces of functions which have an analytic continuation to some strip containing the real axis such that on the boundary of the strip the function belongs to the Sobolev space. Further, we introduce the class of Sobolev functions of two variables which are analytic (in the above sense) with respect to one variable. Such functions describe the families of flow lines of stationary flows. These partially analytic functions form a complex Banach space. The stationary solutions satisfy (in the new coordinates) a quasilinear elliptic equation whose local solvability is proved by using the Banach Analytic Implicit Function Theorem (BAIF Theorem), thus we prove that the set of stationary flows is an analytic manifold in the complex Banach space of the flows (i.e. families of flowlines). In our previous work we realized this idea in the case of stationary flows in a periodic channel with analytic boundaries. In the present work we study a more complicated case of flows in a domain close to the disc, having one stagnation point. We use polar coordinates centered at the (unknown) stagnation point. This results in an elliptic quasilinear equation in the annulus which is degenerate at one component of the boundary. This makes the analysis more difficult. We introduce function spaces which are adaptations of the Kondratev spaces to the partially analytic setup and prove that the problem is Fredholm in those spaces. Further we use the BAIF Theorem, and prove that in our spaces, the set of stationary flows is locally a complexanalytic manifold. Kindly contact Dr. Alexey Kokotov at alexey.kokotov@concordia.ca for more details. 
Title:  Multivariate Change Of Measure As Correction Method In Ethical Pricing  
Speaker:  Éloi D’Amour Bizimana  
Date:  Wednesday, December 13, 2023  
Time:  1:30 PM  
Location:  LB 9214  
Abstract: 
In recent years, multiple global events have drawn society's attention to fairnessrelated issues and various societal movements resulted from them. For many fields, the impact was immediate and substantial, but for others it has been much more timid. Insurance is one of the latter. More specifically, the way fairness is implemented in algorithms used to calculate insurance premiums has not changed in decades due in part to the lack of modernization from regulators and in part to the complexity of the issue. Nonetheless, in preparation for society's growing expectations, researchers have developed many ways to implement algorithmic fairness. An exposition is made on this concept, including qualitative and quantitative definitions of fairness as well as approaches to its implementation found in the literature. In particular, the method developed by Lindholm et al. (2022) is discussed in detail and followed up by the introduction of our own novel approach. This approach is demonstrated on simulated data, and it is shown that it can significantly reduce unfairness according to predetermined metrics. Please contact Dr. Melina Mailhot at melina.mailhot@concordia.ca or Dr. Patrice Gaillardetz at patrice.gaillardetz@concordia.ca for more details. 

Title:  On The Convergence Of Three Applied Stochastic Models Related to Reflected Jump Diffusions, FastSlow Dynamical Systems, and Optimistic Policy Iteration  
Speaker:  Giovanni Zoroddu  
Date:  Friday, December 1, 2023  
Time:  1:00 PM  
Location:  LB 9214  
Abstract: 
This dissertation explores three stochastic models: additive functionals of reflected jumpdiffusion processes, twotime scale dynamical systems forced by αstable Lévy noise, and a variant of the Optimistic Policy Iteration algorithm in Reinforcement Learning. The connecting thread between all three projects is in showing convergence of these objects whose results have direct applied implications. A large deviation principle is established for general additive processes of reflected jumpdiffusions on a bounded domain, both in the normal and oblique setting. A characterization of the large deviation rate function, which quantifies the rate of exponential decay for the rare event probabilities of the additive processes, is provided. This characterization relies on a solution of a partial integrodifferential equation with boundary constraints that is numerically solved with its implementation provided. It is then applied to a few practical examples, in particular, a reflected jumpdiffusion arising from applications to biochemical reactions. We derive the weak convergence of the functional central limit theorem for a fastslow dynamical system driven by two independent, symmetric, and multiplicative αstable noise processes. To do this, a strong averaging principle is established by solving an auxiliary Poisson equation where the regularity properties of the solution are essential to the proof. The latter allows for the order of convergence to the averaged process of 11/α to be established and subsequently used to show weak convergence of the scaled deviations of the slow process from its average. The theory is then applied to a Monte Carlo simulation of an illustrative example. In the Optimistic Policy Iteration algorithm, Monte Carlo simulations of trajectories for some known environments are used to evaluate a value function and greedily update the policy which we show converges to its optimal value almost surely. This is done for undiscounted costs and without restricting which states are used for updating. We employ the greedy lookahead policies used in previous results thereby extending current research to discount factor α=1. The firstvisit variation of this algorithm follows as a corollary, and we further extend previous known results when the first state is picked for updating. Kindly contact Dr. Lea Popovic at lea.popovic@concordia.ca for more details. 

Title:  Absolutely Continuous Invariant Measures For Piecewise Convex Maps Of An Interval With Countable Number Of Branches 
Speaker:  A H M Mahbubur Rahman 
Date:  Wednesday September 27, 2023 
Time:  2:00 PM 
Location:  LB 9214 
Abstract: 
This thesis focuses on  (1) the study of the existence and exactness of Absolutely Continuous Invariant Measures (acim) for piecewise convex maps with a countable number of branches,(2) developing the Ulam’s method for approximation of density function and (3) the study of the existence of Absolutely Continuous Invariant Measures (acim) for piecewise concave maps using conjugation. For the first topic, we investigate the existence and uniqueness of acim for two classes Tpc∞(I), Tpc∞,0(I) of piecewise convex maps τ : I = [0, 1] → [0, 1] with countable number of branches. We provide sufficient conditions under which these maps have a unique acim, and we also give examples where multiple acims exist. Our results are based on the study of the FrobeniusPerron operator associated with the map, and we use analytical techniques to understand the properties of this operator. The main result of this Ph.D. thesis is the generalization of the existence of absolutely continuous invariant measure for piecewise convex maps of an interval with countable number of branches. We consider two classes Tpc∞(I), Tpc∞,0(I) of piecewise convex maps τ : I = [0, 1] → [0, 1] with countable number of branches. For the first class Tpc∞(I), we consider piecewise convex maps τ : I = [0, 1] → [0, 1] with countable number of branches and arbitrary countable number of limit points of partition points separated from 0. For the second class Tpc∞,0(I), we consider piecewise convex maps τ : I = [0, 1] → [0, 1] with countable number of branches with the partition points converging to 0. In the thesis, we study absolutely continuous invariant measures (acim) of τ ∈ Tpc∞(I) and τ ∈ Tpc∞,0(I) respectively. We also consider nonautonomous dynamical systems of maps in Tpc∞(I) or Tpc∞,0(I) and study the existence of acims for the limit map. Moreover, we study exactness of τ ∈ Tpc∞(I) and τ ∈ Tpc∞,0(I) respectively. We give a similar result for piecewise concave maps as well. We also discuss the approximation of acims for piecewise convex maps with countable number of branches using Ulam’s method. We also investigate the existence and uniqueness of ACIMs for two classes, Tpcv∞ (I) and Tpcv∞,1(I), of piecewise concave mapping σ. We use conjugation of piecewise convex map τ with countable number of branches that is defined in chapter 3 which implies that σ preserves a normalized absolutely continuous invariant measure whose density is an increasing function. Kindly contact Dr. Pawel Gora at pawel.gora@concordia.ca for more details. 
Title:  Advancing Model Combination And Uncertainty Integration Techniques With Applications In Actuarial Science 
Speaker:  Sébastien Jessup 
Date:  Wednesday September 27, 2023 
Time:  12:00 pm 
Location:  LB 9214 
Abstract: 
We consider three projects motivated by model uncertainty in multiple fields of actuarial science. The first project investigates the impact of model combination methods on extreme precipitation quantiles. Nonparametric methods rely on different assumptions than parametric methods such as Bayesian Model Averaging (BMA), potentially leading to very different results. Precipitation projections from 24 experts in Montreal and Quebec City are studied, and the difference in results between nonparametric and Bayesian approaches is used to illustrate the uncertainty of model combination. This shows how an actuary using multiple expert models should consider more than one combination method to properly assess the impact of climate change on loss distributions, seeing as a single method can lead to overconfidence in projections. Second, we propose an improvement to BMA to correct the known issue of convergence to a single model and adapt the algorithm to a heteroscedastic context. This improvement stems from including data uncertainty within the BMA algorithm, which considers data as the only observable data. The heteroscedastic adaptation is necessary to use BMA in an actuarial context, where loss is not homoscedastic between different insureds. A simulation study is used to demonstrate the efficiency of the proposed method, and it is applied to granular reserve models using a simulated dataset. This also builds on the work of Avanzi et al. (2022), who used BMA on aggregate reserve models. Finally, we aim to generalize the uncertainty integration approach by allowing for nonconstant weight attribution. This flexibility will allow for recognizing which model works best on different parts of the data in a transparent way. Such an approach can provide a useful tool for actuaries in pricing as well as reserving. Please contact Dr. Melina Mailhot at melina.mailhot@concordia.ca for more information. 
Title:  padic Lfunctions Attached To Dirichlet’s Characters 
Speaker:  Seyed Mohammadhossein Shahabi 
Date:  Tuesday September 12, 2023 
Time:  11:30 AM 
Location:  LB 9214 
Abstract: 
The aim of this thesis is to extend and elaborate on the initial sections of Neal Koblitz’s article titled "A New Proof of Certain Formulas for pAdic LFunctions." Koblitz’s article focuses on the construction of padic Lfunctions associated with Dirichlet’s character and the computation of their values at s = 1. He employs measure theoretic methods to construct the padic Lfunctions and compute the Leopoldt formula Lp(1,χ). To begin, we devote the first section (1.1) to providing a comprehensive proof of Dirichlet’s theorem for prime numbers. This is done because the theorem serves as a noteworthy example of how Dirichlet Lfunctions became relevant in the field of Number Theory. In the second chapter, we introduce the complex version of Dirichlet Lfunctions and Riemann Zeta functions. We explore their analytical properties, such as functional equations and analytic continuation. Subsequently, we construct the field of padic numbers and equip it with the padic norm to facilitate analysis. We introduce measures and perform padic integrations. Finally, we delve into the concept of padic interpolation for the Riemann Zeta function, aiming to establish the padic Zeta function. To accomplish this, we employ Mazur’s measure theoretic approach, utilizing the tools introduced in the third chapter. The thesis concludes by incorporating Koblitz’s work on this subject. For more information, please contact Dr. Adrian Iovita at adrian.iovita@concordia.ca 
Title:  Arithmetic and Computational Aspects of Modular Forms Over Global Fields 
Speaker:  David Ayotte 
Date:  Wednesday, August 30, 2023 
Time:  11:00 AM 
Location:  LB 9214/zoom 
Abstract: 
This thesis consists of two parts. In the first part, we present a positive characteristic analogue of Shimura's theorem on the special values of modular forms at CM points. More precisely, we show using Hayes' theory of Drinfeld modules that the special value at a CM point of an arithmetic Drinfeld modular form of arbitrary rank lies in the Hilbert class field of the CM field up to a period, independent of the chosen modular form. This is achieved via Pink's realisation of Drinfeld modular forms as sections of a sheaf over the compactified Drinfeld modular curve. In the second part of the thesis, we present various computational and algorithmic aspects both for the classical theory (over C) and function field theory. First, we implement the rings of quasimodular forms in SageMath and give some applications such as the symbolic calculation of the derivative of a classical modular form. Second, we explain how to compute objects associated with a Drinfeld modules such as the exponential, the logarithm, and Potemine's set of basic Jinvariants. Lastly, we present a SageMath package for computing with Drinfeld modular forms and their expansion at infinity using the nonstandard Aexpansion theory of López and Petrov. Kindly contact Dr. Giovanni Rosso at giovanni.rosso@concordia.ca for more details. 
Title:  Unified Stochastic SIR Model With Parameter Estimation And Application To The COVID19 Pandemic 
Speaker:  Terry Easlick 
Date:  Monday, August 28, 2023 
Time:  3:30 PM 
Location:  LB 9214/zoom 
Abstract: 
This thesis is comprised of three parts which collectively serve as a study of stochastic epidemiological models, in particular, the susceptible, infected, recovered/removed (SIR) model. I We propose a unified stochastic SIR model driven by Lévy noise. The structural model allows for timedependency, nonlinearity, discontinuity, demography and environmental disturbances. We present concise results on the existence and uniqueness of positive global solutions and investigate the extinction and persistence of the novel model. Examples and simulations are provided to illustrate the main results. II This part is twofold; we investigate the parameter estimation and forecasting of two forms of astochastic SIR model driven by small Lévy noises, and we provide theoretical results on parameter estimation of timedependent drift for Lévy noisedriven stochastic differential equations. A novel algorithm is introduced for approximating the leastsquares estimators, which lack attainable closedforms; moreover, the presented results ensure the consistency of these approximated Estimators. III We apply the previous results to study the COVID19 pandemic using data from New York City, New York. This application yields parameter estimation and predictive analysis, including the unknown period for a periodic transmission function and importation/exportation of infection. Kindly contact Dr. Wei Sun at wei.sun@concordia.ca for more details 
Title:  Backtesting Expectiles With Moment Conditions 
Speaker:  Jesús de Ita Solis 
Date:  Wednesday, August 23, 2023 
Time:  10:00 AM 
Location:  LB 9214/zoom 
Abstract: 
Under the current regulations, banks and insurance companies have the option to use their own internal models to monitor their risk. To this end, ValueatRisk (VaR) and the Expected Shortfall (ES) are typically used as the risk measures to compute their capital requirements. Nevertheless, both present flaws, such as the lack of coherence for VaR and lack of elicitability for ES. Recently, expectile has attracted much attention as a potential alternative to VaR and ES. However, the literature on expectile is mainly focused on its statistical inference, and just few traditional backtesting procedures have been proposed. This thesis proposes a traditional backtesting procedure for the expectile and considers its application on financial data. For more information, please contact Dr. Melina Mailhot at melina.mailhot@concordia.ca or Dr. Yang Lu at yang.lu@concordia.ca 
Title:  Machine Learning Techniques In UsageBased Insurance: Use Of Telematic Data In Auto Insurance 
Speaker:  Helia Alipanah (MSc) 
Date:  Wednesday, August 23, 2023 
Time:  12:30 PM 
Location:  LB 9214 
Abstract: 
The development of big data technologies and invehicle devices has contributed to the growth of UsageBased Insurance (UBI) in recent years. These invehicle devices, such as GPS and sensors, collect certain variables that can represent the driving behaviour of policyholders. This collected data, called telematic data, consist of several variables that have strong relationship with the likelihood of having an accident. Consequently, one can use telematic data to improve risk assessments and personalize car insurance premiums. In this thesis, a synthetic car insurance dataset emulated from a Canadianbased insurance company is used to investigate the use of telematic data in predicting the likelihood of having an accident. More precisely four machine learning techniques—logistic regression, random forests, gradient boosting trees, and feedforward neural networks—are employed to predict the risk of having an accident. Actuaries often use white box machine learning methods like logistic regression for risk assessment due to their interpretability. However, these methods are unable to detect nonlinear relationships between variables accurately. Therefore, more complex machine learning techniques such as random forests, gradient boosting trees, and feedforward neural networks are used to achieve more accurate risk assessment for accidents. In addition, two variable importance assessment methods—Shapley decomposition and marginal performance loss upon feature removal—are employed to provide insights into the feature contributions in the overall predictive performance of the models. For more information, please contact Dr. Jose Garrido at jose.garrido@concordia.ca or Dr. Frédéric Godin at frederic.godin@concordia.ca . 
Title:  On Bézier Curves and Surfaces 
Speaker:  Brandon Lazarus (MSc) 
Date:  Wednesday, August 16, 2023 
Time:  2:00 PM 
Location:  LB 9214 
Abstract: 
The Bézier curve is a continuous parametric curve that is used in numerous applications, such as automobile design and road design. I begin by surveying the fundamental properties of the Bézier curve and provide a variety of examples and calculations. I also survey, but more succinctly, the notion of the Bézier surface, which also has numerous applications in computeraided design software, such as aircraft design. I end by presenting the special types of points that a cubic Bézier curve (with four control points) can have. The configuration of planar control points that I present can be used by computer engineers to produce various shapes with respect to the necessary design requirements and to minimize fluctuations of the curve itself. For more information, please contact Dr. Alina Stancu at alina.stancu@concordia.ca 
Title:  On The Gaussian Product Inequality 
Speaker:  Oliver Russell (PhD) 
Date:  Friday July 21, 2023 
Time:  9:00 AM 
Location:  LB 9214 
Abstract: 
The long standing Gaussian product inequality (GPI) conjecture states that E[X1y1X2y2···Xnyn] ≥ E[X1y1]E[X2y2] ··· E[Xnyn] for any centered Gaussian random vector (X1,...,Xn) and any nonnegative real numbers yj,j=1,...,n. First, we complete the picture of bivariate Gaussian product relations by proving a novel “oppositeGPI” when 1<y1<0 and y2>0: E [X1y1X2y2] ≤ E [X1y1] E [X2y2]. Next, we investigate the three dimensional inequality E [X12X22m2Xn2m3] ≥ E [X12] E [X22m2] E [Xn2m3] for any natural numbers m2, m3.We show that this inequality is implied by a combinatorial inequality which we verify directly for small values of m2 and arbitrary m3. Then, we complete the proof through the discovery of a novel moment ratio inequality which implies this threedimensional GPI. We then extend these threedimensional results to the case where the exponents in the GPI can be real numbers rather than simply even integers. Finally, we describe two computational algorithms involving sumsofsquares representations of polynomials that can be used to resolve the GPI conjecture. To exhibit the power of these novel methods, we apply them to prove new fourand fivedimensional GPIs. For more details, please contact Dr. Wei Sun at wei.sun@concordia.ca. 
Title:  Arithmetic Biases For Binary Quadratic Forms 
Speaker:  Jeremy Schlitt (MSc) 
Date:  Friday July 21, 2023 
Time:  12:00 PM 
Location:  LB 9214 
Abstract: 
The prime number theorem for arithmetic progressions tells us that there are asymptotically as many primes congruent to 1 mod 4 as there are congruent to 3 mod 4. That being said, Chebyshev noticed that (numerically) there almost always seems to be slightly more primes in the 3 class. This simple fact has a highly nontrivial explanation. Rubinstein and Sarnak proved that under the assumption of some natural (yet still unproven) conjectures, there is a way to prove that there are more primes congruent to 3 than congruent to 1 more than half of the time (in an appropriate sense). Many other sets of integers demonstrate a bias towards a certain residue class modulo some number q Recently, Gorodetsky showed that the sums of two squares exhibit a Chebyshevtype bias, and that in this case the conjectures one must assume to prove the existence of the bias are weaker. In this thesis, we present two papers which demonstrate some bias in arithmetic progressions for sets of integers that are represented by a given binary quadratic form. In the first paper, we examine a bias towards the zero residue class for the integers represented by binary quadratic forms. In many cases, we are able to prove that the bias comes from a secondary term in the associated asymptotic expansion (unlike Chebyshev's bias, which lives somewhere at the level of O(x^{1/2+\epsilon).) In some other cases, we are unable to prove that a bias exists, even though it is present numerically. We thus make a conjecture on the general situation which includes the cases we could not prove. Many interesting results on the distribution of the integers represented by a quadratic form are proven along the way, and the paper finishes with some numerical data that is illustrative of the generic data for any quadratic form. In the second paper, we examine a different kind of bias. We ask for the distribution of pairs of sums of two squares in arithmetic progressions, i.e. how many numbers are the sum of two squares, congruent to a mod q, and are such that the next largest sum of two squares is congruent to b mod q? We prove that when q=1 mod 4, we have equidistribution among the q^2 possible pairs of residue classes. That being said, there exist bizarre numerical biases, most notably a negative bias towards repetition. The main purpose of the second paper is to provide a conjecture which explains the bias, via a secondary and tertiary term in the associated asymptotic expansion. We then support this conjecture with both numerical and theoretical evidence. The paper contains many partial results in the direction of the conjecture, as well as some theorems on the sums of two squares that are of independent interest. For example, we provide an integral representation for the number of integers not exceeding x which are the sum of two squares. This integral representation is akin to Li(x) for primes, in that it has a O(x^{1/2+\epsilon}) error term under the Generalized Riemann Hypothesis. Please contact Dr. Chantal David at chantal.david@concordia.ca for more details. 
Title:  A Comparison Of Students’ Models Of Knowledge To Be Learned In College Linear Algebra Courses With Results From Prior Research On Such Models In Real Analysis Courses 
Speaker:  Hadas Brandes (PhD) 
Date:  Monday, June 19, 2023 
Time:  12:00 PM 
Location:  Zoom  Kindly contact Dr. Nadia Hardy at nadia.hardy@concordia.ca for more details. 
Abstract: 
Research from the past two decades (Lithner, 2004; Barbé et al., 2005; Bergé, 2008; Hardy, 2009; Brandes, 2017; Broley, 2020) has dug into the college calculus institution to determine the type of student activity engendered by this institution. This research has found students in collegelevel calculus courses routinize techniques and rely on nonmathematical knowledge to justify the validity of their techniques, such as the authority of their teachers and textbooks (Hardy, 2009). This makes sense in light of research that examined the curricular documents in collegelevel calculus courses (Lithner, 2004; Brandes, 2017): the tasks to be accomplished and the related techniques lend themselves well to routinization and can be replicated without knowing why the techniques are apt or why they work. Broley (2020) investigated the activity of students who had recently passed Analysis 1, the first course in the calculus stream in which the knowledge to be taught might be expected to shift students’ focus away from rote procedure and toward the mathematical theory that undergirds it; but the results question the extent to which such a transition occurs. To accomplish tasks that appear in both Analysis 1 and in differential calculus, participants activated routines acquired in calculus and could not mobilize the related mathematical knowledge from Analysis 1 (Broley and Hardy, 2022). This research has come to understand collegelevel calculus students’ practices through a focus on the institutional nature of calculus courses, using Chevallard's (1985, 1992, 1999) Anthropological Theory of the Didactic. These investigations into the type of practices students develop in college calculus found them to be nonmathematical. But no equivalent research has checked into students’ learning in other domains of mathematics. This leaves unanswered a rather big question: to what extent can results about students' practices be explained by difficulties inherent to the mathematics at stake in college calculus? Do students develop such practices in other introductory mathematics courses? We propose to contribute to this research by taking a step toward answering this last question. Is students’ behavior in calculus replicated in linear algebra courses of the same level? Two courses in the college linear algebra stream seem appropriate venues for investigation: a college linear algebra course on matrix and vector algebra, which we'll call Linear Algebra 1 (LA1), and a followup linear algebra course, Linear Algebra 2 (LA2), where the knowledge to be taught might be expected to shift focus away from rote procedure and toward the mathematical theory that frames it. We wish to tackle the two so we may attend, as Broley (2020) has, to the potential transition from nonmathematical to mathematical bodies of knowledge. For our research, we adopted the methodology and theoretical framework previously used by (Lithner, 2004; Barbé et al., 2005; Bergé, 2008; Hardy, 2009; Brandes, 2017; Broley, 2020) to investigate students’ practices in these two courses. We have three objectives. First, to identify the knowledge students are expected to learn in LA1 and LA2, as indicated by problems on the final exams in these courses. Second, to identify the nature of the knowledge students from these courses mobilize when they solve linear algebra tasks; is it mathematical or nonmathematical? These first two objectives will serve to achieve our third: to determine if students' practices, as observed by research on the learning done in college calculus, are replicated in linear algebra. 
Title:  Boundedness of Operators on Local Hardy Spaces and Periodic Solutions of Stochastic Partial Differential Equations with RegimeSwitching 
Speaker:  Chun Ho Lau (PhD) 
Date:  Friday June 2, 2023 
Time:  9:00 am 
Location:  LB 9214 
Abstract:  In the first part of the thesis, we discuss the boundedness of inhomogeneous singular integral operators suitable for local Hardy spaces as well as their commutators. First, we consider the equivalence of different localizations of a given convolution operator by giving minimal conditions on the localizing functions; in the case of the Riesz transforms this results in equivalent characterizations of $h^1$. Then, we provide weaker integral conditions on the kernel of the operator and sufficient and necessary cancellation conditions to ensure the boundedness on local Hardy spaces for all values of $p$. Finally, we introduce a new class of atoms and use them to establish the boundedness of the commutators of inhomogeneous singular integral operators with $\bmo$ function. In the second part of the thesis, we investigate periodic solutions of a class of stochastic partial differential equations driven by degenerate noises with regimeswitching. First, we consider the existence and uniqueness of solutions to the equations. Then, we discuss the existence and uniqueness of periodic measures for the equations. In particular, we establish the uniqueness of periodic measures by proving the strong Feller property and irreducibility of semigroups associated with the equations. Finally, we use the stochastic fractional porous medium equation as an example to illustrate the main results. 
Title:  The Application of Machine LearningBased Prediction Models For Cardio Metabolic Risk Among A Representative US Adult Population: A CrossSectional Study of NHANES 19992006 
Speaker:  Jijie Xu (MSc) 
Date:  Thursday May 18, 2023 
Time:  3:30 pm 
Location:  Via Zoom  Please contact Dr. Lisa Kakinami at lisa.kakinami@concordia.ca for more details. 
Abstract:  Introduction: Common measures of adiposity (such as body mass index [BMI]) are only proxies. In contrast, dualenergy Xray absorptiometry (DXA) is more precise to measure body composition. Therefore, this thesis utilized an unsupervised machine learning technique to group individuals based on similarities in their fat and muscle mass bodycomposition from DXA. Associations between the newly developed bodycomposition phenotypes with cardiometabolic risks were compared to phenotypes using a median split. Methods: Data were from National Health and Nutrition Examination Survey (NHANES: 19992006 cycles, n=5,566; split into 70/30% training and test datasets), a representative U.S. population. The Kmeans cluster phenotypes based on partitioning observations from deciles of fatmass and musclemass adjusted for age and sex were identified. Model fit was assessed using the silhouette and elbow method. Performance of logistic regression models to identify unfavorable cardiometabolic risks using either the Kmeans or the 50th percentile cutoff phenotypes was assessed with the area under the receiver operating characteristic (ROCAUC). Analyses were performed separately for males and females and incorporated weighting and the complex sampling design. 
Title:  Islands And Ellipses In 2D Dynamical Systems 
Speaker:  Ted Szylowiec (MSc) 
Date:  Wednesday May 10, 2023 
Time:  1:00 pm 
Location:  LB 9214 
Abstract:  From the dynamics of 2D tent maps and generalized tent maps with memory, we present natural examples of attractors which are chaotic when viewed upclose, but periodic when viewed from afar. We prove that these examples support absolutely continuous invariant measures (ACIMs) by means of a combinatorial computerassisted technique. Then we examine a certain family of 2D generalized tent maps with memory, using geometrical methods. With these methods, we can determine a complete picture of the long term behavior of all orbits. Finally, we look at some puzzling phenomena and questions which arose during our research. 
Title:  DiscreteTime ArbitrageFree NelsonSiegel Model and its Applications to Participating Life Insurance Contracts and Swaptions Pricing 
Speaker:  Ramin Eghbalzadeh (PhD) 
Date:  Monday May 8, 2023 
Time:  9:30 am 
Location:  LB 9214 
Abstract:  This dissertation explores the importance of interest rate modeling in finance and actuarial science. It emphasizes the significance of yield curve modeling in pricing financial instruments, such as participating life insurance contracts and swaptions. The dissertation extends the work of previous studies and proposes a slightly different version of the discretetime arbitragefree NelsonSiegel model (DTAFNS), providing a closedform expression for riskfree spot rates and demonstrating its superior outofsample predictive ability. Additionally, the dissertation focuses on stochastic interest rates and mortality dynamics' impact on the pricing, reserving, and risk measurement approaches of participating life insurance contracts, with the introduction of a shadow reserve to improve accuracy. Lastly, the dissertation outlines procedures for pricing swaptions under the DTAFNS model. Overall, this dissertation contributes to the stability of the financial sector and protecting the financial wellbeing of individuals and institutions. 
Title:  Contraction of Hypersurfaces in Euclidean Space by Powers of Principal Curvatures 
Speaker:  Meraj Hosseini (PhD) 
Date:  Wednesday May 3, 2023 
Time:  1:30 pm 
Location:  LB 9214 
Abstract:  In the first part of this thesis, we study the contracting planar flow on the space of smooth, strictly convex, simple closed curves by an power of their curvature for 0 < a < 1. We show that under certain initial conditions, properly renormalized solutions of the flow converge to limiting shapes that solve different classes of LpMinkowski problem for p < 0. To prove our results, we introduce a new method of switching between rescalings. In the second part, we study, with a focus on surfaces of revolution, a nonhomogeneous flow in ℝ3 that is a generalization of the flow we studied in the first part where ai > 0 for i = 1, 2, X is the embedding of a smooth, closed, strictly convex surface in ℝ3 , 𝜅1, 𝜅2 are the principal curvatures and ν is the normal vector to the surface in ℝ3. We show that convex solutions to equation (2) remain convex, as long as they exist, and shrink to a point in finite time. Under suitable rescaling, solutions converge to a certain convex hypersurface. For the third part of the thesis, we propose to study the properties and the asymptotic behaviour of the following flow which is a generalization of the flow considered in ℝ3 where ai > 0 for i = 1, 2, · · · , n. 
Title:  Development and Application of Children's Sex and AgeSpecific FatMass and MuscleMass Reference Curves using the LMS Methodology 
Speaker:  Stephanie Saputra (MSc) 
Date:  Tuesday May 2, 2023 
Time:  10:30 am 
Location:  LB 9214 
Abstract:  Body mass index cannot distinguish between fatmass and musclemass, which may result in obesity misclassification. A dualenergy xray absorptiometry (DXA)derived phenotype classification based on fatmass and musclemass has been proposed for adults (>18 yo). We extend this research by developing children’s fatmass and musclemass reference curves and determining their utility in identifying cardiometabolic risk. Children’s (≤17 yo) DXA data in NHANES, a US national health survey (n=6,120) were used to generate sex and agespecific deciles of appendicular skeletal muscle index and fat mass index (kg/m2) with the Lambda Mu Sigma (LMS) method. The final curves were selected through goodness of fit (AIC, Qtests, detrended QQ plot). Four phenotypes (high [H] or low [L], adiposity [A] and muscle mass [M]: HAHM, HALM, LAHM, LALM) were identified using the literature’s guidelines above/below the median compared to samesex and sameage peers. The curves and their corresponding phenotypes were applied to QUALITY data, a longitudinal cohort (n=630, 810 yo in 2005) to assess whether the phenotypes correctly identified cardiometabolic risk using multiple linear regression at baseline, followup one (20082010), or followup two (20152017). Models were adjusted for age, sex, and Tanner’s stage. Chained equation was used to impute missing values in QUALITY. Compared to LAHM, LALM was associated with lower glucose at baseline; HAHM was associated with lower HDLc and higher LDLc, triglycerides, and HOMAIR; HALM was associated with elevated triglycerides and HOMAIR at all timepoints (all p<0.05). These phenotypes allowed for discrimination of crosssectional cardiometabolic risks, but further longitudinal exploration is recommended. 
Title:  Three Limit Theorems for Applied Stochastic Differential Equations with Jumps 
Speaker:  Giovanni Zoroddu (PhD) 
Date:  Thursday March 23, 2023 
Time:  2:00 pm 
Location:  Via Zoom  Please contact Dr. Lea Popovic for more details 
Abstract:  We consider two stochastic models with jumps: a reflected jump diffusion and a fastslow dynamical system forced by $\alpha$stable noise. For the former, we establish a large deviation principle for additive functionals of its path; that is, its asymptotic behavior far from its mean. We characterize the rate of exponential decay for these probabilities as a consequence of the unique solution to a partialintegro differential equation and illustrate how one may approximate such quantities numerically. For the latter, using the regularity properties to a solution of a related Poisson equation, we derive an averaging principle, where we establish that the slow process is asymptotically near its averaged equation to an order of $1\frac{1}{\alpha}$. In turn, this rate of convergence is used to scale the difference between the slow and averaged processes and derive the weak convergence of these scaled deviations, thereby establish a functional central limit theorem. 
Title:  Catastrophe Insurance Risk: Estimation of the Tail Distortion Risk Measure and Calculation of Voronoi Deviance Residuals, with Applications in Earthquake and Wildfire Insurance Modeling. 
Speaker:  Roba Bairakdar (PhD) 
Date:  Monday February 20, 2023 
Time:  10:00 am 
Location:  Via Zoom  Please contact Dr. Melina Mailhot for more details. 
Abstract:  In this thesis, we focus on catastrophic events in the context of insurance and risk management. Insurance risk arising from catastrophes such as earthquakes is one of the components of the Minimum Capital Test for federally regulated property and casualty insurance companies. Given the spatial heterogeneity of earthquakes, the ability to assess whether the spatiotemporal model fits are adequate in certain locations is crucial in obtaining usable models. Accordingly, we extend the use of Voronoi residuals to calculate deviance Voronoi residuals. We also create a simulationbased approach, in which losses and insurance claim payments are calculated by relying on earthquake hazard maps of Canada. As an alternative to the current guidelines of OSFI, a formula to calculate the countrywide minimum capital test is proposed based on the correlation between the provinces. Finally, an interactive web application is provided which allows the user to simulate earthquake damage and the resulting financial losses and insurance claims, at a chosen epicenter location. Homeowners' insurance in wildfireprone areas can be a very risky business that some insurers may not be willing to undertake. We create an actuarial spatial model for the likelihood of wildfire occurrence over a fine grid map of North America. Several models are used, such as generalized linear models and treebased machine learning algorithms. A detailed analysis and comparison of the models show a best fit using random forests. Sensitivity tests help in assessing the effect of future changes in the covariates of the model. A downscaling exercise is performed, focusing on some highrisk states and provinces. The model provides the foundation for actuaries to price, reserve, and manage the financial risk from severe wildfires. We explore the first and secondorder asymptotic expansions of the generalized tail distortion risk measure for extreme risks. We propose to use the firstorder asymptotic expansion in order to provide an estimator for this risk measure. The asymptotic normality of the estimator at intermediate and extreme confidence levels are shown, separately. Additionally, we provide biascorrected estimators, where we focus on the case where the tail index $\gamma$ is estimated by the Hill estimator. We perform a simulation study to assess the performances of the proposed estimators proposed and we compare them with other estimators in the literature. Finally, we showcase out estimator on several reallife actuarial data sets. 
Title:  Special Values of Triple Product padic Lfunctions Associated With Finite Slope Families and padic AbelJacobi Maps. 
Speaker:  TingHan Huang (PhD) 
Date:  Monday February 20, 2023 
Time:  10:00 am 
Location:  SLB 92104  Please contact Dr. Giovanni Rosso or Dr. Adrian Iovita for more details. 
Abstract:  In this work, I prove a padic GrossZagier formula which relates the special value of the triple product padic Lfunction associated with finite slope families at a balanced classical weight, to the padic AbelJacobi image of the generalized diagonal in the product of three KugaSato varieties, evaluated at a certain differential form. This generalizes the result of H. Darmon and V. Rotger for Hida families. 
Title:  Symplectic Aspects of Gaudin Integrable Systems and Szegö Kernel Variational Method 
Speaker:  Ramtin Sasani (PhD) 
Date:  Tuesday, January 31, 2023 
Time:  4:00 pm 
Location:  SLB 92104 and via Zoom. Please contact Dr. Marco Bertola for more details. 
Abstract:  In this thesis, we will study the symplectic aspects of classical Gaudin systems, an important type of integrable dynamical systems at both classical and quantum levels. After a review of integrability and the Lax representation of integrable dynamical systems, we will investigate the analytical properties of Gaudin model via its spectral curve. The main focus is to reconstruct the Lax matrix using the analytical information of the system and subsequently, provide a symplectic structure for the phase space. We will also calculate the symplectic potential in terms of actionangle coordinates using Szegö kernel variational method. A brief look into the spectral transform aspect as well as the study of variational properties of vector of Riemann constants will also follow. 
Title:  Sparse Recovery Under Structure 
Speaker:  Sina MohammadTaheri (PhD) 
Date:  Monday, December 19, 2022 
Time:  10:00 am 
Location:  SLB 92104 
Abstract:  Sparse recovery generally aims at reconstructing a sparse vector (i.e., a vector having most of its coefficients equal to zero), given linear measurements performed via a mixture (or sensing) matrix, typically underdetermined, in the presence of additive noise. Notably, sparse recovery problems can be studied in the case where sparse vectors exhibit an underlying structure. In this thesis proposal, we will investigate two types of structure, namely weighted sparsity and sparsity in levels. As algorithms play a major role in sparse recovery problems, we will propose a variant of Orthogonal Matching Pursuit (OMP), a wellknown algorithm in the realm of sparse recovery, for the weighted sparsity and review the previously proposed OMP in levels. Finally, we will explore research pathways to transfer these sparse recovery algorithms under structure to (deep) neural networks through the recently developed paradigm of “algorithm unrolling”. Applications in medical imaging (compressive MRI) and highdimensional function approximation will be of our particular interest. 
Title:  Stationary Distributions for Asymmetrical Autocatalytic Reaction Networks with Discretenessinduced Transitions (DITs) 
Speaker:  Cameron Gallinger (MSc) 
Date:  Thursday, December 15, 2022 
Time:  12:00 pm (Noon) 
Location:  SLB 92104 
Abstract:  The phenomenon of discretenessinduced transitions is highly stochastic dependent dynamics observed in a family of autocatalytic chemical reaction networks including the acclaimed Togashi Kaneko model. These reaction networks describe the behaviour of several different species interacting with each other, with the counts of species concentrating in different extreme possible values and occasional fast switching between them. This phenomenon is only observed under some regimes of rate parameters in the network, where stochastic effects of small counts of species take effect. The dynamics for networks in this family is ergodic with a unique stationary distribution. While an analytic expression for the stationary distribution in the special case of symmetric autocatalytic behaviour was derived by Bibbona, Kim, and Wiuf, not much is known about it in the general case. Here we provide a candidate distribution for reaction networks when the autocatalytic rates are different. The distribution was inspired by a model in population genetics, the Moran model with genic selection, which shares many similar reaction dynamics to our autocatalytic networks. We show that this distribution is stationary when autocatalytic rates are equal, and that it is close to stationary when they are not equal. 
Title:  Misconceptions About Limits in the Transition from Calculus to Real Analysis 
Speaker:  MarcOlivier Ouellet (MSc) 
Date:  Friday, December 9, 2022 
Time:  11:00 am 
Location:  SLB 92104 
Abstract:  Misconceptions about limits in introductory Calculus such as the infamous “a function never reaches its limit” have been thoroughly studied in previous research. However, their resolution is rarely documented. Our objective is to contribute to the understanding of the “vanishing” of common misconceptions about limits as students progress from Calculus to Analysis. In addition, we investigate the possibility that early Calculus misconceptions may influence the learning of Real Analysis in such a way that new, related misconceptions are developed about more advanced concepts. To this end, we created a questionnaire devised to uncover seven of the welldocumented Calculus misconceptions, as well as three conjectured misconceptions related to introductory Analysis concepts. The questionnaire was administered to ten students actively enrolled in a first or second Real Analysis course. To analyze participants’ answers, we introduced a model of misconception classification which includes six levels. Using this model, we identified consistent incorrect reasonings indicating the possibility that instruction after elementary Calculus has not contributed to the resolution of some misconceptions. We observed that certain students’ answers exhibited what we refer to as “transitional behavior” from one level to another and discuss what this may mean in terms of overcoming misconceptions. In addition, we identified one instance of a student’s learning of Real Analysis potentially being influenced by their Calculus misconceptions. Finally, we briefly considered the presence of misconceptions about fundamental mathematics, such as logical argumentation and mathematical notation, and new misconceptions that students may develop as they learn more advanced mathematics. 
Title:  On Geometrical and Analytical Aspects of Moduli Spaces of Quadratic Differentials 
Speaker:  Roman Klimov (PhD) 
Date:  Thursday, December 1, 2022 
Time:  3:00 pm 
Location:  SLB 362 
Abstract:  In this dissertation, we consider moduli spaces of meromorphic quadratic differentials in homological coordinates and applications of underlying deformation theory of AhlforsRauch type. Another application of the deformation theory lies within the symplectic geometry of the monodromy map of the Schrödinger equation on a Riemann surface with a meromorphic potential having second order poles. We discuss the conditions for the base projective connection, which induces its own set of Darboux homological coordinates, to imply the Goldman Poisson structure on the character variety. Using this result, we perform generalized WKB expansion of the generating function of monodromy symplectomorphism (the YangYang function) and compute its leading asymptotics. 
Title:  Exploration of ThrowIns in Soccer Using Machine Learning Algorithms 
Speaker:  Andreas Bancheri (MSc) 
Date:  Wednesday, November 30, 2022 
Time:  4:00 pm 
Location:  SLB 92104 
Abstract:  The evolving field of sports analytics is still in the early stages of its adoption. Moreover, soccer analytics utilizing tracking data is even further limited. This research is motivated by Liverpool's integration of a department for throwin research, assisting them in winning a league title. This research project makes use of the (generously given) German national soccer team (DFB) tracking and event data which includes all player movement during a game, and more specifically, movement before and after a throwin. The probability of a throwin being completed (according to two mutually exclusive definitions) is estimated using various metrics developed using the aforementioned tracking and event data. Binary classification models are used to estimate the completion probability of a given throwin. The results show that the model provides an encouraging framework of achieving the goal of a universal throwin metric. Therefore, any given throwin may be evaluated, providing a meaningful tool to soccer teams, in the footsteps of xG (expected goal) or xPass (expected pass) models. 
Title:  Sensitivity Testing Using Expectiles with Applications in Extremes 
Speaker:  Emily Wright (MSc) 
Date:  Monday, August 29, 2022 
Time:  1:30 pm 
Location:  Room LB 92104 and via Zoom. For more information, please contact Dr. Mélina Mailhot 
Abstract:  Climate change is leading to an increase in the severity and prevalence of natural catastrophes. From a statistical and actuarial perspective, it is desirable to measure the potential impact of changes in different aspects of these extreme events. Sensitivity analysis is used to measure and characterize uncertainty of a model based on these changes, where a baseline model includes a number of covariates mapped to an output via an aggregation function. Given a defined stress on the baseline distribution, a type of sensitivity analysis used in actuarial mathematics, Reverse Sensitivity Testing, is suitable for several types of models (including black box models) and uses different risk measures along with the Kullback–Leibler divergence (KL divergence) as a measure of discrepancy between the baseline probability measure and the stressed probability measure. An expansion of Reverse Sensitivity Testing is provided to include both a coherent and elicitable risk measure; expectiles. Since the KL divergence is considered to be a pessimistic divergence for extreme values, the Renyi divergence, which is a broader divergence, is included as an extension ideal for extreme events given a user specified order parameter. Both the KL divergence and the Renyi divergence are implemented on a standard normal random variable, a numerical example, and then applied to extreme loss data from a natural catastrophe that hit Western Canada in 2020. 
Title:  Overconvergent Modular Forms, Theoretical and Computational Aspects 
Speaker:  Alexandre Johnson (MSc) 
Date:  Tuesday, August 23, 2022 
Time:  2:00 pm 
Location:  Room LB 92104 and via Zoom. For more information, please contact Dr. Giovanni Rosso 
Abstract:  In this thesis, we perform a review of the theory of overconvergent modular forms, then we explore the distribution of the eigenvalues of the Hecke operator T_p by considering their padic valuations. We begin by covering algebraic and geometric definitions of modular forms, then expanding these definitions to overconvergent modular forms. We then introduce algortithms, from “Computations with classical and padic modular forms” by Alan G. B. Lauder, which provide a method for calculating the padic valuations of the aforementioned eigenvalues. In order to implement these algorithms, programs were written for the Sagemath computer algebra program to perform the necessary calculations. These programs were used to collect lists of padic valuations, for various values of p and for spaces of modular forms of various weights and of various levels. The collected data confirms the fact that the GouveaMazur conjecture is false, but also indicates that it may be a useful approximation of the true behavior at large weights or at large values of p, at least for the first few slopes. It shows the existence of “plateaus” of weights which have the same slopes, up to the precision used, even at low values of p and k. The reason for the existence of these “plateaus” is unknown. 
Title:  Dirichlet Twists of Elliptic Curves over Function Fields 
Speaker:  Antoine ComeauLapointe (PhD) 
Date:  Tuesday, August 23, 2022 
Time:  10:00 am 
Location:  On Line Via Zoom. For more information, please contact Dr. Chantal David 
Abstract:  Some of the most fundamental questions about $L$functions are concerned with the location of their zeros, in particular at the central point, or on the critical line. Following the work of Montgomery and then of Katz and Sarnak, number theorists have learned that it is very fruitful to study families of $L$functions rather than individual $L$functions. Given a family of $L$functions, it is common to classify it according to its symmetry type. The symmetry type can be either symplectic, orthogonal, or unitary, which refers to the corresponding ensemble from random matrix theory that models most accurately the distribution of the zeros of the family. This thesis presents two papers studying the zeros of the family of Dirichlet twists of the $L$function of an elliptic curve $E$ over $\mathbb{F}_q[t]$. In the first paper (Chapter 2), we show that the onelevel density (the study of the lowlying zeros) for this family agrees with the conjecture of Katz and Sarnak based on random matrix theory, for test functions with limited support on the Fourier transform. For quadratic twists, the support of the Fourier transforms of the test functions is restricted to the interval (1,1), and we observe an orthogonal symmetry. For higher order twists, the support is restricted to (1/2,1/2) and we observe a unitary symmetry. For quadratic twists, the support is large enough to obtain a positive proportion of $L$functions which do not vanish at the central point. In the second paper (Chapter 3), we are taking the opposite point of view, and we construct certain elliptic curves $\mathbb{F}_q[t]$ with infinitely many twists of high order vanishing at the central point, generalizing a construction of Li and DonepudiLi for Dirichlet $L$functions. This construction only works when $E/\mathbb{F}_q[t]$ is a constant curve. In the general case where $E$ is not a constant curve, we performed extensive numerical computations that are compatible with the conjectures of DavidFearnleyKisilevsky and MazurRubin over number fields, which predict that such vanishing should be rare. The last chapter presents an algorithm to construct the factorizations of the monic polynomials, a description of the zeros of $L(E\otimes\chi,u)$, and a family of quadratic twists such that the rank of $L(\chi,u)$ goes to infinity. 
Title:  Applications of Multiple Dirichlet Series in Analytic Number Theory 
Speaker:  Martin Čech (PhD) 
Date:  Friday, June 17, 2022 
Time:  10:00 am 
Location:  Online via Zoom. For more information, please contact Dr. Chantal David 
Abstract:  We consider several classical problems in analytic number theory from the point of view of multiple Dirichlet series. In Chapter 1, we review the required background and give an overview of the thesis. 𝑆(𝑋,𝑌) = Σ Σ ( m )

Title:  Arithmetic Aspects of GSp2g : padic Families of Siegel Modular Forms, Eigenvarieties and Families of Galois Representations 
Speaker:  JuFeng Wu (PhD) 
Date:  Thursday, May 12, 2022 
Time:  10:00 am 
Location:  Online via Zoom. For more information, please contact Dr. Giovanni Rosso 
Abstract:  This thesis reports the three articles [Wu21a, DRW21, Wu21b] written by the author and his collaborators. These three papers concern various arithmetic aspects of the algebraic group GSp2g, which are interrelated under the theme of eigenvarieties. We first present a construction of sheaves of overconvergnet Siegel modular forms by using the perfectoid method, originally introduced by ChojeckiHansenJohansson for automorphic forms on compact Shimura curves over Q. These sheaves are then proven to be isomorphic to the ones constructed by AndreattaIovitaPilloni. Using perfectoid methods, we establish an overconvergent EichlerShimura morphism for Siegel modular forms, generalising the result of AndreattalovitaStevens for elliptic modular forms. More precisely, we establish a Hecke and Galoisequivariant morphism from the overconvergent cohomology groups associated with GSp2g to the space of overconvergent Siegel modular forms. It was asked by AndreattaIovitaPilloni whether the classical points of the eigenvariety parametrising the finiteslope cuspidal Siegel eigenforms is eta le over the weight space. Inspired by Kim's pairing presented in the book of Bella"iche, which allows one to study the ramification locus of the eigencurve, we generalise Kim's pairing to study the ramification locus of the cuspidal eigenvariety for GSp2g, providing some partial answer to the question asked by AndreattaIovitaPilloni. Finally, it is expected that such a pairing not only allows one to study the geometry of the eigenvariety but also carries interesting arithmetic information. Inspired by the book of BellaïicheChenevier, we study families of Galois representations over the cuspidal eigenvariety for GSp2g· Under some reasonable hypotheses as well as some conditions, we deduce the vanishing of the adjoint Selmer group associated with the Galois representation associated with a finiteslope cuspidal eigenclass in the cohomology of the Siegel modular variety. 
Title:  Relationship Between Isothermal and Geodesic Polar Coordinate Systems 
Speaker:  Mehrad Alavipour (MSc) 
Date:  Friday, May 5, 2022 
Time:  1:00 pm 
Location:  Online via Zoom. For more information, please contact Dr. Alexey Kokotov 
Abstract:  The main result of the thesis is an asymptotic formula establishing a correspondence between two at first sight unrelated systems of local coordinates on a twodimensional real analytic Riemannian manifold: the socalled isothermal local parameter and the Riemann normal coordinates. This formula was stated without proof in 1992 Fay’s memoir on analytic torsion, a weaker statement was proved in Walsh’s 2012 PhD thesis. A survey of basic facts from differential geometry used in our proof is also given. 
Title:  Quantitative Trading in North American Power Markets 
Speaker:  Dominic Andoh (MSc) 
Date:  Wednesday, February 23, 2022 
Time:  1:00 pm 
Location:  Online via Zoom. For more information, please contact Dr. Cody Hyndman 
Abstract:  Shortterm load forecasting (STLF) in electrical grids is critical for efficiency and reliability. Many countries in the west have deregulated their electric power industry, allowing for a free and competitive market; this has made load forecasting a more critical task for estimating future spot prices. Load forecasting is a complex task due to seasonal variation and the nonstationarity of historical load data. Also, multicollinearity among exogenous variables adds to the complexities of STLF. We use data provided by PlantE Corp, an investor in the New York Control Area electricity market. We propose STLF models and test them against the benchmark New York Independent System Operator (NYISO) model; we propose three different models for STLF. The first is a hybrid model consisting of a clustering part and a weighted Euclidean distance norm component; we name it the ClusterWED model. The other two models are deep learning models we shall call BiLSTM and AttnLSTM model. Both are based on the encoderdecoder architecture. The encoder part of the BiLSTM model comprises a bidirectional layer. The decoder is a unidirectional LSTM layer. We incorporate the attention mechanism into the AttnLSTM model, where we assign weights to all the hidden states of the encoder before making the next predictions in the decoder. The encoder and decoder for the AttnLSTM model are both unidirectional LSTM layers. Though none of our proposed models outperformed the NYISO model due to the disparities in the input information, the results from the ClusterWED model prove that we can perform a complex task like STLF using simple nonlinear models. Also, the results from the BiLSTM model demonstrate the applicability of deep learning when adapted for structured time series data. The generalization and consistency of the BiLSTM model suggest that we could achieve competitive performance against the benchmark once the information gap is bridged. 
Title:  Inference Procedures for CopulaBased Models of Bivariate Dependence 
Speaker:  Mr. Magloire LoudeguiDjimdou (PhD) 
Date:  Friday, December 10, 2021 
Time:  10:00 a.m. 
Location:  Online via Zoom. For more information, please contact Dr. Arusharka Sen 
Abstract:  In this thesis, we develop inference procedures for copulabased models of bivariate dependence. We first investigate the distribution of Kendall’s functions for joint survivors since Kendall’s functions are important for identifying Archimedean copula models. We then provide two estimators for the generator of an Archimedean copula. We also propose a plugin estimator for Kendall’s tau and a maximum pseudolikelihood estimation for the copula model parameters in cases where the survival times are subject to bivariate random censoring. These tests are based on the usual (univariate) KaplanMeier estimator and a recently proposed estimator for the bivariate case. Keywords: Archimedean copula, Kendall distribution, generator, distribution, estimator, asymptotic variance, influence function. 
Title:  The Painlevé II Hierarchy: Geometry and Applications 
Speaker:  Ms. Sofia Tarricone (PhD) 
Date:  Friday October 15, 2021 
Time:  10:00 a.m. 
Location:  Room SLB 9214 and Online via Zoom For more information, please contact Dr. Marco Bertola 
Abstract:  The Painlevé II hierarchy is a sequence of nonlinear ODEs, with the Painlevé II equation as first member. Each member of the hierarchy admits a Lax pair in terms of isomonodromic deformations of a rank 2 system of linear ODEs, with polynomial coefficient for the homogeneous case. It was recently proved that the TracyWidom formula for the HastingsMcLeod solution of the homogeneous PII equation can be extended to analogue solutions of the homogeneous PII hierarchy using Fredholm determinants of higher order Airy kernels. These integral operators are used in the theory of determinantal point processes with applications in statistical mechanics, random matrix theory, random growth models and other fields. From this starting point, this PhD thesis explored the following directions. We found a formula of TracyWidom type connecting the Fredholm determinants of matrixvalued analogue of the higher order Airy kernels with particular solution of a matrixvalued PII hierarchy. The result is achieved by using a matrixvalued RiemannHilbert problem to study these Fredholm determinants and by deriving a blockmatrix Lax pair for the relevant hierarchy. We also found another generalization of the TracyWidom formula, this time relating the Fredholm determinants of finitetemperature versions of higher order Airy kernels to parti cular solutions of an integrodifferential Painlevé II hierarchy. In this setting, a suitable operatorvalued RiemannHilbert problem is used to study the relevant Fredholm determinant. The study of its solution produces in the end an operatorvalued Lax pair that naturally encodes an integrodifferential Painlevé II hierarchy. 
Title:  Computational Aspect of Drinfeld Modular Forms 
Speaker:  Mr. David Ayotte (PhD) 
Date:  Thursday, September 2, 2021 
Time:  10:00 a.m. 
Location:  For more information regarding this online defence, please contact Dr. Giovanni Rosso 
Abstract:  The goal of this Ph.D. research is to study Drinfeld modular forms from a computational point of view. In particular, we study the notion of Aexpansion for Drinfeld modular forms. This notion can be useful for computing the Hecke action and to obtain a certain multiplicity one result for a specific set of cuspidal forms (which fails in the general case). 
Title:  Moments of Cubic Hecke LFunctions 
Speaker:  Mr. Arihant Jain (MSc) 
Date:  Tuesday August 17, 2021 
Time:  10:00 a.m. 
Location:  For more information regarding this online defence, please contact Dr. Chantal David 
Abstract:  Moments of families of Lfunctions provide understanding of their size and also about their distribution. The aim of this thesis is to calculate the asymptotics of the first moment of Lfunctions associated to primitive cubic Hecke characters over Q(ω) and upper bounds for 2kth moments for the same family. Both of these results assume Generalized Riemann Hypothesis. We consider the full family of characters which results in a main term of order x log x. We also calculate conditional upper bounds for 2kth moments for the same family and conclude that there are x primitive characters of conductor at most x for which the Lfunction doesn’t vanish at the central point. 
Title:  Neural Networks in Insurance 
Speaker:  Ms. Magali Goulet (MSc) 
Date:  Wednesday August 11, 2021 
Time:  9:30 a.m. 
Location:  For more information regarding this online defence, please contact Dr. Mélina Mailhot 
Abstract:  To date, in the insurance industry, the premium for a given risk is based on the expected claim amount since the models used are only meant to calculate a mean response. However, getting more information about the distribution of each single risk would be useful for risk assessment. A method in Neural Networks (NN) called Tractable Approximate Gaussian Inference (TAGI) by Goulet et al. (2020) allows to study each response individually since each output follows its own Normal distribution. The main contributions of this thesis are to make this technique available through an open source package, to apply TAGI in insurance and compare it to other techniques and to study risk measures with it. 
Title:  Pricing and Hedging Financial Derivatives with Reinforcement Learning Methods 
Speaker:  Mr. Alexandre Carbonneau (PhD) 
Date:  Tuesday, June 29, 2021 
Time:  1:00 p.m. 
Location:  For more information regarding this online defence, please contact Dr. Frédéric Godin 
Abstract:  This thesis studies the problem of pricing and hedging financial derivatives with reinforcement learning. Throughout all four papers, the underlying global hedging problems are solved using the deep hedging algorithm with the representation of global hedging policies as neural networks. The first paper, “Equal Risk Pricing of Derivatives with Deep Hedging”, shows how the deep hedging algorithm can be applied to solve the two underlying global hedging problems of the equal risk pricing framework for the valuation of European financial derivatives. The second paper, “Deep Hedging of LongTerm Financial Derivatives”, studies the problem of global hedging very longterm financial derivatives which are analogous, under some assumptions, to options embedded in guarantees of variable annuities. The third paper, “Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments”, studies derivative prices generated by the equal risk pricing framework for longterm options when shorterterm options are used as hedging instruments. The fourth paper, “Deep equal risk pricing of financial derivatives with nontranslation invariant risk measures”, investigates the use of nontranslation invariant risk measures within the equal risk pricing framework. 
Title:  Quantization of CalogeroPainlevé System and MultiParticle Quantum Painlevé Equations IIVI 
Speaker:  Ms. Fatane Mobasheramini (PhD) 
Date:  Tuesday, April 13, 2021 
Time:  10:30 a.m. 
Location:  For more information regarding this online defence, please contact Dr. Marco Bertola 
Abstract:  In this dissertation, we implement canonical quantization within the framework of the socalled CalogeroPainlevé correspondence for isomonodromic systems. The classical systems possess a group of symmetries and in the quantum version, we implement the (quantum) Hamiltonian reduction using the HarishChandra homomorphism. This allows reducing the matrix operators to Weylinvariant operators on the space of eigenvalues. We then consider the scalar quantum Painlevé equations as Hamiltonian systems and generalize them to multiparticle systems; this allows us to formulate the multiparticle quantum timedependent Hamiltonians for the Schrödinger equation ℏ𝜕𝑡Ψ=𝐻𝐽Ψ ,𝐽=𝐼𝐼,…,𝑉𝐼. We then generalize certain integral representations of solutions of quantum Painlevé equations to the multiparticle case. These integral representations are in the form of special 𝛽 ensembles of eigenvalues and can be constructed for all the Painlevé equations except the first one. They play the role, in the quantum world, of rational solutions in the classical world. These special solutions exist only for particular values of the quantum Hamiltonian reduction parameter (or coupling constant) 𝜅. We elucidate the special values of the corresponding parameters appearing in the quantized CalogeroPainlevé equations IIVI. 
Title:  The Development of (Non)Mathematical Practices through Paths of Activities and Students’ Positioning: The Case of Real Analysis 
Speaker:  Ms.Laura Broley (PhD) 
Date:  Thursday, August 27, 2020 
Time:  1:00 p.m. 
Location:  Via Zoom 
Abstract:  Previous research has found that within elementary university courses in single variable and multivariable Calculus, the activities proposed to students may enable and encourage the development of nonmathematical practices. More specifically, the research has shown that students can obtain good passing grades by learning highly routinized techniques for a restricted set of task types, with little to no understanding of the mathematical theories that justify the choice and validity of the techniques. We were interested in knowing what happens as students progress to more advanced courses in Analysis. The study presented in this thesis focussed on a first Real Analysis course at a large urban North American university. To frame our study, we turned to the Anthropological Theory of the Didactic, which offers theoretical tools for modelling practices as they exist within and across institutions. We analyzed various course materials to develop models of practices students may have been expected to learn in the course. These were then used to inform our construction of a taskbased interview that would allow us to elicit and model practices students had actually learned. Interviews were conducted with fifteen students shortly after they passed the course. In our qualitative analyses of the resulting data, we found that students’ practices were (non)mathematical in different ways and to varying degrees. Moreover, this seemed to be linked not only to the kinds of activities students had been offered in the course, but also to the characteristically different ways in which students may have interacted with those activities. As theoretical tools for thinking about these links, we introduce the notion of a path to a practice and a framework of five positions that students may adopt in a university mathematics course institution: the Student, the Skeptic, the Mathematician in Training, the Enthusiast, and the Learner. We discuss the possibility of designing paths of activities that might perturb students’ positioning and encourage the development of practices that are more mathematical in nature. 
Title:  Financial Risk Management in Electricity Markets 
Speaker:  Ms. Maedeh Mehranfar (MSc) 
Date:  Tuesday, August 25, 2020 
Time:  10:00 a.m. 
Location:  For more information regarding this online defence, please contact Dr. Frédéric Godin 
Abstract:  This research studies a decision problem to allocate an electricity trading firm’s budget to its trading strategies using a risk management framework. The considered problem consists of maximizing a firm’s profit while controlling two risk measures: the variance of the portfolio and the conditional value at risk. The dependence structure of the returns associated with different trading strategies is modelled using vine copulas and it is assumed that the marginal distribution of the returns originates from the Johnson family of distributions. The studied problem is formulated as a stochastic integer quadratic program and solve it with a commercial optimization software. The proposed mathematical program is assessed on the firm’s portfolio and the obtained results are discussed. 
Title:  Selfnolar Planar Polytopes: When Finding the Polar is Rotating by Pi 
Speaker:  Mr. John Mark Fortier (MSc) 
Date:  Tuesday, August 25, 2020 
Time:  9:30 a.m. 
Location:  For more information regarding this online defence, please contact Dr. Alina Stancu 
Abstract:  The impetus for our work was a preprint by Alathea Jensen, titled selfpolar polytopes. In the preprint, Jensen describes an intriguing method to add vertices to a selfpolar polytope while maintaining selfpolarity. This method, applied exclusively to selfnolar planar polytopes, is our main focus for our work here. We expound upon the method, as well as clarify the underlining theoretical framework it was derived from. In doing so, we have built up our own setup and framework and proved the theoretical steps independently, often differently than the original paper. In addition, we prove some noteworthy properties of selfnolar sets such as: all selfnolar sets are convex, the family of all selfnolar sets is uncountable, and the set of all selfnolar planar polytopes is dense in the set of all selfnolar planar sets. We also give proofs concerning the length of the boundary of a selfnolar set with smooth boundary, the center of mass of selfnolar polytopes and the Mahler volume product. Moreover, we prove an original theorem that can be used as a practical method to construct selfnolar polytopes. 
Title:  Geometric Inequalities and Bounded Mean Oscillation 
Speaker:  Mr. Ryan Gibara (PhD) 
Date:  Friday, August 14, 2020 
Time:  9:00 a.m. 
Location:  Via Zoom 
Abstract:  In this thesis, we study the space of functions of bounded mean oscillation (BMO) on shapes. We prove the boundedness of important nonlinear operators, such as maximal functions and rearrangements, on this space and analyze how the bounds are affected by the underlying geometry of the shapes. We provide a general definition of BMO on a domain in R^n, where mean oscillation is taken with respect to a basis of shapes, i.e. a collection of open sets covering the domain. We prove many properties inherent to BMO that are valid for any choice of basis; in particular, BMO is shown to be complete. Many shapewise inequalities, which hold for every shape in a given basis, are proven with sharp constants. Moreover, a sharp norm inequality, which holds for the BMO norm that involves taking a supremum over all shapes in a given basis, is obtained for the truncation of a BMO function. When the shapes exhibit some product structure, a product decomposition is obtained for BMO. We consider the boundedness of maximal functions on BMO on shapes in R^n. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, the collection of functions of bounded lower oscillation. When the basis of shapes does not possess an engulfing property but exhibits a product structure with respect to lowerdimensional shapes coming from bases that do possess an engulfing property, we show that the corresponding maximal function is bounded from BMO to a space we define and call rectangular BLO. We obtain boundedness and continuity results for rearrangements on BMO. This allows for an improvement of the known bound for the basis of cubes. We show, by example, that the decreasing rearrangement is not continuous on BMO, but that it is both bounded and continuous on VMO, the subspace of functions of vanishing mean oscillation. Boundedness for the symmetric decreasing rearrangement is then established for the basis of balls in R^n. 
Title:  Some Fluctuation Results Related to Drawdown Times for Spectrally Negative Levy Processes and on Estimation of Entropy and Residual Entropy for Nonnegative Random Variables 
Speaker:  Mr. Nhat Linh Vu (PhD) 
Date:  Tuesday, August 11, 2020 
Time:   
Location:  Via Zoom 
Abstract:  Part I: Some Fluctuation Results on Drawdown Times for Spectrally Negative Levy Processes In this thesis, we first introduce and review some fluctuation theory of Levy processes, especially spectrally negative Levy processes with and without tax. Then we consider a more realistic model by associate drawdown times, which is a function of the running maximum, into these fluctuation results. Particularly, we present the expressions for the classical twosided exit problems for these processes with drawdown times in terms of scale functions. Also, we find the expressions for the discounted present values of tax payments with drawdown time in place of ruin time. Finally, we obtain the solution to the occupation times of the general spectrally negative Levy processes spends in drawdown interval killed on either exiting a fix upper level or a drawdown lower level. Part II: On Estimation of Entropy and Residual Entropy for Nonnegative Random Variables Entropy has become more and more essential in statistics and machine learning. A large number of its applications can be found in data transmission, cryptography, signal processing, network theory, bioinformatics, and so on. Therefore, the question of entropy estimation comes naturally. Generally, if we consider the entropy of a random variable knowing that it has survived up to time t, then it is defined as the residual entropy. In this paper we focus on entropy and residual entropy estimation for nonnegative random variable. We first present a quick review on properties of popular existing estimators. Then we propose some candidates for entropy and residual entropy estimator along with simulation study and comparison among estimators. 
Title:  Heuristic Conjectures for Moments of Cubic LFunctions Over Function Fields 
Speaker:  Mr. Brian How (MSc) 
Date:  Friday, June 26, 2020 
Time:  1:00 p.m. 
Location:  For more information regarding this online defence, please contact Dr.Chantal David 
Abstract:  Let Lq(s, χ) be the Dirichlet Lfunction associated to χ, a cubic Dirichlet character with conductor of degree d over the polynomial ring Fq[T]. Following similar work by Keating and Snaith for moments of Riemann zetafunction, Conrey, Farmer, Keating, Rubinstein, and Snaith [CFKRS 2005] introduced a framework for proposing conjectural formulae for integral moments of general Lfunctions with the help of random matrix theory. In this thesis we review the heuristic found in [CFKRS 2005] and apply their work in order to propose moments for Lq(s, χ). cubic Lfunctions over function fields. We find asymptotic formulae when q ≡1 (mod 3), the Kummer case, and when q ≡2 (mod 3), the nonKummer case. Moreover, while the authors of [CFKRS 2005] provide only the framework for proposing (k,k)moments of primitive Lfunctions, we extend their work following the work of David, Lalín, and Nam to propose (k,l)moments of cubic Lfunctions where k ≥ l ≥ 1 [DLN]. Furthermore, we provide explicit computations that elucidate the combinatorics of leading order moments and find a general form as well. 
Title:  On Properties of Ruled Surfaces and their Asymptotic Curves 
Speaker:  Ms. Sokphally Ky (MSc) 
Date:  Thursday, June 11, 2020 
Time:  4:00 p.m. 
Location:  For more information regarding this online defence, please contact Dr. Alina Stancu 
Abstract:  Ruled surfaces are widely used in mechanical industries, robotic designs, and architecture in functional and fascinating constructions. Thus, ruled surfaces have not only drawn interest from mathematicians, but also from many scientists such as mechanical engineers, computer scientists, as well as architects. In this paper, we study ruled surfaces and their properties from the point of view of differential geometry, and we derive specific relations between certain ruled surfaces and particular curves lying on these surfaces. We investigate the main features of differential geometric properties of ruled surfaces such as their metrics, striction curves, Gauss curvature, mean curvature, and lastly geodesics. We then narrow our focus to two special ruled surfaces: the rectifying developable ruled surface and the principal normal ruled surface of a curve. Working on the properties of these two ruled surfaces, we have seen that certain space curves like cylindrical helix and Bertrand curves, as well as Darboux vector fields on these specific ruled surfaces are important elements in certain characterizations of these two ruled surfaces. This latter part of the thesis centers around a paper by Izmuiya and Takeuchi, for which we have considered our own proofs. Along the way, we also touch on the question of uniqueness of striction curves of doubly ruled surfaces. 
Title:  Efficient Probabilistic Pricing Algorithms for Multiple Exercise Options 
Speaker:  Mr.Nicolas Breton Essis (PhD) 
Date:  Friday, May 1, 2020 
Time:  10:00 a.m. 
Location:  Via Zoom 
Abstract:   
Title:  Special Comparison Theorems For KleinGordon Equation In d ≥ 1 Dimensions 
Speaker:  Mr. Hassan Harb (PhD) 
Date:  Thursday, January 30, 2020 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We first study boundstate solutions of the KleinGordon equation for vector potentials which in one spatial dimension have the form V(x) = vf(x), where f(x)≤0 is the shape of a finite symmetric centra=l potential that is monotone nondecreasing on [0, ꝏ) and vanishes as x→ ꝏ , and v>0 is the coupling parameter. We characterize the graph of spectral functions of the form v= G(E) which represent solutions of the eigenproblem in the coupling parameter v for a given E: they are concave, and at most unimodal with a maximum near the lower limit E = m of the energy E ԑ (m, m). This formulation of the spectral problem immediately extends to central potentials in d > 1 spatial dimensions. Secondly, for each of the dimension cases, d=1 and d ≥ 2, a comparison theorem is proven, to the effect that if two potential shapes are ordered f_1(r) ≤ f_2(r), then so are the corresponding pairs of spectral functions G_1(E) ≤ G_2(E) for each of the existing eigenvalues. These results remove the restriction to positive energies necessitated by earlier comparison theorems for the KleinGordon equation by Hall and Aliyu. Corresponding results are obtained when scalar potentials S(x) are also included. We then weaken the condition for the ground states by proving that if ∫^{x}_{0}[ƒ_{2}(t)  ƒ_{1}(t]φ(t)dt ≥ 0, the corresponding coupling parameters remain ordered, where φ_{i}= 1, or φ_{i} is the bound state solution of the KleinGordon equation with potential V_{i}, i = 1, 2. 
Title:  SiebergWitten TauFunction on Hurwitz Spaces 
Speaker:  Ms. Meghan White (MSc) 
Date:  Thursday, January 23, 2020 
Time:  4:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We provide a proof of the form taken by the SiebergWitten TauFunction on the Hurwitz space of Nfold ramified covers of CP1 by a compact Riemann surface of genus g, as a result derived in [11] for a special class of monodromy data. To this end, we examine the RiemannHilbert problem with N x N quasipermutation monodromies, whose corresponding isomonodromic taufunction contains the SiebergWitten taufunction as one of three factors. We present the solution of the RiemannHilbert problem following [9]. Along the way, we give elementary proofs of variational formulas on Hurwitz spaces, including the Rauch formulas. 
Title:  Individual Claims Reserving: Using Machine Learning Methods 
Speaker:  Mr. Dong Qiu (MSc) 
Date:  Friday, December 6, 2019 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  To date, most methods for loss reserving are still used on aggregate data, arranged in a triangular form such as the ChainLadder (CL) Method and the overdispersed Poisson (ODP) Method. With the booming of machine learning methods and the significant increment of computing power, the loss of information resulting from the aggregation of the individual claims data into accident and development year buckets is no longer justifiable. Machine learning methods like Neural Networks (NN) and Random Forest (RF) are then applied and the results are compared with the traditional methods on both simulated data and real data (aggregate at company level). 
Title:  Green Function and SelfAdjoint Laplacians on Polyhedral Surfaces 
Speaker:  Mr. Kelvin Lagota (PhD) 
Date:  Monday, November 25, 2019 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  
Title:  A Brief Review of Support Vector Machines and a Proposal for a New Kernel via Localization Heuristics 
Speaker:  Mr. Malik Balogoun (MA) 
Date:  Thusday, August 29, 2019 
Time:  2:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this paper, an attempt of solution is brought to a particular problem of binary classification case in the framework of support vector machine. The case displays observations from two classes, and uniformly distributed on a space so that linear separation by a hyperplane is only possible in tiny cubes (or rectangles) of that space. The general approach to classification in the input space is then extended with the design of a new ad hoc kernel that is expected to perform better in the feature space than the most common kernels found in the literature. Theoretical discussions to support the validity, the convergence to Bayes classifier of the new designed kernel, and its application to simulated dataset will be our core contribution to one a way we can approach a classification problem.

Title:  Skewed Spatial Modeling for Arsenic Contamination in Bangladesh 
Speaker:  Mr. Qi Zhang (MA) 
Date:  Thursday, August 29, 2019 
Time:  11:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Bangladesh has been facing serious problem in arsenic contamination for more than two decades. Drinking and irrigating contaminated water put the health of more than 85 million people at risk. The project “Groundwater Studies for Arsenic Contamination in Bangladesh” led by British Geological Survey had been conducted during 1998 to 2001. A few studies have been carried out from different perspectives. The district Comilla is considered to be the most severed region with highest arsenicrelated deaths according to Flanagan, Johnston, and Zheng, 2012. In this thesis, we examine the arsenic groundwater concentration in Comilla district. We propose spatial models for making inference under Bayesian framework. We demonstrate that models based on the gamma distribution with spatial structure capture the characteristics of arsenic levels, appropriately compared to other models. We also perform spatial interpolation (kriging) to describe the situation of the arsenic levels across all Comilla. 
Title:  WorstCase Valuation of EquityLinked Products Using RiskMinimizing Strategies 
Speaker:  Mr. Emmanuel OseiMireku MSc) 
Date:  Tuesday, August 27, 2019 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The global market for life insurance products has been stable over the years. However, equitylinked products which form about fifteen percent of the total life insurance market has experienced a decline in premiums written. The impact of model risk when hedging these investment guarantees has been found to be significant. We propose a framework to determine the worstcase value of an equitylinked product through partial hedging using quantile and conditional valueatrisk measures. The model integrates both the mortality and the financial risk associated with these products to estimate the value as well as the hedging strategy. We rely on robust optimization techniques for the worst case hedging strategy. To demonstrate the versatility of the framework, we present numerical examples of pointtopoint equityindexed annuities in multinomial lattice dynamics. 
Title:  Decomposition of Risk in Life Insurance Based on the Martingale Representation Theorem 
Speaker:  Mr. Edwin Ng (MSc) 
Date:  Thursday, August 1, 2019 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Numerous methods have been proposed throughout the literature for decomposing liabilities into risk factors. Such analysis is of great importance because it allows for explaining the impact of each source of risk in relation to the total risk, and thus it allows actuaries to have a certain degree of control over uncertainties. In an insurance context, such sources usually consist of the mortality risk, represented in this paper by the systematic and by the unsystematic mortality risk, and of the investment risk. The objective of this thesis is to consider the Martingale Representation Theorem (MRT) introduced by Schilling et al., (2015) for such risk decomposition, because this method allows for a detailed analysis of the influence of each source of risk. The proposed dynamic models used in this thesis are the LeeCarter model for the mortality rates and, the arbitragefree NelsonSiegel (AFNS) models for the interest rates. These models are necessary in providing accuracy by improving the overall predictive performance. Once, the risk decomposition has been achieved, quantifying the relative importance of each risk factor under different risk measurements is then proceeded. The numerical results are based on annuities and insurances portfolios. It is found that for extended coverage periods, investment risk represents most of the risk while for shorter terms, the unsystematic mortality risk takes larger importance. It is also found that the systematic mortality risk is almost negligible. 
Title:  Yield Curve Modelling: A Comparison of Principal Components Analysis and the DiscreteTime Vasicek Model 
Speaker:  Ms. Irene Asare (MSc) 
Date:  Wednesday, July 31, 2019 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The term structure of interest rates is relevant to economists as it reflects the information available to the market about the time value of money in the future. Affine term structure models such as short rate models have been used in interest rate modelling over the past years to determine the mechanisms driving the term structure. Machine learning approaches are explored in this thesis and compared to the traditional econometric approach, specifically the Vasicek model. Multifactor Vasicek models are considered as the one factor model is found not adequate to characterize the term structure of interest rates. Since the short rates are not observable the Kalman filter approach is used in estimating the parameters of the Vasicek model. This thesis utilizes the Canadian zerocoupon bond price data in the implementation of both methods and it is observed from both methods that increasing the number of factors to three increases the ability to capture the curvature of the yield curve. The first factor is identified to be responsible for the level of the yield curve, the second factor the slope and third factor the curvature of the yield curve. This is consistent with results obtained from previous work on term structure models. The results from this work indicates that the machine learning technique, specifically the first three principal components of the Principal Component Analysis (PCA), outperforms the Vasicek model in fitting the yield curve. 
Title:  Absolutely Continuous Invariant Measures for Piecewise Convex Maps of Interval with Infinite Number of Branches 
Speaker:  Mr. Md Hafizur Rahman (MSc) 
Date:  Tuesday, July 2, 2019 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The main results of this Master's Thesis is the generalization of the existenceof absolutely continuous invariant measure for piecewise convex maps of an interval from a case with finite number of branches to the one with infinitely many branches. We give a similar result for piecewise concave maps as well. We also provide examples of piecewise convex maps without ACIM. 
Title:  Application of the Distributed Lag Models for Examining Associations Between the Built Environment and Obesity Risk in Children, Quality Study 
Speaker:  Ms. Anna Smyrnova (MSc) 
Date:  Thursday, July 4, 2019 
Time:  3:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Features of the neighbourhood environment are associated with physical activity and nutrition habits in children and may be a key determinant for obesity risk. Studies commonly use a fixed, prespecified buffer size for the spatial scale to construct environment measures and apply traditional methods of linear regression to calculate risk estimates. However, incorrect spatial scales can introduce biases. Whether the spatial scale changes depending on a person’s age and sex is largely unknown. Distributed lag models (DLM) were recently proposed as an alternative methodology to fixed, prespecified buffers. The DLM coefficients follow a smooth association over distance, and a prespecification of buffer size is not required. Therefore, the DLMs may provide a more accurate estimation of association strength, as well as the point in which the association disappears or is no longer clinically meaningful. Using data from the QUALITY cohort (an ongoing longitudinal investigation of the natural history of obesity in Quebec youth, N=630, Mage=9.6 at baseline), we aimed to apply the DLM to determine whether the association between the residential neighbourhood built environment (BE) and obesity risk in children differed depending on age and sex. A second objective aimed to compare the DLM model with that of a linear regression model (which used prespecified circular buffer sizes). 
Title:  Modeling and Measuring Insurance Risks for a Hierarchical Copula Model Considering IFRS 17 Framework 
Speaker:  Mr. Carlos Araiza Iturria (MSc) 
Date:  Wednesday, June 26, 2019 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  A stochastic approach to insurance risk modeling and measurement that is compliant with IFRS 17 is proposed. The compliance is achieved through the use of a rankbased hierarchical copula which accounts for the dependence between the various lines of business of the Canadian auto insurance industry. A model for the marginal IBNR losses of each line of business based on double generalized linear models is also developed. Development year and accident year effect factors along with an autoregressive feature for residuals enable modeling the dependence between the various entries of the IBNR loss triangles in a given line of business. Capital requirements calculations are then performed through simulation; numbers obtained with univariate and multivariate risk measures are compared. Moreover, a risk adjustment for nonfinancial risk required by IFRS 17 is also computed through a cost of capital approach. 
Title:  Critical Lvalues of Primitive Forms Twisted by Dirichlet Characters 
Speaker:  Mr. Jungbae Nam (PhD) 
Date:  Thursday, December 13, 2018 
Time:  10:30 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Let f be a primitive form of level N and weight k > 1 with nebentypus ε and χ be a primitive Dirichlet character of conductor fχ with (N, fχ) = 1. Then, we consider the twist of f by χ and its Dirichlet Lseries denoted by L(f, s, χ). Those central Lvalues (or even vanishings and nonvanishings of them) are believed (partially true) to encode important arithmetic invariants of algebraic objects over various fields as the class number formula for number fields. In this thesis, we study the central Lvalues of f twisted by chi of prime orders and present three nonvanishing theorems on some families of twists. More precisely, we first study for f of k > 1 twisted by χ of order a prime order l using Hecke operators and modular symbols and present some numerical results on vanishings. Next, we study for elliptic curves twisted by primitive cubic characters using special family which is supported on primes. Lastly, we study for elliptic curves twisted by primitive quadratic characters using Galois cohomology 
Title:  Global Hedging with Options 
Speaker:  Ms. Behnoosh Zamanlooy (MSc) 
Date:  Tuesday, December 11, 2018 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The classical global hedging approach presented in the literature (see Schweizer [1995]) involves using only the underlying asset to hedge a given contingent claim. The current thesis extends this approach by allowing for the use of a portfolio comprised of the underlying as well as other options written on that same underlying to be used as hedging instruments. Classical quadratic global hedging results such as the dynamic programming solution approach are adapted to this framework and are used to solve the global hedging problem presented here. The performance of this methodology is then investigated and benchmarked against the classical global hedging, as well as the traditional delta and deltagamma hedging approaches. Various numerical analyses of the hedging errors, turnover and the shapes of quantities involved in dynamic programming solution approach are performed. It is found that optionbased global hedging, where options are used as hedging instruments, outperforms other methodologies by yielding the lowest quadratic hedging error as expected. Situations where optionbased global hedging has the most significant advantage over the other hedging methodologies are identified and discussed. 
Title:  Comparison of Weight Growth Models in a Sample of Children from 6 to 15 Years 
Speaker:  Ms. Neha Wadhawan (MSc) 
Date:  Wednesday, September 19, 2018 
Time:  3:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Human growth is a complex, natural developmental phenomenon comprised of prenatal (fetal) and postnatal (infancy, childhood, adolescence, and adulthood) growth. Weight is an ecosensitive growth measurement that responds more rapidly to illness and loss of appetite than any other anthropometric measurement. Modelling postnatal growth in children's weight is of particular interest in order to identify those at greatest risk for serious health outcomes later in adult life such as obesity, hypertension, cardiovascular disease, and diabetes. Traditionally, the most commonly used parametric growth models (JenssBayley, Reed 1st order, and Reed 2nd order) have been recommended for children from birth to 6 years of age but the literature on their performance in an older age range of children is limited. The Adapted JenssBayley was developed to extend the models from birth to puberty. In contrast, the recently developed SITAR (SuperImposition by Translation And Rotation) model has no age range constraints, and has been shown to be superior when compared to the previous models (JenssBayley and Reed 1st order) for modeling weight from birth to four years of age. No study has yet assessed the comparison and performance of these models in an older age range of children. This present study aims to extend the previous work by comparing these models (JenssBayley, Reed 1st order, Reed 2nd order, Adapted JenssBayley, and SITAR) to model longitudinal weight in an age range of children that starts from middle childhood and includes puberty (6 to 15 years) in the Quebec Longitudinal Study of Child Development (QLSCD) cohort (n = 2,120). Results demonstrate that the SITAR model outperformed the other four models but should be reassessed in additional studies with longer followup. 
Title:  Large Deviations for the Local Time of a Jump Diffusion with Two Sided Reflection 
Speaker:  Mr. Giovanni Zoroddu (MSc) 
Date:  Thursday, August 30, 2018 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Let X be a jump diffusion, then its reflection at the boundaries 0 and b>0 forms the process V. The amount by which V must reflect to stay within its boundaries is added to a process called the local time. This thesis establishes a large deviation principle for the local time of a reflected jump diffusion. Upon generalizing the notion of the local time to an additive functional, we establish the desired result through a Markov process argument. By applying Ito's formula to a suitably chosen process M and in proving that M is a martingale, we find its associated integrodifferential equation. M can then be used to find the limiting behavior of the cumulant generating function which allows the large deviation principle to be established by means of the GärtnerEllis theorem. These theoretical results are then illustrated with two specific examples. We first find analytical results for these examples and then test them in a Monte Carlo simulation study and by numerically solving the integrodifferential equation. 
Title:  New Kernels For Density and Regression Estimation via Randomized Histogram 
Speaker:  Ms. Ruhi Ruhi (MSc) 
Date:  Tuesday, August 28, 2018 
Time:  2:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In early the 20's, the first person to notice the link between Random Forest (RF) and Kernel Methods, Leo Breiman, pointed out that Random Forests grown using independent and identically distributed random variables in tree construction is equivalent to kernel acting on true distribution. Later, Scornet defined Kernel based Random Forest (KeRF) estimates and gave explicit expression for the kernels based on Centered RF and Uniform RF. In this paper, we will study the general expression for the connection function (kernel function) of an RF when splits/cuts are performed according to uniform distribution and also according to any general distribution. We also establish the consistency of KeRF estimates in both cases and their asymptotic normality. 
Title:  Registration and Display of Functional Data 
Speaker:  Mr. Mahdi Bahkshi (MSc) 
Date:  Tuesday, August 28, 2018 
Time:  12:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Functional data refer to data which are in the form of functions or smooth curves that are assessed at a finite, but large subset of some interval. In this thesis, we explore methods of functional data analysis, especially curve registration, in the context of climate changes in a group of 16 cities of the United States. In the first step, spline functions were developed in order to convert the raw data into functional objects. Data are available in function forms, but the mean function which was obtained by the unregistered curve fails to produce a satisfactory estimator. This means that the mean function does not resemble any of the observed curves. A significant problem with most functional data analyses is that of misaligned curves (Ramsay & Silverman, 2005). Curve registration is one method in functional data analysis that attempts to solve this problem. In the second step, we used curve registration method based on “landmarks alignment” and “continuous monotone registration” in order to construct a precise measurement of the average temperature. The results show the differences between unregistered data and registered data and a significant rise of the temperature in U.S. cities within the last few decades. 
Title:  Support Vector Machines with Convex Combination of Kernels 
Speaker:  Ms. Farnoosh Rahimi (MSc) 
Date:  Tuesday, August 28, 2018 
Time:  10:30 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Support Vector Machine (SVMs) are renowned for their excellent performance in solving datamining problems such as classification, regression and feature selection. In the field of statistical classification, SVMs classify data points into different groups based on finding the hyperplane that maximizes the margin between the two classes. SVMs can also use kernel functions to map the data into a higher dimensional space in case a hyperplane cannot be used to do the separation linearly. Using specific kernels allows us to model a particular feature space, and a suitable kernel can improve the SVMs' performance to classify data more accurately. We present a method to combine existing kernels in order to produce a new kernel which improves the accuracy of the classification and reduce the process time. We will discuss the theoretical and computational issues on SVMs. We are going to implement our method on a simulated dataset to see how it works, and then we will apply it to some large realworld datasets. 
Title:  Arbitragefree Regularization, Geometric Learning, and NonEuclidean Filtering in Finance 
Speaker:  Mr. Anastasis Kratsios (PhD) 
Date:  Monday, August 27, 2018 
Time:  9:30 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This thesis brings together elements of differential geometry, machine learning, and pathwise stochastic analysis to answer problems in mathematical finance. The overarching theme is the development of new stochastic machine learning algorithms which incorporate arbitragefree and geometric features into their estimation procedures in order to give more accurate forecasts and preserve the geometric and financial structure in the data. This thesis is divided into three parts. The first part introduces the nonEuclidean upgrading (NEU) metaalgorithm which builds the universal reconfiguration and universal approximation properties into any objective learning algorithm. These properties state that a procedure can reproduce any dataset exactly and approximate any function to arbitrary precision, respectively. This is done through an unsupervised learning procedure which identifies a geometry optimizing the relationship between a dataset and the objective learning algorithm used to explain it. The effectiveness of this procedure is supported both theoretically and numerically. The numerical implementations find that NEUordinary least squares outperforms leading regularized regression algorithms and that NEUPCA explains more variance with one NEUprincipal component than PCA does with four classical principal components. The second part of the thesis introduces a computationally efficient characterization of intrinsic conditional expectation for CartanHadamard manifolds. This alternative characterization provides an explicit way of computing nonEuclidean conditional expectation by using geometric transformations of specific Euclidean conditional expectations. This reduces many nonconvex intrinsic estimation problems to transformations of wellstudied Euclidean conditional expectations. As a consequence, computationally tractable nonEuclidean filtering equations are derived and used to successfully forecast efficient portfolios by exploiting their geometry. The third and final part of this thesis introduces a flexible modeling framework and a stochastic learning methodology for incorporating arbitragefree features into many asset price models. The procedure works by minimally deforming the structure of a model until the objective measure acts as a martingale measure for that model. Reformulations of classical noarbitrage results such as NFLVR, the minimal martingale measure, and the arbitragefree NelsonSiegel correction of the NelsonSiegel model are all derived as solutions to specific arbitragefree regularization problems. The flexibility and generality of this framework allows classical noarbitrage pricing theory to be extended to models that admit arbitrage opportunities but are deformable into arbitragefree models. Numerical implications are investigated in each of the three parts. 
Title:  The Shift from Classic to Modern Probability: A Historical Study with Didactical and Epistemological Reflexions 
Speaker:  Mr. Vinicius Gontijo Lauar (MSc) 
Date:  Friday, August 24, 2018 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this thesis, we describe the historical shift from the classical to the modern definition of probability. We present the key ideas and insights in that process, from the first definition of Bernoulli, to Kolmogorov's modern foundations discussing some of the limitations of the old approach and the efforts of many mathematicians to achieve a satisfactory definition of probability. For our study, we've looked, as much as possible, at original sources and provided detailed proofs of some important results that the authors have written in an abbreviated style. We then use these historical results to investigate the conceptualization of probability proposed and fostered by undergraduate and graduate probability textbooks through their theoretical discourse and proposed exercises. Our findings show that, despite textbooks give an axiomatic definition of probability, the main aspects of the modern approach are overshadowed by other contents. Undergraduate books may be stimulating the development of classical probability with many exercises using proportional reasoning while graduate books concentrate the exercises on other mathematical contents such as measure and set theory without necessarily proposing a reflection on the modern conceptualization of probability. 
Title:  Understanding Inquiry, an Inquiry into Understanding: A Conception of Inquiry Based Learning in Mathematics 
Speaker:  Mr. Julian Frasinescu (MTM) 
Date:  Thursday, August 23, 2018 
Time:  1:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  IBL (Inquiry Based Learning) is a group of educational approaches centered on the student and aiming at developing higherlevel thinking, as well as an adequate set of Knowledge, Skills, and Attitudes (KSA). IBL is at the center of recent educational research and practice, and is expanding quickly outside of schools: in this research we propose such forms of instruction as Guided SelfStudy, Guided Problem Solving, Inquiry Based Homeschooling, IB elearning, and particularly a mixed (InquiryExpository) form of lecturing, named IBLecturing. The research comprises a thorough review of previous research in IBL; it clarifies what is and what is not Inquiry Based Learning, and the distinctions between its various forms: Inquiry Learning, Discovery Learning, Case Study, Problem Based Learning, Project Based Learning, Experiential Learning, etc. There is a continuum between Pure Inquiry and Pure Expository approaches, and the extreme forms are very infrequently encountered. A new cognitive taxonomy adapted to the needs of higherlevel thinking and its promotion in the study of mathematics is also presented. This research comprises an illustration of the modeling by an expert (teacher, trainer, etc.) of the heuristics and of the cognitive and metacognitive strategies employed by mathematicians for solving problems and building proofs. A challenging problem has been administered to a group of gifted students from secondary school, in order to get more information about the possibility of implementing Guided Problem Solving. Various opportunities for further research are indicated, for example applying the recent advances of cognitive psychology on the role of Working Memory (WM) in higherlevel thinking. 
Title:  Analysis on Infinite Trees and Their Boundaries 
Speaker:  Ms. Chana Pevzner (MSc) 
Date:  Monday, July 30, 2018 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The aim of this thesis is to understand the results of Björn, Björn, Gill and Shanmugalingam [BBGS], who give an analogue of the famous Trace Theorem for Sobolev spaces on the infinite Kary tree and its boundary. In order to do so, we investigate the properties of a tree as a metric measure space, namely the doubling condition and Poincaré inequality, and study the boundary in terms of geodesic rays as well as random walks. We review the definitions of the appropriate Sobolev and Besov spaces and the proof of the Trace Theorem in [BBGS]. 
Title:  Optimization of Random Forest Based Models Applying Genetic Algorithm 
Speaker:  Ms. Zahra Aback (MSc) 
Date:  Friday, July 20, 2018 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this century access to large and complex datasets is much easier. These datasets are large in dimension and volume, and researchers are interested in methods that are able to handle this types of data and at the same time produce accurate results.Machine learning methods are particularly efficient for this type of data, where the emphasis is on data analysis, and not on fitting a statistical model. A very popular method from this group is Random Forest which has been applied in different areas of study on two types of problems: classification and regression. The former is more popular, while the latter can be applied to produce acceptable results. Moreover, many efficient techniques for missing value imputation were added to Random Forest over time. One of these methods which can handle all types of variables is MissForest. There are several studies that applied different approaches to improve the performance of classification type of Random Forest, but there are not many studies available for regression type. In the present study, it was evaluated if the performance of regression type of Random Forest and MissForest could be improved by applying Genetic Algorithm as an optimization method. The experiments were conducted on five datasets to minimize the MSE of Random Forest and imputation error of MissForest. The results showed the superiority of the proposed method to the classical Random Forest. 
Title:  Some Results for FOdefinable Constraint Satisfaction Problems Described by Digraph Homomorphisms 
Speaker:  Mr. Patrick Moore MSc) 
Date:  Thursday, May 17, 2018 
Time:  10:30 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Constraint satisfaction problems, or CSPs, are a naturally occurring class of problems which involve assigning values to variables while respecting a set of constraints. When studying the computational and descriptive complexity of such problems it is convenient to use the equivalent formulation, introduced by Feder and Vardi, that CSPs are homomorphism problems. In this context we ask if there exists a homomorphism to some target structure. Using this view many tools and ideas have been introduced in combinatorics, logic and algebra for studying the complexity of CSPs. In this thesis we concentrate on combinatorics and give characterization results based on digraph properties. Where previous studies focused on CSPs defined by a single digraph with lists we extend our relational structures to consist of many binary relations which each individually describe a distinct digraph on the structures universe. A majority of our results are obtained by using an algorithm introduced by Larose, Loten and Tardif which determines whether a structure defines a CSP whose homomorphism problem can be represented by first order logic. Using this tool we begin by completely classifying which of these structures are FOdefinable when each of the relations defines a transitive tournament. We then generalize a characterization theorem, first given by Lemaître, to include structures containing any finite number of digraph relations and lists. We conclude with examples of obstructions and properties that can determine if a particular relational structure has a CSP which is FOdefinable and how to construct such structures. 
Title:  On Estimators of a Spectral Density Function 
Speaker:  Ms. Chengyin Wang (MSc) 
Date:  Monday, May 14, 2018 
Time:  11:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This paper presents two main approaches to estimating the spectral density of a stationary time series, that are based on the classical estimation which is the periodogram. Both of them are related to the nonparametric density estimation. One is the Kernel spectral density estimator while the other one is the Bernstein polynomial spectral density estimator. Then we have introduced the method to determine the optimal parameters of a spectral density of a stationary zeromean process in each estimator. Finally, the paper conduct simulation experiments to examine the finite sample properties of the proposed spectral density estimators and associated tests. 
Title:  Transformation Based on Circular Density Estimators 
Speaker:  Ms. Yuhan Cao (MSc) 
Date:  Monday, May 14, 2018 
Time:  9:30 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Circular density estimation has been discussed for a long time. In this thesis, we would like to introduce two transformation methods to estimate the circular density. One is derived from kernel density estimator and the other one comes from the Bernstein polynomial estimator (see Chaubey (2017)). We know both kernel density estimation (see Silverman (1986)) and Bernstein polynomial estimation (See Babu and Chaubey (2002)) are appropriate for estimating linear data, and we also could transform the linear data to circular data and vice versa, so we transformed the linear estimation to a circular one and we would like to see which estimator leads to a better transformation. We will conduct a simulation study to compare their estimation abilities based on three distributions. The present result shows that kernel density estimation has a stronger ability to alleviate the boundary problems than Bernstein polynomial density estimation, however, they performs pretty much similar when we estimate the central part of distribution. So in general we can say, kernel density estimator leads to a little bit better transformation and further research may be needed 
Title:  ACIMs for NonAutonomous Discrete Time Dynamical Systems; A Generalization of Straube’s Theorem 
Speaker:  Mr. Chris Keefe (MSc) 
Date:  Thursday, March 22, 2018 
Time:  11:30 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This Master’s thesis provides sufficient conditions under which a NonAutonomous Dynamical System has an absolutely continuous invariant measure. The main results of this work are an extension of the KrylovBogoliubov theorem and Straube’s theorem, both of which provide existence conditions for invariant measures of single transformation dynamical systems, to a uniformly convergent sequence of transformations of a compact metric space, which we define to be a nonautonomous dynamical system. 
Title:  On the Upper Bound of Petty’s Conjecture in 3 Dimensions 
Speaker:  Ms. Emilie Cyrenne (MSc) 
Date:  Thursday, March 8, 2018 
Time:  11:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Among the various important aspects within the theory of convex geometry is that of the field of affine isoperimetric inequalities. Our focus deals with validating the upper bound of the Petty conjecture relating the volume of a convex body and that of its associated projection body. We begin our study by providing some background properties pertaining to convexity as seen through the lens of Minkowski theory. We then show that the Petty conjecture holds true in a certain class of 3dimensional nonaffine deformations of simplices. More precisely, we prove that any simplex in attains the upper bound in comparison to any deformation of a simplex by a Minkowski sum with a unitary line segment. As part of our theoretical analysis, we make use of mixed volumes and Maclaurin series expansion in order to simplify the targeted functionals. Finally, we provide an example validating what is known in the literature as the reverse and direct Petty projection inequality. In all cases, Mathematica is used extensively as our means of visualizing the plots of our selected convex bodies and corresponding projection bodies. 
Title:  How Do Students Know They Are Right and How Does One Research It? 
Speaker:  Ms. Natalia Vasilyeva (MTM) 
Date:  Monday, January 15, 2018 
Time:  9:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Although standards of rigor in mathematics are subject to debate among philosophers, mathematicians and educators, proof remains fundamental to mathematics and distinguishes mathematics from other sciences. There is no doubt that the ability to appreciate, understand and construct proofs is necessary for students at all levels, in particular for students in advanced undergraduate and graduate mathematics courses. However, studies show that learning and teaching proof may be problematic and students experience difficulties in mathematical reasoning and proving. This thesis is influenced by Lakatos’ (1976) view of mathematics as a ‘quasiempirical’ science and the role of experimentation in mathematicians’ practice. The purpose of this thesis was to gain insight into undergraduate students’ ways of validating the results of their mathematical thinking. How do they know that they are right? While working on my research, I also faced methodological difficulties. In the thesis, I included my earliest experiences as a novice researcher in mathematics education and described the process of choosing, testing and adapting a theoretical framework for analyzing a set of MAST 217 (Introduction to Mathematical Thinking) students’ solutions of a problem involving investigation. The adjusted CPiMI (Cognitive Processes in Mathematical Investigation, Yeo, 2017) model allowed me to analyze students’ solutions and draw conclusions about the ways they solve the problem and justify their results. Also I placed the result of this study in the context of previous research. 
Title:  Modeling Nested Copulas with GLMM Marginals for Longitudinal Data 
Speaker:  Ms.Roba Bairakdar (MSc) 
Date:  Tuesday, December 19, 2017 
Time:  2:30 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  A flexible approach for modeling longitudinal data is proposed. The model consists of nested bivariate copulas with Generalized Linear Mixed Models (GLMM) marginals, which are tested and validated by means of likelihood ratio tests and compared via their AICc and BIC values. The copulas are joined together through a vine structure. Rankbased methods are used for the estimation of the copula parameters, and appropriate model validation methods are used such as the Cramér Von Mises goodnessoffit test. This model allows flexibility in the choice of the marginal distributions, provided by the family of the GLMM. Additionally, a wide variety of copula families can be fitted to the tree structure, allowing different nested dependence structures. This methodology is tested by an application on real data in a biostatistics study. 
Title:  The Longitudinal Effect of Structural Brain Measurements on Cognitive Abilities 
Speaker:  Ms.Fatemeh Hosseininasabnaja (MSc) 
Date:  Monday, December 11, 2017 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Loss of brain tissues and cognitive abilities are natural processes of aging, and they are related to each other. These changes in cognition and brain structure are different among the cognitively normal elderly and those with Alzheimer’s disease (AD). Despite the great development in the longitudinal study of decline in brain volume and cognitive abilities, previous studies are limited by their small number of data collection waves and inadequate adjustments for important factors (such as a genetic factor). These limitations diminish the power to detect changes in brain tissues and cognitive abilities over a longer period of time. In this study, firstly, we aimed to explore the longitudinal association between cognitive abilities and global and regional structural brain variables among individuals with normal cognitive status, mild cognitive impairment (MCI), and AD using mixed effects models. Secondly, we investigated the effect of education on the relationship between cognition and brain structure. Lastly, we utilized latent class growth analysis in order to study the change in cognition between different MCI subclasses based on their functional abilities. The data in this study were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) which contained 6 time points over three years (n = 686). The results showed that cognitive abilities decreased over time across different groups, and the rate of decline in cognition depended on the whole brain volume. Importantly, the effect of brain volume on the rate of decline in cognitive abilities was greater among MCI subjects who progressed to AD (pMCI) and participants with AD. Ventricle enlargement in the pMCI group also showed a significant influence on the rate of cognitive decline. Lastly, based on an assessment of functional abilities at baseline, this study demonstrated an efficient methodology to identify MCI subjects who are most atrisk for cognitive impairment progression. 
Title:  Sieve Methods and its Application in Problematic Galois Theory 
Speaker:  Mr. Salik Bahar (MA) 
Date:  Monday, September 25, 2017 
Time:  1:00 p.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  David Hilbert [Hil92] showed that for an irreducible polynomial F (X, T ) ∈ ℚ(T )[X] there are infinitely many rational numbers t for which F (X, t) is irreducible in ℚ[X]. In 1936 van der Waerden [vdW34] gave a quantitative form of this assertion. Consider the set of degree n monic polynomials with integer coefficients restricted to a box ai ≤ B. Van der Waerden showed that a polynomial drawn at random from this set has Galois group Sn with probability going to 1 as B tends to infinity. In the first part of the thesis, we introduce the Large Sieve Method and apply it to solve Probabilistic Galois Theory problems over rational numbers. We estimate, En(B), the number of polynomials of degree n and height at most B whose Galois group is a proper subgroup of the symmetric group Sn. Van der Waerden conjectured that En(B) ≪ Bn—1. P.X. Gallagher [Gal73] utilized an extension of the Large Sieve Method to obtain an estimate of En(B)= O(Bn—1/2 log1—𝝲 B), where 𝜸∼ (2𝛑n)—1/2. In the second part of the thesis, we state and prove a quantitative form of the Hilbert’s Irreducibility Theorem by using an extension of the Gallagher’s Larger Sieve method over integral points. David Zywina [Zyw10] showed that combining the Large and Larger sieve Methods together, one can obtain a sharper estimate of En(B)= O(Bn—1/2 
Title:  TwoSample Test for Time Series 
Speaker:  Ms. Abeer Alzahrani (MSc) 
Date:  Monday, September 11, 2017 
Time:  10:00 a.m. 
Location:  LB 92104 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this thesis, we consider the twosample problem of time series. Given two time series data x1,...,xn and y1,...,ym, we would like to test whether they follow the same time series model. First, we develop a unified procedure for this testing problem. The procedure consists of three steps: testing stationarity, comparing correlation structures and comparing residual distributions. Then, we apply the established procedure to analyze real data. We also propose a modification to a nonparametric twosample test, which can be applied to high dimensional data with equal means and variances. 
Title:  The Bare Necessities for Doing Undergraduate Multivariable Calculus 
Speaker:  Ms. Hadas Brandes (MSc) 
Date:  Monday, September 11, 2017 
Time:  2:00 p.m. 
Location:  LB 646 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Students in two mathematics streams at Concordia University start their programs on similar footing in terms of prerequisite courses; their paths soon split in the two directions set by the Pure and Applied Mathematics (MATH) courses and the Major in Mathematics and Statistics (MAST) courses. In particular, likely during their first year of studies, the students set out to take a twoterm arrangement of Multivariable Calculus in the form of MAST 218 – 219 and MATH 264 – 265, respectively. There is an ongoing discussion about the distinction between the MAST and MATH courses, and how it is justified. This thesis seeks to address the matter by identifying the mathematics that is essential for students to learn in order to succeed in each of these courses. We apply the Anthropological Theory of the Didactic (ATD) in order to model the knowledge to be taught and to be learned in MAST 218 and MATH 264, as decreed by the curricular documents and course assessments. The ATD describes units of mathematical knowledge in terms of a practical block (tasks to be done and techniques to accomplish them) and a theoretical block that frames and justifies the practical block. We use these notions to model the knowledge to be taught and learned in each course and reflect on the implications of the inclusion and exclusion of certain units of knowledge in the minimal core of what students need to learn. Based on these models, we infer that the learning of Multivariable Calculus in both courses follows in a tradition observed in singlevariable calculus courses, whereby students develop compartmentalized units of knowledge. That is, we find that it is necessary for students in MAST 218 and MATH 264 to specialize in techniques that apply to certain routine tasks, and to this end, it suffices to learn bits and pieces of theoretical knowledge that are not unified in a mathematicallyinformed way. We briefly consider potential implications of such learning in the wider context of the MATH and MAST programs. 
Title:  Optimal Measure Transformations and Optimal Trading 
Speaker:  Mr. Renjie Wang (PhD Oral Examination) 
Date:  Monday, August 28, 2017 
Time:  9:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We first associate the bond price with an optimal measure transformation problem which is closely related to decoupled nonlinear forwardbackward stochastic differential equation (FBSDE).1 In the defaultfree case we prove the equivalence of the optimal measure transformation problem and an optimal stochastic control problem of Gombani and Runggaldier (Math. Financ. 23(4):659686, 2013) for bond price in the framework of quadratic term structure models. The measure which solves the optimal measure transformation problem is the forward measure. These connections explain why the forward measure transformation employed in the FBSDE approach of Hyndman (Math. Financ. Econ. 2(2):107128, 2009) is effective. We obtain explicit solutions to FBSDEs with jumps in affine term structure models and quadratic term structure models, which extend Hyndman (Math. Financ. Econ. 2(2):107128, 2009). From the optimal measure transformation problem for defaultable bonds, we derive FBSDEs with random terminal condition to which we give a partially explicit solution. The futures price and the forward price of a risky asset are also considered in the framework of optimal measure transformation problems. In the second part we consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold.2 Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset. We consider the perspective of small investors whose trades do not induce market impact and who possess different levels of information about the liquidation trigger mechanism and the market impact. We classify these market participants into three types: fully informed, partially informed and uninformed investors. We consider the portfolio optimization problems and compare the optimal trading and wealth processes for the three classes of investors theoretically and by numerical illustrations. Finally we study the portfolio optimization problems with risk constraints and make comparison with the results without risk constraints. 1. Based on the paper with Cody Hyndman. 
Title:  On Some Refinements of the Embedding of Critical Sobolev Spaces into BMO, and a Study of Stability for Parabolic Equations with Time Delay 
Speaker:  Mr. Almaz Butaev (PhD Oral Examination) 
Date:  Monday, August 28, 2017 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Van Schaftinen [76] showed that the inequalities of Bourgain and Brezis [11], [12] give rise to new function spaces that refine the classical embedding W^{1,n }(R^{n}) ⊂ BMO(R^{n}). It was suggested by Van Schaftingen [76] that similar results should hold in the setting of bounded domains Ω ⊂ R^{n }for bmo_{r} (Ω) and bmo_{z} (Ω) classes. The first part of this thesis contains the proofs of these conjectures as well as the development of a nonhomogeneous theory of Van Schaftingen spaces on R^{n}. Based on the results in the nonhomogeneous setting, we are able to show that the refined embeddings can also be established for bmo spaces on Riemannian manifolds with bounded geometry, introduced by Taylor [68]. The stability of parabolic equations with time delay plays important role in the study of nonlinear reactiondiffusion equations with time delay. While the stability regions for such equations without convection on bounded time intervals were described by Travis and Webb [70], the problem remained unaddressed for the equations with convection. The need to determine exact regions of stability for such equations appeared in the context of the works Mei on the Nicholson equation with delay [50]. In the second part of this thesis, we study the parabolic equations with and without convection on R. It has been shown that the presence of convection terms can change the regions of stability. The implications for the stability problems for nonlinear equations are also discussed. 
Title:  What Algebra Do Calculus Students Need to Know? 
Speaker:  Ms. Sabrina Giovanniello (MTM) 
Date:  Thursday, August 24, 2017 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Students taking a Calculus course for the first time at Concordia University are mature students returning to school after an extended period of time away from formal education, or students lacking the prerequisites to enter into a science, technology, engineering, or mathematics (STEM) related field. Thus, an introductory Calculus course is the gateway for many STEM programs, inhibiting students’ academic progression if not passed. Calculus tends to be construed as a very difficult subject. This impression may be due to the fact that this course is taught in a condensed form, with limited class time, new knowledge (concept, type of problem, technique or method) introduced every week, and little practice time. Calculus requires higher order thinking in mathematics, compared to what students have previously encountered, as well as many algebraic techniques. As will be shown in this thesis, algebra plays an important role in solving problems that usually make up the final examination in this course. Through detailed theoretical analysis of problems in one typical final examination, and solutions produced by 63 students, we have identified the prerequisite algebraic knowledge for the course and the specific difficulties, misconceptions and false rules experienced and developed by students lacking this knowledge. We have also shown how the results of our analyses can be used in the construction of a “placement test” for the course – an instrument that could serve the goal of lessening the failure rate in the course, and attrition in STEM programs, by avoiding having underprepared students. 
Title:  CIsoperimetricType Inequalities for GChordal StarShaped Sets in ℝ𝒏 
Speaker:  Ms. Zahraa Abbas (MSc) 
Date:  Wednesday, August 9, 2017 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This paper generalizes certain existing isoperimetrictype inequalities from ℝ2 to higher dimensions. These inequalities provide lower bounds for the ndimensional volume and, respectively, surface area of certain starshaped bodies in ℝ𝑛 and characterize the equality cases. More specifically, we work with gchordal starshaped bodies, a natural generalization of equichordal compact sets. A compact set in ℝ𝑛 is said to be equichordal if there exists a point in the interior of the set such that all chords passing through this point consist of a segment of equal length. To justify the significance of our results, we provide several means of constructing gchordal starshaped bodies. The method used to prove the above inequalities is further employed in finding new lower bounds for the dual quermassintegrals of gchordal starshaped sets in ℝ𝑛 and, more generally, lower bounds for the dual mixed volumes involving these star bodies. Finally, some of the previous results will be generalized to 𝐿𝑛stars, starshaped sets whose radial functions are nth power integrable over the unit sphere 𝑆𝑛−1. 
Title:  Computing the Average Root Number of a OneParameter Family of Elliptic Curves Defined Over Q 
Speaker:  Mr. Iakovos (Jake) Chinis (MSc) 
Date:  Monday, August 7, 2017 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  It is well known that the root number of any elliptic curve defined over Q can be written as an infinite product of local root numbers w_{p}, over all places p of Q, with w_{p}=+/ 1 for all p and such that w_{p}=1 for all but finitelymany p. By considering a oneparameter family of elliptic curves defined over Q, we might ask ourselves if there is any bias in the distribution (or parity) of the root numbers at each specialization. From the work of Helfgott in his Ph.D. thesis, we know (at least conjecturally) that the average root number of an elliptic curve defined over Q(T) is zero as soon as there is a place of multiplicative reduction over Q(T) other than deg. In this thesis, we are concerned with elliptic curves defined over Q(T) with no place of multiplicative reduction over Q(T), except possibly at deg. More precisely, we will use the work of Helfgott to compute the average root number of an explicit family of elliptic curves defined over Q and show that this family is "paritybiased" infinitelyoften. 
Title:  Multivariate Robust VectorValued Range ValueatRisk 
Speaker:  Ms Lu Cao (MA) 
Date:  Tuesday, July 25, 2017 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The dependence between random variables has to be accounted for modeling risk measures in a multivariate setting. In this thesis, we propose a bivariate extension of the robust risk measure Range ValueatRisk (RVaR) based on bivariate lower and upper orthant ValueatRisk (VaR) and Tail ValueatRisk (TVaR) introduced by Cossette et al. (2013, 2015). They are shown to possess properties similar to bivariate TVaR, such as translation invariance, positive homogeneity and monotonicity. Examples with different copulas are provided. Also, we present the consistent empirical estimators of bivariate RVaR along with the simulation. The robustness of estimators of bivariate VaR, TVaR and RVaR are discussed with the help of their sensitivity functions. We conclude that the bivariate VaR and RVaR are robust statistics 
Title:  Decomposing Liabilities in Annuity Portfolios using Martingale Representation Theorem Decomposition 
Speaker:  Mr. Chengrong Xie (MSc) 
Date:  Monday, July 24, 2017 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  A life annuity is a series of payments made at fixed intervals while the annuitant is alive. It has been a major part of actuarial science for a long time and it plays an important role in life insurance operations. In order to explore the interaction of various risks in an annuity portfolio, we decompose the liabilities by using the so called Martingale Representation Theorem (MRT) decomposition. The MRT decomposition satisfies all 6 meaningful properties proposed by Schilling et al. (2015). Before presenting some numerical examples to illustrate its applicability, several stochastic mortality models are compared and the RenshawHaberman (RH) model is chosen as our projection model. Then we compare two onefactor short rate models and estimate the parameters of CIR model to construct the stochastic interest rate setting. Finally, we allocate risk capitals to risk factors obtained from the MRT decomposition according to the Euler principle and analyze them when the age of cohort and the deferred term change. 
Title:  Analytical Structure of Stationary Flows of an Ideal Incompressible Fluid 
Speaker:  Mr. Alexander Danielski (MSc) 
Date:  Friday, April 28, 2017 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The Euler equations describing the flow of an incompressible, inviscid fluid of uniform density were first published by Euler in 1757. One of the outstanding achievements of mathematical fluid dynamics was the discovery that the particle trajectories of such flows are real analytic curves, despite limited regularity of the initial flow (Serfati, Shnirelman, Frisch&Zeligovsky, Kappeler, Inci, Nadirashvili, Constantin, Vicol, and others). Hence, the flow lines of stationary solutions to the Euler equations are real analytic curves. In this work we consider a twodimensional stationary flow in a periodic strip. Our goal is to incorporate the analytic structure of the flow lines into the solution of the problem. The equation for the stream function is transformed to new variables, more appropriate for the further analysis. New classes of functions are introduced to take into account the partial analytic structure of solutions. This makes it possible to regard the problem as an analytic operator equation in a complex Banach space. The Implicit Function theorem for complex Banach spaces is applied to establish existence of unique solutions to the problem and the analytic dependence of these solutions on the parameters. Our approach avoids working in the Frechet spaces and using the NashHamilton Implicit Function Theorem used by the previous authors (Sverak&Choffrut), and provides stronger results. 
Title:  Hybrid Hidden Markov Model and Generalized Linear Model for Auto Insurance Premiums 
Speaker:  Mr. Lucas Berry (MA) 
Date:  Friday, December 9, 2016 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We describe a new approach to estimate the pure premium for automobile insurance. Using the theory of hidden Markov models (HMM) we derive a Poissongamma HMM and a hybrid between HMMs and generalized linear models (HMMGLM). The hidden state is meant to represent a driver's skill thus capturing an unseen variable. The Poissongamma HMM and HMMGLM have two emissions, severity and claim count, making it easier to compare to current actuarial models. The proposed models help deal with the over dispersion problem in claim counts and introduces dependence between the severity and claim count. We derive maximum likelihood estimates for the parameters of the proposed models and then using simulations with the Expectation Maximization algorithm we compare the three methods: GLMs, HMMs and HMMGLMs. We show that in some instances the HMMGLM outperforms the standard GLM, while the Poissongamma HMM underperforms the other models. Thus in certain situations it may be worth the added complexity of a HMMGLM. 
Title:  On Some Circular Distributions Induced by Inverse Stereographic Projection 
Speaker:  Mr. Shamal Chandra Karmaker (MSc) 
Date:  Monday, November 14, 2016 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In earlier studies of circular data, mostly circular distributions were considered and many biological data sets were assumed to be symmetric. However, presently interest has increased for skewed circular distributions as the assumption of symmetry may not be meaningful for some data. This thesis introduces three skewed circular models based on inverse stereographic projection, introduced by Minh and Farnum (2003), by considering three different versions of skewedt considered in the literature, namely Azzalini skewedt, twopiece skewedt and Jones and Faddy skewedt. Shape properties of the resulting distributions along with estimation of parameters using maximum likelihood are discussed in this thesis. Further, three real data sets (Bruderer and Jenni, 1990; Holzmann et al., 2006; Fisher, 1993) are used to illustrate the application of the new model and its extension to finite mixture modelling. Goodness of fit of the new distributions is studied using maximum loglikelihood and Akaike information criterion. It is found that Azzalini and JonesFaddy skewedt versions are good competitors; however the JonesFaddy version is computationally more tractable. 
Title:  Undergraduate Students' Mathematical Behaviour: A Narrative Inquiry 
Speaker:  Ms. Erin Murray (MSc) 
Date:  Friday, September 9, 2016 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This thesis presents a study of the mathematical behaviour of students in a first year undergraduate course entitled Introduction to Mathematical Thinking. Previous data collected from a design experiment in the same course (see Hardy et al. 2013) proved insufficient to discuss/characterize the mathematical behaviour that emerged in the classroom. I suggest that a new generation of research in this area needs to address the lived experiences of students as they are learning to think mathematically. This thesis is motivated by two research goals: (1) to construct a rich characterization of mathematical behaviours, and (2) to explore a methodological approach that allows us to discuss and construct accounts of these behaviours as they emerge in institutional education settings (in this case an undergraduate classroom). The educational philosophy of John Dewey, who claims that all education comes about through experience, is central to the theoretical perspective of this research. Drawing on previous characterizations, a model of mathematical behaviour is proposed and used as a tool for characterizing students’ mathematical behaviours. In order to foreground individual experience, I use Clandinin and Connolly’s (2000) methodological framework to conduct a narrative inquiry. This methodology allows me to construct meaningful narrative depictions of students’ mathematical behaviour, and to explore the significance of these experiences within the continuity and wholeness of their individual narratives. The findings from this research provide rich characterizations of some elements of mathematical behaviour, and offer insight into my own experiences using narrative inquiry methodology. Implications for teaching and future research are discussed. 
Title:  Overconvergent EichlerShimura Isomorphisms on Shimura Curves over Totally Real Field 
Speaker:  Ms. Shan Gao (PhD Oral Examination) 
Date:  Thursday, September 8, 2016 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (click here to view) 
Title:  Some Fluctuation identities of HyperExponential JumpDiffusion Processes 
Speaker:  Mr. Linh Vu (MSc) 
Date:  Monday, August 29, 2016 
Time:  3:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Meromorphic Lévy processes have attracted the attention of a lot of researchers recently due to its special structure of the WienerHopf factors as rational functions of infinite degree written in terms of poles and roots of the Laplace exponent, all of which are real numbers. With these WienerHopf factors in hand, we can explicitly derive the expression of fluctuation identities that concern the first passage problems for finite and infinite intervals for the Meromorphic Lévy process and the resulting process reflected at its infimum. In this thesis, we consider some fluctuation identities of some classes of Meromorphic jumpdiffusion processes with either the double exponential jumps or more general the hyperexponential jumps. We study solutions to the onesided and twosided exit problems, and potential measure of the process killed on exiting a finite or infinite intervals. Also, we obtain some results to the process reflected at its infimum. 
Title:  Deformations of Galois Representations 
Speaker:  Ms. Clara Lacroce (MSc) 
Date:  Thursday, August 25, 2016 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (click here to view) 
Title:  Cure Rate Estimation Under Case1 Interval Censoring Via Smoothing 
Speaker:  Ms. Mehrnoosh Malekiha (MSc) 
Date:  Tuesday, August 23, 2016 
Time:  11:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Estimating curerate is a popular research subject in testing the reliability of treatment for terminal diseases such as cancers and HIV. So far, the publications mainly proposed estimation techniques based on parametric methods, with a few exceptions. In this thesis, under case1 interval censoring, we develop and propose two novel nonparametric estimators that improve upon previously proposed estimation techniques (Sen and Tan, 2008), using smoothing. We show our estimators are strongly consistent. In addition, their asymptotic normality is studied and we applied proposed estimator to estimate curerate on data collected for lung tumor in mice (Finkelstein and Wolfe, 1985). Finally, the smoothing parameter for optimum estimation has been determined by using Jackknife method. 
Title:  Distribution of the Number of Points on Abelian Curves over Finite Fields 
Speaker:  Mr. Patrick Meisner (PhD Oral Examination) 
Date:  Monday, August 22, 2016 
Time:  11:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (click here to view) 
Title:  A New Approach to the Planar Fractional Minkowski Problem via Curvature Flows 
Speaker:  Mr. Shardul Vikram (MSc) 
Date:  Tuesday, August 16, 2016 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The L_{p}Minkowski problem, a generalization of the classical Minkowski problem, was defined by Lutwak in the '90s. For a fixed real number p, it asks what are the necessary and sufficient conditions on a finite Borel measure on 𝕊^{n1} so that it is the L_{p} surface area measure of a convex body in ℝ^{n}. For p=1, one has the classical Minkowski problem in which the L_{p} surface area is the usual surface area of a compact set embedded in ℝ^{n}. Under certain technical assumptions, the planar L_{p}Minkowski problem reduces to the study of positive, πperiodic solutions, h: [0, 2π] ® (0,¥) to the nonlinear equation h^{1p} (h˝ + h) = y for a given smooth function y: [0, 2 π] ® (0,¥). In this thesis, we give a new proof of the existence of solutions of the planar L_{p}Minkowski problem for 0 < p < 1. To do so, we consider a parabolic anisotropic curvature flow on the space of strictly convex bodies 𝙺 Î ℝ^{2}, which are symmetric with respect to the origin. The connection between solutions to a parabolic equation, the flow, and a corresponding elliptic equation, the L_{p}Minkowski problem, has been long conjectured by the specialists and this is yet another instance where it has been used. 
Title:  Spectral Comparison Theorems in Relativistic Quantum Mechanics 
Speaker:  Mr. Petr Zorin (PhD Oral Examination) 
Date:  Monday, August 1, 2016 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (click here to view) 
Title:  Machine Learning Techniques for Detecting Hierarchical Interactions in Insurance Claims Models 
Speaker:  Ms. Sandra Maria Nawar (MSc) 
Date:  Friday, July 22, 2016 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This thesis presents an intuitive way to do predictive modeling in actuarial science. Generalized Linear Models (GLMs) are the standard tool for predictive modeling in the actuarial literature and in actuarial practice, yet GLMs can be quite restrictive. The aim of this work is to model claims and to propose solutions to current actuarial problems such as high variability in large datasets, variable selection, overfitting, dealing with highly correlated variables and detecting nonlinear effects such as interactions. The proposed approach is a hierarchical groupLassotype model that can efficiently handle variable selection and interaction detection between variables while enforcing strong hierarchy. This is achieved by imposing a penalty on the coefficients at the individual and group level. By optimizing the penalized objective function the model performs variable selection and estimation. Additionally, the model automatically detects interactions which is another important factor to achieve a high predictive power. For those purposes the groupLasso method is investigated for the Poisson and gamma distributions to perform frequencyseverity modeling. 
Title:  Dynamic Hedging Strategies Based on Changing the Pricing Parameters for Compound Ratchets 
Speaker:  Ms. Samia ElKhoury (MSc) 
Date:  Thursday, July 21, 2016 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  EquityIndexed Annuity products (EIAs) are becoming increasingly popular as they are taxdeferred accumulation vehicles that offer participation in the equity market growth while keeping the initial capital protected. This thesis focuses in particular on a special type of EIAs; the Compound Ratchet (CR). Sellers of this product, such as insurance companies and banks, retain the right to change one of the pricing parameters on each contract anniversary date, with promising not to cross a certain predetermined threshold. Changing these parameters can sometimes have an impact on the value of the EIA, which makes them interesting to study, especially when the issuer's changing policy is not clear. In order to reproduce the pattern of these changing parameters, a new approach of dynamically hedging the CR EIA and simultaneously protecting the issuer from hedging risk is proposed and tested. Assuming the BlackScholes financial framework and in the absence of mortality risk, closedform solutions for the price and value of the CR EIA at any time throughout the contract term are obtained and then used to find the Greeks, which are in turn used build the hedging strategies. In reality, trading can only be done in discrete time, which produces hedging errors. A detailed numerical example shows that the Gammahedging strategy outperforms the Deltahedging strategy by reducing the magnitude of these errors. However hedging risk still exists, therefore, the new approach is applied to transfer the errors from the issuer to the buyer by dynamically changing the pricing parameters. Additionally in the numerical example, the distribution of these parameters is extracted and analyzed, as well as the resulting reduction in the hedging errors, which represent the reduced cost for the issuer. 
Title:  Obstacles to the effective teaching of probability 
Speaker:  Mr. JeanMarc Miszaniec (MTM) 
Date:  Friday, April 29, 2016 
Time:  9:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Some Topics on Dirichlet Forms and NonSymmetric Markov Processes 
Speaker:  Mr. Jing Zhang (PhD) 
Date:  Friday, April 1, 2016 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Reciprocity Law for Flat Conformal Metrics with Conical Singularities 
Speaker:  Mr. Lukasz Obara (MA) 
Date:  Friday, January 15, 2016 
Time:  2:00 p.m. 
Location:  LB 912 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We study an analogue of Weils reciprocity law for flat conical conformal metrics on compact Riemann surfaces. We give a survey of Troyanov’s paper concerning flat conical metrics. The main result of this thesis establishes a relation among three flat conformally equivalent metric with conical singularities. 
Title:  HighDimensional Behaviour of Some Multivariate TwoSample Tests 
Speaker:  Mr. Shan Shi (MSc) 
Date:  Monday, December 14, 2015 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  It is a difficult problem to test the equality of distribution of two independent pdimensional (p>1) samples (of sizes m and n, say) in a nonparametric framework. It is not only because we need deal with issues such as tractability of the null distribution of teststatistics but also the fact that the latter are rarely distributionfree. Several notable nonparametric tests for comparing multivariate distributions are the multivariate runs test of Friedman and Rafsky (1979), the nearestneighbour test of Henze (1988) and the interpoint distancebased test of Baringhaus and Franz (BF) (2004). Biswas and Ghosh (BG) (2014) recently have shown that in a high dimension, low samplesize (HDLSS) scenario, i.e. where p goes to infinity but m, n are small or fixed, all the tests mentioned do not perform well. However, the BGtest is shown to be consistent in the case of HDLSS. In this work, we study the asymptotic behaviours of BF and BG tests when m, n and p go to infinity and min(m, n) = o(p). Our results reveal when these tests are expected to work well and when they are not. Results are illustrated by simulated data. 
Title:  A Diffusion Approximation of a Three Species FitnessDependent Population 
Speaker:  Mr. Liam Peuckert (MSc) 
Date:  Monday, October 19, 2015 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We introduce a continuous time Markov chain to model the ecological competition in the population of 3 species with fitness governed by a modified Moran process based on environmental resources in a limited niche of constant total population N. We run simulations to observe population behavior under different N and initial conditions. We then propose a model approximation which for large N converges to an ODE over most of the population space, with the population following a deterministic trajectory until it reaches an asymptotically stable line. We then prove that the approximation converges to a one dimensional diffusion forced onto the stable line until the first extinction occurs. We use the drift and diffusion coefficients of the diffusion to calculate the expected probability of first extinction for specific species, as well as the expected time until first extinction. Finally, we compare these with data obtained via simulations to show that the approximation is a good fit. 
Title:  Issuing a Convertible Bond with CallSpread Overlay: Incorporating the Eﬀects of Convertible Arbitrage 
Speaker:  Ms. Samira Shirgir (MSc) 
Date:  Friday, September 4, 2015 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In recent years, companies issuing convertible bonds enter into some transactions simultaneously in order to mitigate some of the negative impacts of issuing convertible bonds such as dilution of existing shares. One of the popular concurrent transactions is call spread overlay which reduces the dilution impact. This thesis explores the motivation of using these combined transactions from the perspective of the issuers, investors, and underwriters. We apply a binomial method to price the convertible bonds with callspread which are subject to default risk. Based on previous empirical studies convertible bond issuers experience a drop in their stock price due to the activities of convertible bond arbitrageurs when the issuance of convertible bonds is announced. We propose a model to estimate the drop in the stock price due to convertible bond arbitrage activities, at the time of planning the issue and designing the security that will be oﬀered. We examine the features of the model with simulated and realworld data. 
Title:  Sources of Mature Students’ Difficulties in Solving Different Types of Word Problems in Mathematics 
Speaker:  Ms. MariaJosée Bran Lopez (MTM) 
Date:  Thursday, September 3, 2015 
Time:  2:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  There are many different types of research done on algebra learning. In particular, word problems have been used to analyze students’ thought process and to identify difficulties in algebraic thinking. In this thesis, we show the importance of quantitative reasoning in problem solving. We gave 14 mature students, who were retaking an introductory course on algebra, four word problems of different types to solve: a connected problem, a disconnected problem, a problem with contradictory data and a problem where students were asked to assess the correctness of a fictional solution. In selecting these types of problems we have drawn on the research of Sylvine Schmidt and Nadine Bednarz on the difficulties of passing from arithmetic to algebra in mathematical problem solving. We present the students’ solutions and a detailed analysis of these solutions, seeking to identify the sources of the difficulty these students had in producing correct solutions. We sought these sources in the defects of quantitative reasoning, arithmetic mistakes, and algebraic mistakes. The attention to quantitative reasoning was inspired by the research of Pat Thompson and Stacey Brown. Defects of quantitative reasoning appeared to be an important reason why the students massively failed to solve the problems correctly, more important than their lack of technical algebraic skills. Therefore, teaching procedures and algebraic technical skills is not enough for students to develop problem solving skills. There should be a focus on developing students’ quantitative reasoning. Students need to have a good understanding of relations between quantities. Defects of quantitative reasoning create obstacles that prevent mature students from successfully solving any type of word problem. 
Title:  Mathematics for Engineers and Engineers’ Mathematics 
Speaker:  Mr. David Pearce (MTM) 
Date:  Tuesday, September 1, 2015 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This thesis compares the mathematics of engineers with that of mathematicians, and demonstrates how engineers use mathematics in their professional practice. The mathematics engineering students and math majors are expected to learn, for example in linear algebra and calculus courses, are analyzed in order to identify and describe the types of tasks given to both groups of students, and to determine if there are any significant differences. Following this analysis I demonstrate how engineers use the mathematics they learn to develop mathematical models which can be put to practical use in accomplishing tasks in their professional practice. Examples of mathematical models from the studies of statics, mechanics of materials, and structural analysis are presented, culminating in a discussion of the use of matrices in matrix structural analysis and the physical representation of eigenvectors and what they mean to a structural engineer. The comparison, analyses, and demonstrations are performed from an anthropological point of view using the Anthropological Theory of Didactics (ATD). From this perspective it will be shown that the similarities between the mathematical praxeologies of engineers and mathematicians are limited principally to the tasks and techniques, while the differences are found in the level of the technology and theory. 
Title:  The Search for the Compactified Kerr 
Speaker:  Mr. Borislav Mavrin (MSc) 
Date:  Tuesday, August 25, 2015 
Time:  1:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Einstein’s equations is a system of coupled nonlinear equations, which in general cannot be solved explicitly. The search for physically meaningful solutions is still under way. Probably, the most famous and physically relevant solutions are due to Schwarzschild and Kerr. Compactified (in one or more dimensions) analogs of the classical solutions are interesting from the point of view of higherdimensional theories, in particular the string theory.The periodic analog of the Schwarzschild solution was constructed in works of R. C. Myers, D. Korotkin and H. Nicolai. The problem of constructing the periodic analog of Kerr solution is still unsolved. The construction of the general solution to this problem is rather complicated due to nonlinearities of the corresponding equations. As a first step towards understanding of periodic Kerr solution it is reasonable to study its asymptotic behaviour at infinity.The objective of the current thesis was to analyze the possible asymptotic behaviour of the hypothetic periodic analog of Kerr solution by solving Einstein's equations in two different forms. 
Title:  Bridging Risk Measures and Classical Risk Processes 
Speaker:  Mr. Wenjun Jiang (M.Sc.) 
Date:  Monday, August 24, 2015 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The CramerLundberg model has been studied for a long time. It describes the basic risk process of an insurance company. Many interesting actuarial problems have been solved with this model and under its simplifying assumptions. In particular, the uncertainty of the risk process comes from several elements: the claim frequency intensity parameter, the claim severity and the premium rate. Establishing an efficient method to measure the risk of such process is meaningful to insurance companies. Although several methods have been proposed, none of these fully reflects the influence of each element of the risk process. In this thesis, we try to analyze this risk from different perspectives. First, we analyze the survival probability for infinitesimalperiod, we derive a risk measure that only relies on the distribution of the claim severity. The second way is comparing the coefficient adjustment graphically. Then we extend the method proposed by Loisel and Trufin (2014). Finally, inspired by the concept of the policyholder deficit, we construct a new risk measure based on a solvency criteria which includes all the above risk elements. The fifth chapter makes use of the risk measures reviewed in this thesis to solve the optimal capital allocation problem. The optimal allocation strategy can be set out by use of the Lagrange method and some recent findings on such problems. 
Title:  The Distribution of Points on Hyperelliptic Curves Over Fq of Genus g in Finite Extensions of Fq 
Speaker:  Ms. Manal Al Zahrani (MSc) 
Date:  Wednesday, August 19, 2015 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  For a fixed q and any n ≥ 1, the number of Fqn points on a hyperelliptic curve over Fq of genus g can be written as qn +1+S, where S is a certain character sum. We show that S behaves as a sum of qn + 1 independent random variables as g → ∞, with values depending on the parity of n. We get our result by generalizing the result of Kurlberg and Rudnick for the distribution of the affine Fqpoints to any finite extension Fqn of Fq, and using the techniques of Bucur, David, Feigon, and Lalin to also consider the points at infinity over the full space of hyperelliptic curves of genus g. 
Title:  Multivariate Risk Measures and a Consistent Estimator for the Orthant Based Tail ValueatRisk 
Speaker:  Mr. Nicholas Beck (MSc) 
Date:  Wednesday, August 19, 2015 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Multivariate risk measures is a rapidly growing field of research. The advancement of dependence modelling has lent itself to this progress. Presently, a variety of parametric methods have spawned from these developments, extending univariate measures such as ValueatRisk (VaR) and Tail ValueatRisk (TVaR) to the multivariate context. With the inception of these measures comes the requirement to estimate them. In particular, the development of consistent estimators is crucial for applications in financial and actuarial industries alike. For adequate sample sizes, consistent estimation allows for accurate evaluation of the underlying risks without preimposition of a statistical model. In this thesis, several risk measures are presented in the univariate case and extended to the multivariate framework. Quantifying the dependence between risks is accomplished through the use of copulas. Several families of copulas, elliptical, Archimedean and extreme value, and examples of each are presented along with properties. With these dependence relations in place, multivariate extensions of VaR, TVaR and Conditional Tail Expectation (CTE) are all presented. Much of the focus is given to the bivariate lower and upper orthant TVaR. In particular, we are interested in developing consistent estimators for these two measures. In fact, it will be shown that the presented estimators are strongly consistent for the true parametric value. To accomplish this, the strong consistency of the orthant based VaR curve, which can be shown in two ways, is used in tandem with the dominated convergence theorem. With strong consistency established, some numerical examples are then presented demonstrating the strength of these estimators. 
Title:  Affine Integral Quantization on a Coadjoint Orbit of the Poincaré Group in (1 + 1)spacetime Dimensions and Applications 
Speaker:  Mr. Haridas Das (MSc) 
Date:  Monday, August 3, 2015 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this thesis we study an example of a recently proposed technique of integral quantization by looking at the Poincaré group in (1+1)spacetime dimensions, denoted P_+^↑ (1,1), which contains the affine group of the line as a subgroup. The cotangent bundle of the quotient of P_+^↑ (1,1) by the affine group has the natural structure of a physical phase space. We do an integral quantization of functions on this phase space, using coherent states coming from a certain representation of P_+^↑ (1,1). The representation in question corresponds to the “zeromass” or “lightcone” situation, which when restricted to the affine subgroup gives the unique unitary irreducible representation of that group. This representation is also the one naturally associated to the above mentioned coadjoint orbit. The coherent states are labeled by points of the affine group and are obtained using the action of that group on a specially chosen vector in the Hilbert space of the representation. They satisfy a resolution of the identity, which can be computed using either the left or the right Haar measure of the affine group. The integral quantization is done using both choices and we obtain a relationship between the two quantized operators corresponding to the same phase space function. 
Title:  Solutions of the inverse FrobeniusPerron Problem 
Speaker:  Ms. Nijun Wei (MSc) 
Date:  Monday, July 6, 2015 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The FrobeniusPerron operator describes the evolution of density functions in a dynamical system. Finding the fixed points of this operator is referred to as the FrobeniusPerron problem. This thesis discusses the inverse FrobeniusPerron problem (IFPP), which seeks the transformation that generates a prescribed invariant probability density. In particular, we present in detail five different ways of solving the IFPP, including approaches using conjugation and differential equation, and two matrix solutions. We also generalize Pingel’s method [1] to the case of twopiece maps. 
Title:  The fourth moment of automorphic Lfunctions at prime power level 
Speaker:  Ms. Olga Balkanova (PhD) 
Date:  Tuesday, April 7, 2015 
Time:  9:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  On the construction and topology of multitype ancestral trees 
Speaker:  Ms. Mariolys Rivas (PhD) 
Date:  Friday, September 5, 2014 
Time:  2:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  On variational formulas on spaces of quadratic differentials 
Speaker:  Mr. Shahab Azarfar (M.Sc.) 
Date:  Friday, August 29, 2014 
Time:  3:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We study the variational formulas for the normalized Abelian differentials and matrix of bperiods on Hurwitz spaces, the moduli spaces of holomorphic Abelian differentials and quadratic differentials over compact Riemann surfaces. As the main result of the thesis, we find a complete set of local vector fields on the nonhyperelliptic connected component of the principal stratum of the moduli space of holomorphic quadratic differentials preserving the moduli of the base Riemann surface. 
Title:  On Modular forms, Hecke Operators, Replication and Sporadic Groups 
Speaker:  Mr. Rodrigo Farinha Matias (Ph.D.) 
Date:  Thursday, August 28, 2014 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Partial Hedging of EquityLinked Products in the Presence of Policyholder Surrender Using Risk Measures 
Speaker:  Mr. Mehran Moghtadai (M.Sc.) 
Date:  Thursday, August 28, 2014 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Throughout the past couple of decades, the surge in the sale of equity linked products has led to many discussions on the valuation of surrender options embedded in these products. However, most studies treat such options as American/Bermudian style options. In this thesis, a different approach is presented where only a portion of the policyholders react optimally, due to the belief that not all policyholders are rational. Through this method, a probability of surrender is found and the product is partially hedged by iteratively reducing the measure of risk to a nonpositive value. This partial hedging framework is versatile since few assumptions are made. To demonstrate this, the initial capital requirement for an equity linked product is found under a bivariate equity/interest model with a copula based dependence structure. A numerical example is presented in order to demonstrate some of the dynamics of this valuation method. In addition, a surprising result is found during the adjustment of the surrender parameters which directly implies that under a particular valuation method, an increased number of policy surrenders causes a drop in the initial capital requirement. This counterintuitive result is directly caused by the partial hedging method. 
Title:  New Perspectives and Methods in Loss Reserving Using Generalized Linear Models 
Speaker:  Mr. Jian Tao (M.Sc.) 
Date:  Wednesday, August 27, 2014 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Loss reserving has been one of the most challenging tasks that actuaries face since the appearance of insurance contracts. The most popular statistical methods in the loss reserving literature are the Chain Ladder Method and the Bornhuetter Ferguson Method. Recently, Generalized Linear Models (GLMs) have been used increasingly in insurance model fitting. Some aggregate loss reserving models have been developed within the framework of GLMs (especially Tweedie distributions). In this thesis we look at loss reserving from the perspective of individual risk classes. A structural loss reserving model is built which combines the exposure, the loss emergence pattern and the loss development pattern together, again within the framework of GLMs. Incurred but not reported (IBNR) losses and Reported but not settled (RBNS) losses are forecasted separately. Finally, we use out of sample tests to show that our method is superior to the traditional methods. In the third chapter we also extend the theory of limited fluctuation credibility for GLMs to one for GLMMs. Some criteria and algorithms are given. This is a byproduct of our work but is interesting in its own sake. The asymptotic variance of the estimators is derived, both for the marginal mean and the cluster specific mean. Keywords: GLMs, GLMMs, IBNR, RBNS, UMSEP, asymptotic variance, full credibility, loss reserving, individual risk classes. 
Title:  RiemannHilbert approach to Gap Probabilities of Determinantal Point Processed 
Speaker:  Ms. Manuela Girotti (Ph.D.) 
Date:  Wednesday, August 27, 2014 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Hardy Spaces and Differentiation of the Integral in the Product Setting 
Speaker:  Ms. Raquel Cabral (Ph.D.) 
Date:  Monday, August 25, 2014 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  On imputation techniques in survey sampling 
Speaker:  Ms. Hui Rong Zhu (M.Sc.) 
Date:  Monday, August 25, 2014 
Time:  12:15 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Some nonparametric imputation techniques, including two categories: single imputation and multiple imputation, are introduced and studied. The theories of evaluation: the bias, the variance, and the mean squared error of some estimators used in this thesis are presented. Finally, some imputation techniques are applied to a real case. These modes are compared to find their advantages, disadvantages and applicability. 
Title:  A comparison study on the performance of gamma kernels within nonparametric imputation methods 
Speaker:  Mr. Mianbo Wang (M.Sc.) 
Date:  Monday, August 25, 2014 
Time:  11:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The defects when the symmetric kernels are employed into the nonnegative data have been widely discussed. Of those asymmetric kernels, two estimators have been compared within the gamma kernel regression: one is proposed by Chaubey et. al. (2010), the other is proposed by Shi and Song (2013). In this study, we try to explore the performance of both estimators by applying them into nonparametric imputation methods under strongly ignorable missing at random assumption, which is seldom investigated in previous research. With kernelweighted regression and doublerobustness methods, the former estimator with the parameter =0 shows a bit better performance when the regression function is equal to 0 at x=0, although this advantage is very limited. While under other circumstances, the comparison is inconclusive, that needs to be further explored in the future. 
Title:  SetValued Maps and Their Applications 
Speaker:  Mr. Joe Pharaon (M.A.) 
Date:  Thursday, August 14, 2014 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The serious investigation of setvalued maps began only in the mid1900s when mathematicians realized that their uses go far beyond a mere generalization of singlevalued maps. We explore their fundamental properties and emphasize their continuity. We present extensions of fixed point theorems to the setvalued case and we conclude with an application to Game Theory. 
Title:  Alternative Approaches to Significant Zero Crossings (SiZer) Method for Feature Detection in NonParametric Univariate Curve Estimation 
Speaker:  Mr. Boyan Semerdjiev (M.Sc.) 
Date:  Wednesday, July 23, 2014 
Time:  3:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This work presents several methods for feature detection in density estimation of univariate data. Two versions of the original Significant Zero Crossings for Derivatives (SiZer) method and two other SiZer approaches for signal detection with Euler and Hadwiger characteristics are explored. The latter are based on approximating levelcrossing probabilities by expected number of upcrossings. In addition, a method for twosample density comparison is proposed, based on the discussed SiZer methodologies. Estimating a single best bandwidth parameter value is difficult. Therefore, all signal detection and comparison approaches utilize the concept of scalespace and color maps, allowing consideration of curve smoothing at multiple bandwidth levels simultaneously. Finally, the proposed methodologies do not compete and are therefore not compared. Instead, they complement each other and combining the observations from all of them together allows for better statistical inference of the data set. 
Title:  Van Der Corput's Lemma in Number Theory and Analysis and its Applications to Abelian Varieties with Prescribed Groups 
Speaker:  Ms. Valentine Chiche Lapierre (M.Sc.) 
Date:  Friday, June 27, 2014 
Time:  4:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Let A be an Abelian variety over a finite field Fq. We are interested in knowing the distribution of the groups A(Fq) of rational points on A as we run over all varieties defined over Fq. In particular, we want to show that they are in general not too “split”. For the case of dimension 1 (elliptic curves) and dimension 2 (Abelian surfaces), there are some theoretical results due to David and her collaborators, but the general case is open. We are interested in Abelian Varieties of dimension 3. We use Rybakov's criterion, which relates the existence of a given abstract group as the group of points of some Abelian variety to properties of the characteristic polynomial of the variety. We can use it to derive precise properties and then we use the fact that some sequence of monomials of five variables is uniformly distributed modulo one to obtain stronger results that will hold with probability one. By Weyl's criterion, equidistribution follows by bounding exponential sums, and in order to do so, we will use a combination of different methods. We are particularly interested in Van Der Corput's lemma. It has a continuous version that exhibits the decay of oscillatory integrals and a discrete version that gives a bound for exponential sums. We will see the relation between these two versions and how they apply to the original problem of Abelian varieties. 
Title:  A cristalline criterion for good reduction on semistable K3surfaces over a padic field 
Speaker:  Mr. Rogelio PerezBuendia (Ph.D.) 
Date:  Friday, January 10, 2014 
Time:  3:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Fourier methods for numerical solution of FBSDEs with applications in mathematical finance 
Speaker:  Mr. Polynice Oyono Ngou (Ph.D.) 
Date:  Friday, January 10, 2014 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We present a Fourier analysis approach to numerical solution offorwardbackward stochastic differential equations (FBSDEs) and propose two implementations. Using the Euler time discretization for backward stochastic differential equations (BSDEs), Fourier analysis allows to express the conditional expectations included in the time discretization in terms of Fourier integrals. The space discretization of these integrals then leads to expressions involving discrete Fourier transforms (DFTs) so that the FFT algorithm can be used. We quickly presents the convolution method on a uniform space grid. Locally, this firrst implementation produces a truncation error, a space discretization error and an additional extrapolation error. Even if the extrapolation error is convergent in time, the resulting absolute error may be high at the boundaries of the uniform space grid. In order to solve this problem, we propose a treelike grid for the space discretization which suppresses the extrapolation error leading to a globally convergent numerical solution for the BSDE. The method is then extended to FBSDEs with bounded coeffcients, reflected FBSDEs and higher order time discretizations of FBSDEs. Numerical examples from finance illustrate its performance. 
Title:  Determinants of PseudoLaplacians on compact Riemannian manifolds and uniform bounds of eigenfunctions on tori 
Speaker:  Mr. Tayeb Aissiou (Ph.D.) 
Date:  Thursday, December 12, 2013 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  On Low Dimensional Galilei Groups and Their Applications 
Speaker:  Mr. Syed Chowdhury (Ph.D.) 
Date:  Friday, December 6, 2013 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Pricing Catastrophic Mortality Bonds Using State Space Models 
Speaker:  Mr. Zhifeng Zhang (M.Sc.) 
Date:  Monday, October 21, 2013 
Time:  2:45 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Catastrophic mortality bonds are designed to hedge against the mortality risks. Its payoff at maturity depends on the realized mortality index over the life of the bond, therefore modeling the mortality index is the main concern in our study. Since mortality shocks are detected using outlier analysis, nonGaussian state space models with a fattailed error term is proposed to fit the mortality index and handle shocks. By comparing several state space models with different fattailed distributions, an ARIMA process for the baseline mortality and the $t$distribution for capturing mortality shocks are chosen. We obtain the price of the mortality bond using the proposed model and estimate the market price of risk. It appears that the market of risk is lower than the ones obtained in the literature, which is consistent with the industrial empirical results from Wang (2004). This implies that our model is capable to handle mortality risks. 
Title:  On measure theory textbooks and their use by professors in graduatelevel courses 
Speaker:  Mr. Felix Sidokhine (M.Sc.) 
Date:  Friday, September 6, 2013 
Time:  11:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Previous research has reported on students' uses of mathematics textbooks at preuniversity and undergraduate levels. Also, some research has been done on textbooks as standalone objects, looking at their format and didactic and mathematical discourses. However, very few researchers have investigated instructors' uses of textbooks. In this thesis we do so at the graduate level; in particular, we investigate instructors' uses of measure theory textbooks. We chose measure theory because of its important role as a foundation for much of what is modern analysis, a branch of mathematics with many applications such as electronics, signal processing and even statistics. We chose the graduate level because textbooks are known to have an important role in the teaching and learning of graduate mathematics courses. In the first part of our research, we draw on Eco's notion of model reader and characterized the target instructor audience of four measure theory textbooks. We also analyzed the mathematical knowledge that these textbooks contain in light of a review of the history of the development of measure theory. Finally, we analyzed the textbooks affordances for teaching from the perspective of Sierpinska's notion of apodictic vs. liberal textbooks. In the second part of our research, we interviewed three university professors in order to understand their beliefs about textbooks, mathematics and learning. In particular, we identified different types of instructors and have been able to match them with textbooks whose use in their teaching activity is likely to be most effective. 
Title:  Symplectic Structures on Spaces of Polygons 
Speaker:  Mr. Tuan Nguyen (M.Sc.) 
Date:  Thursday, September 5, 2013 
Time:  3:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  All polygons of fixed side lengths make up a space on which one may put symplectic structures. In my thesis, I describe two ways to do this; these ways, making use of a method called symplectic reduction, are due to HaussmannKnutson and independently to KapovichMillson, and have been shown to be equivalent by HausmannKnutson. Furthermore, one may have a group action on a symplectic manifold. If the group is a torus whose dimension is half of that of the manifold, and if the action is an effective Hamiltonian action, then the manifold corresponds to a figure in the threedimensional space called a Delzant polytope; in fact, Delzant polytopes completely classify such manifolds. By a result of KapovichMilllson, on the space of polygons of m sides of fixed side lengths, one may construct such a torus action if the m3 diagonals of the polygons do no vanish. The space of polygons then corresponds to a Delzant polytope, and may then be identified with other symplectic manifolds corresponding to the same polytope. I describe in the thesis the case when polygons have 4 sides or 5 sides. 
Title:  The KugaSatake construction: a modular interpretation 
Speaker:  Ms. Alice Pozzi 
Date:  Friday, August 30, 2013 
Time:  12:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Given a polarized complex K3 surface, one can attach to it a complex abelian variety, called KugaSatake variety. The KugaSatake variety is determined by the singular cohomology of the K3 surface; on the other hand, this singular cohomology can be recovered by means of the weight 1Hodge structure associated to the KugaSatake variety. Despite the transcendental origin of this construction, KugaSatake varieties have interesting arithmetic properties. KugaSatake varieties of K3 surfaces defined over number fields descend to finite extension of the field of definition. This property suggests that the KugaSatake construction can be interpreted as a map between moduli spaces. More precisely, one can define a morphism, called KugaSatake map, between the moduli space of K3 surfaces and the moduli space of abelian varieties with polarization and level structure. This morphism, defined over a number field, is obtained by regarding the classical construction as a map between an orthogonal Shimura variety, closely related to the moduli space of K3 surfaces, and the Siegel modular variety. The most remarkable fact is that the KugaSatake map extends to positive characteristic for almost all primes, associating to K3 surfaces abelian varieties over finite fields. This can be proven applying a result by Faltings on the extension of abelian schemes and the good reduction property of KugaSatake varieties. 
Title:  Generalized Linear Models for a Dependent Aggregate Claims Model 
Speaker:  Ms. Juliana Schulz (M.Sc.) 
Date:  Thursday, August 29, 2013 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  The Minimum Flow Cost Hamiltonian Tour Problem 
Speaker:  Mr. Camilo Ortiz (M.Sc.) 
Date:  Wednesday, August 14, 2013 
Time:  9:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this thesis we introduce the minimum flow cost Hamiltonian tour problem (FCHT). Given a graph and positive flow between pair of vertices, the FCHT consists of finding a Hamiltonian tour that minimizes the total cost for sending flows between pairs of vertices thorough the shortest path on the cycle. We prove that the FCHT belongs to the class of NPhard problems and study the polyhedral structure of its set of feasible solutions. In particular, we present five different MIP formulations which are theoretically and computationally compared. We also develop some approximate and exact solution procedures to solve the FCHT. We present a combinatorial bound, two heuristic procedures, one greedy deterministic method and the other a greedy randomized adaptive search procedure. Finally, a branchandcut algorithm is also proposed to optimally solve the problem. 
Title:  Stochastic Mortality Modelling with Lévy Processes based on GLM's 
Speaker:  Mr. Sayed Saeed Ahmadi (Ph.D.) 
Date:  Monday, August 5, 2013 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Providing College Level Calculus Students with Opportunities to Engage in Theoretical Thinking 
Speaker:  Ms. Dalia Challita (M.T.M.) 
Date:  Wednesday, June 19, 2013 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Previous research has reported an absence of a theoretical thinking component in college level Calculus courses. This absence has been linked with institutional constraints which often pervade these courses. In this thesis, we provide empirical evidence that students can be engaged in theoretical thinking in a college level Calculus course, despite the existing institutional constraints and without having to readjust the course outline or materials and assessments. Students enrolled in a Calculus course were presented with optional tasks intended to engage them in theoretical thinking. We analyze the data from the perspective of Sierpinska, Nnadozie, and Oktac’s (2002) model of theoretical thinking; all students attending class engaged in these optional tasks and our analysis shows that on average, more than half of them engaged in theoretical thinking. We place our study in the context of previous research in the teaching and learning of university introductory (and remedial) level mathematics and of the role that Calculus courses play in the mathematics education of undergraduate students. 
Title:  Slope Conditions for Stability of ACIMs of Dynamical Systems 
Speaker:  Mr. Zhengyang Li (Ph.D.) 
Date:  Monday, June 10, 2013 
Time:  12:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Experimenting With Discursive and NonDiscursive Styles of Teaching Absolute Value Inequalities to Mature Students 
Speaker:  Ms. Maria Tutino (M.T.M.) 
Date:  Friday, April 12, 2013 
Time:  12:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This research is a followup of Sierpinska, Bobos, and Pruncut’s 2011 study, which experimented with three teaching approaches to teaching absolute value inequalities (AVI), visual, procedural, and theoretical, presented over an audio lecture with slides. The study demonstrated that participants treated with the visual approach were more likely to engage in theoretical thinking than those treated with the other two approaches. In the present experiment, two groups of participants enrolled in prerequisite mathematics courses at a large, urban North American University were taught AVI with the visual approach using two different teaching styles: discursive (permitting and actively encouraging teacherstudent interactions during the lecture) and nondiscursive (not allowing teacherstudent interactions during the lecture). In Sierpinska et al.’s study, the nondiscursive style was used in all three approaches (the lectures were recorded and the teacher was not present in person). In the present study, a live teacher was lecturing in both treatments. Another difference was that in Sierpinska et al.’s study lectures were delivered individually to each participant, while in the present study, all participants in a group were treated simultaneously. Therefore, in the discursive approach, not only teacherstudent but also studentstudent interactions during the lecture were possible. The aim of this research was to explore the conjecture that the discursive approach is more likely to promote theoretical thinking in students. The group exposed to the discursive approach was, therefore, my experimental group and the other played the role of the control group. The conjecture was not confirmed, but the two approaches seem to have provoked different aspects of theoretical thinking. The experimental group was found to be more reflective, while the control group tended to be more systemic in their thinking. Some striking results, not predicted by Sierpinska et al.’s study, were also found with respect to reflective thinking, definitional thinking, proving behavior, and analytic thinking. 
Title:  Some Support Properties for a Class of ɅFlemingViot Processes 
Speaker:  Ms. Huili Liu (Ph.D.) 
Date:  Thursday, March 28, 2013 
Time:  9:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  An Analysis of Students’ Difficulties Learning Group Theory 
Speaker:  Ms. Julie Lewis (M.Sc.) 
Date:  Monday, March 25, 2013 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Research in mathematics education and anecdotal data suggest that undergraduate students often find their introductory courses to group theory course particularly difficult. Research in this area, however, is scarce. In this thesis, I consider students’ difficulties in their first group theory course and conjecture that they have two distinct sources. The first source of difficulties would pertain to a conceptual understanding of what group theory is and what it studies. The second would relate to the modern abstract formulation of the topics learned in a group theory course and the need to interpret and write meaningful statements in modern algebra. To support this hypothesis, the group concept is explored through a historical perspective which examines the motivations behind developing group theory and its practical uses. Modern algebra is also viewed in a historical context in terms of three defining characteristics of algebra; namely, symbolism, justifications and the study of objects versus relationships. Finally, a pilot study was conducted with 4 students who had recently completed a group theory course and their responses are analyzed in terms of their conceptual understanding of group theory and modern algebra. The analysis supports the hypothesis of the two sources. Based on the results, I propose a remediation strategy and point in the direction of future research. 
Title:  CentroAffine Normal Flows and Their Applications 
Speaker:  Mr. Mohammad Najafi Ivaki (Ph.D.) 
Date:  Monday, December 3, 2012 
Time:  11:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title: 
Rankin LFunctions and the Birch and SwinnertonDyer Conjecture 
Speaker:  Mr. Reza Sadoughianzadeh (M.Sc.) 
Date:  Tuesday, September 11, 2012 
Time:  1:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title: 
Teaching the Singular Value Decomposition of Matrices: A Computational Approach 
Speaker:  Mr. Zoltan Lazar (M.T.M.) 
Date:  Monday, September 10, 2012 
Time:  1:15 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this thesis, I present a small experiment of teaching the singular value decomposition of matrices using a computational approach. The experiment took place in the summer of 2011 and consisted in two sessions of lectures of four hours each, in the computer lab, on the premises of Concordia University. The same four students (“Carrie”, ”Chal”, ”Desse” and “Nat”) attended both sessions. The underlying methodology was to introduce theoretical results, let participants explore them using mathematical software and then generalize and formalize them. Participants’ responses to test questions were collected and analyzed, and the results are presented in the fourth chapter. The goals of the experiment were to assess the participants’ preparedness for this topic and their level of acceptance of this teaching technique. One of the immediate conclusions is that without a good understanding of the “building blocks” concepts of linear algebra the topic of singular value decomposition of matrices could prove challenging for undergraduate students. The participants showed interest in the teaching method, but mentioned that more time would be required to really benefit from the numerical advantages and from the vast applications of the singular value decomposition. 
Title: 
Statistical Analysis of Volatility Surfaces 
Speaker:  Mr. Dimitris Lianoudakis (M.Sc.) 
Date:  Friday, September 7, 2012 
Time:  12:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Option prices can be represented by their corresponding implied volatilities. Implied volatility is dependent on both the strike price and the time to maturity. This dependence creates a mapping known as the implied volatility surface (IVS). The volatility surface is known to practitioners as being synonymous with option prices. These surfaces change dynamically and have distinct features that can be modeled and broken down into a small number of factors. Using time series data of option prices on the S&P500 index, we study the dynamics of the implied volatility surface and deduce a factor model which best represents the surface. We explore the different methods of smoothing the IVS and derive the local volatility function. Using standard dimension reduction techniques and more recent nonlinear manifold statistics, we aim to identify and explain these distinct features and show how the surface can be represented by a small number of these prominent factors. A thorough analysis is conducted using principal component analysis (PCA) and common principal component analysis (CPC). We introduce a new form of dimension reduction technique known as principal geodesic analysis (PGA) and give an example. We try to set up a geometric framework for the volatility surface with the aim of applying PGA. 
Title: 
Galois theory for schemes 
Speaker:  Ms. Shan Gao (M.Sc.) 
Date:  Wednesday, August 29, 2012 
Time:  3:40 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The main object of study of this thesis is the \'etale fundamnetal group of a connected scheme. This profinite group is defined as the automorphism group of a fiber functor defined on the category of finite \'etale covers of our base scheme. 
Title: 
Pricing Ratchet EIA under Heston’s Stochastic Volatility with Deterministic Interest 
Speaker:  Mr. Dezhao Han (M.Sc.) 
Date:  Wednesday, August 29, 2012 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Since its introduction in 1995, Equityindexed annuities (EIAs) are paid increasing attention. In 2008 it represents 42% of the annuities sold by agents, but after the 2008 financial crisis the number shrank to 25% in 2010. Thus pricing and hedging EIAs is an interesting topic. Researches have been done on pricing different kinds of EIAs, their hedging strategies as well as their optimal stopping strategies. However, the underlying asset is always assumed to follow the geometric Brownian motion that is the BlackSholes (BS) model. The BS model is plagued by its assumption of constant volatility, while stochastic volatility models become increasingly popular. In this paper we assume the asset price follows Heston’s stochastic volatility model with deterministic interest, and introduce two methods to price the Ratchet EIA. The first method is called JTPDF (joint transition probability density function) method. Given the JTPDF of the asset price and stochastic variance in Heston’s framework, pricing Ratchet EIA is a problem on solving multiple integrals. We solve the multiple integral using Quasi Monte Carlo method and the importance sampling technique. We call the other method CE (conditional expectation) approach. Conditioning on the path of volatility, we first price the Rachet EIA analytically in BS framework. Then the price in Heston’s framework can be evaluated by simulating the path of volatility. Greeks for the Ratchet EIA can also be calculated by the JTPDF or CE methods. At the end, we did some sensitivity tests for Ratchet EIAs’ prices and Greeks. Keywords: stochastic volatility, equityindexed annuity, highdimensional integrals, simulating Heston’s stochastic volatility, Greeks of Ratchet EIA 
Title: 
On the stability of the absolutely continuous invariant measure of certain class of maps with deterministic perturbation 
Speaker:  Mr. Ivo Pendev (M.Sc.) 
Date:  Tuesday, August 28, 2012 
Time:  1:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Keller showed the instability of the absolutely continuous invariant measure (acim) for the family of Wshaped maps. This instability is the result of the invariant neighborhood of the fixed turning point at 1/2. The construction of these maps, for which the renowned LasotaYorke inequality fails to prove stability (due to the magnitude of the slopes in the limiting map), has recently been generalized. In the EslamiMisiurewicz paper, a map was defined, whose third iterate has a fixed turning point at 1/2, raising the question of the stability of the map. The goal of this thesis is to show the stability of this map. We define a family of deterministic perturbation of the map and we express their invariant densities as an infinite sum with the purpose of showing that the normalized invariant densities are uniformly bounded. This result is used to show the stability of absolutely continuous invariant measure of this transformation. 
Title: 
Relating modulus and Poincaré inequalities on modified Sierpiński carpets 
Speaker:  Mr. Andrew Fenwick (M.A.) 
Date:  Tuesday, August 28, 2012 
Time:  11:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This thesis investigates the question of whether a doubling metric measure space supports a Poincaré inequality and explains the relationship between the existence of such an inequality and the nontriviality of the respective modulus. It discusses in detail a general class of modified Sierpiński carpets presented by Mackay, Tyson, and Wildrick [14], which are the first examples of spaces that support Poincaré inequalities for a renormalized Lebesgue measure that are also compact subsets of Euclidean space with empty interior. It describes the intricate relationship between the sequence used in the construction of a modified Sierpiński carpet and the validity of Poincaré inequalities on that space. 
Title: 
Computations on the Birch and SwinnertonDyer conjecture for elliptic curves over pure cubic extensions 
Speaker:  Ms. Céline Maistret (M.Sc..) 
Date:  Monday, August 6, 2012 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The Birch and SwinnertonDyer conjecture remains an open problem. In this thesis, we propose to give numerical evidence toward this conjecture when restricted to elliptic curves over pure cubic extensions. We present the general conjecture for elliptic curves over number fields and detail each arithmetic invariants involved. Assuming the conjecture holds, for given elliptic curves E over specific number fields K, we compute the order of the ShafarevichTate group of E(K). 
Title: 
Concentration of Measure and Ricci Curvature 
Speaker:  Mr. Ryan Benty (M.A.) 
Date:  Wednesday, July 25, 2012 
Time:  11:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In 1917, Paul Levy proved his classical isoperimetric inequality on the Ndimensional sphere. In the 1970's, Mikhail Gromov extended this inequality to all Riemannian manifolds with Ricci curvature bounded below by that of The Nsphere. Around the same time, the Concentration of Measure phenomenon was being put forth and studied by Vitali Milman. The relation between Concentration of Measure and Ricci curvature was realized shortly thereafter. Elaborating on several articles, we begin by explicitly presenting a proof of the Concentration of Measure Inequality for the Nsphere as the archetypical space of positive curvature, followed by a complete proof extending this result to all Riemannian manifolds with Ricci curvature bounded below by that of the Nsphere in the process, we present a detailed technical proof of the GromovLevy isoperimetric inequality. Following Yann Ollivier, we note and prove a Concentration of Measure inequality on the discrete Hamming cube, and discuss his extension of Ricci curvature to general metric spaces, particularly discrete metric measure spaces. We show that this “coarse” Ricci curvature on the Hamming cube is positive and present Ollivier's Concentration of Measure inequality for all spaces admitting positive coarse Ricci curvature. In addition, we calculate the coarse Ricci curvature for several discrete metric spaces. 
Title:  An upper bound for the average number of amicable pairs 
Speaker:  Mr. James Park (Ph.D.) 
Date:  Wednesday, June 7, 2012 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Amicable numbers have been known since Pythagoras and are defined to be two different numbers so related that the sum of the proper divisors of each is equal to the other number. In 2009 Silverman and Stange provided an elliptic curve analogue to amicable numbers. Let E be an elliptic curve over Q. They defined a pair (p, q) of rational primes to be an amicable pair for E if E has good reduction at these primes and the number of points on the reductions Ep and Eq satisfy #Ep(Fp) = q and #Eq(Fq) = p. Let QE(X) denote the number of amicable pairs (p, q) for E/Q with p<= X. Then they conjectured that QE(X) ~ X/(\log X) 2 if E does not have complex multiplication. In this thesis I will provide an upper bound for the average of QE(X) over the family of all elliptic curves which is very close to the conjectural asymptotic of Silverman and Stange. 
Title:  Determinant of PseudoLaplacians 
Speaker:  Mr. Tayeb Aissiou (Ph.D.) 
Date:  Wednesday, May 30, 2012 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Let X be a compact Riemannian manifold of dimension two or three and let P be a point of X. We derive comparison formulas relating the zetaregularized determinant of an arbitrary selfadjoint extension of (symmetric) Laplace operator with domain, consisting of smooth functions with compact supports which do not contain P, to the zetaregularized determinant of the selfadjoint Laplacian on X. 
Title:  Normal Form Analysis of a MeanField Inhibitory Neuron Model 
Speaker:  Ms. Loukia Tsakanikas (M.Sc.) 
Date:  Monday, April 23, 2012 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In neuroscience one of the open problems is the creation of the alpha rhythm detected by the electroencephalogram (EEG). One hypothesis is that the alpha rhythm is created by the inhibitory neurons only. The mesoscopic approach to understand the brain is the most appropriate to mathematically modelize the EEG records of the human scalp. In this thesis we use a local, meanfield potential model restricted to the inhibitory neuron population only to reproduce the alpha rhythm. We perform extensive bifurcation analysis of the system using AUTO. We use Kuznetsov's method that combines the center manifold reduction and normal form theory to analytically compute the normal form coefficients of the model. The bifurcation diagram is largely organized around a codimension 3 degenerate BogdanovTakens point. Alpha rhythm oscillations are detected as periodic solutions. 
Title:  Secondary School Mathematics Teachers use of Technology through the Lens of Instrumentation Theory 
Speaker:  Mr. Nicolas Boileau (M.T.M.) 
Date:  Wednesday, April 11, 2012 
Time:  3:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  The primary goal of our research was to gain a sense of the technology that secondary school mathematics teachers in Montreal, Quebec are currently using, how they are using it, and some of the reasons why they use the technology that they do, in the ways that they do. The secondary goal was to test the effectiveness of our approach in obtaining this information. The approach consisted of interviewing two local secondary school mathematics teachers. The interview questions prodded at what Instrumentation Theory suggests to be some of the fundamental aspects of one’s interactions with technology; the ‘artifact’ (the particular technology), the subject (the user of that technology), the ‘task’ that the subject tries to complete with the artifact, the ‘instrumented techniques’ that she/he employs to complete the task (which reveal some of their ‘schemes of use’), and the process through which the subject and the artifact interact and ‘shape’ each other, called ‘an instrumental genesis’. The teachers’ responses to the interview questions revealed that, although they both used most of the same technology (with a few exceptions), significant differences existed between the ways that they used some of them, why certain technologies were used, and why others were not. The two teachers also differed in their views on the value of their instrumented techniques. These findings are discussed in light of the literature review, demonstrating some of the effectiveness of our approach. We believe that our approach was useful as it allowed us to elicit detailed descriptions of these two teachers’ uses of technology and because it facilitated the analysis of the data (as the questions were based on the same theoretical framework that was then used to analyze the teachers’ responses). We conclude with some suggestions for future research. One of the suggestions addresses ways in which our approach could be improved to give researchers who might use it in the future more informative responses. 
Title:  A SkewNormal CopulaDriven Generalized Linear Mixed Model for Longitudinal Data 
Speaker:  Mr. Mohamad Elmasri (M.Sc.) 
Date:  Tuesday, April 10, 2012 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  ArellanoValle et al. [2005] studied the effect of generalizing the presumed normality structures of a linear mixed model (LMM) random effect and error to a skewnormal distribution, to adequately fit a broader range of longitudinal data. Closed forms of marginal distributions were explicitly indicated along with a maximum likelihood formation. Working with the results found by ArellanoValle et al.[2005], this paper extends to an even wider set of models for longitudinal data based on the exponential family of distributions. This is achieved by combining a skewnormal copula and a general exponential family distribution, where a generalized linear model (GLM) framework is applied. Some special cases are discussed, in particular, the exponential and gamma distribution. Simulations with multiple link functions are shown. A real data example is also analyzed. 
Title:  The Use of Blogs in Ontario Secondary Mathematics Education 
Speaker:  Ms. Christy Lyons (M.T.M.) 
Date:  Monday, April 2 , 2012 
Time:  11:45 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Blogging was such a popular activity in the mid2000s that “blog” was chosen as the word of the year in 2004 by MerriamWebster. This thesis examines whether this popularity for blogging transferred to the mathematics classroom; if so, in what ways are mathematics teachers using blogs in relation to their teaching activities and if not, in which ways they are willing to use them. Previous research shows that teachers use classroom blogs to promote collaboration, to allow conversation with outside experts, as a positive tool for ESL students because of access to online translators, to provide a voice for quiet students who might not speak up in class, to encourage critical thinking skills and as a venue for reflective thinking or metacognition. Twentyone Ontario Secondary Mathematics teachers were surveyed to determine their personal, professional and classroom blogging views and habits. Although only one teacher reported on having operated a classroom blog, teachers showed an interest for blogs and blogging activities (e.g., seventysix percent were willing to read blogs for professional development and fortyfive percent would be willing to operate blogs in their classrooms in the future). On the whole, interest for blogs and blogging activities seems to grow slowly but firmly. Based on teachers’ responses and previous research, I discuss the possible benefits of bloggingrelated activities in secondary classrooms. 
Title:  Students’ Understanding of Real, Rational, and Irrational Numbers 
Speaker:  Ms. Deidre Maher Arbour (M.T.M.) 
Date:  Friday, March 30, 2012 
Time:  1:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  This thesis presents a study of the understanding of real, rational, and irrational numbers by 30 fourth semester college science students in the Montreal region. The written answers to a set of seven questions were analyzed to determine the students’ interpretations of mathematical signs according to C. S. Pierce’s classifications and to describe their modes of thought according to Vygotsky’s theory of concept development. From these interpretations, we are able to reconstruct a facsimile of what the students’ concept images are as they pertain to the sets in question. Finding the concept images to be idiosyncratic and rarely in agreement with what conventional mathematics holds to be true, we examine the way the number systems are approached in school and in the field of mathematics and use this, along with the analyses, to make pedagogical recommendations. 
Title:  Motivating Adult Students Taking a Basic Algebra Course in a University Setting 
Speaker:  Ms. Carol Beddard (M.T.M.) 
Date:  Wednesday, March 28, 2012 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Understanding the motivation of students learning mathematics and using this understanding to strengthen motivation can serve to improve mathematics instruction for students, especially students who may dislike math. Motivation is modeled as arising from an interaction of needs, goals and dimensions of the self, resulting in behavior that is regulated by feedback and external factors. In this study, the motivation of university students in a preparatory algebra class is investigated. The study uses a ConjectureDriven design in the teaching situation of MATH 200 – Fundamental Concepts of Algebra which is a required course for many students. That they have to take a basic algebra course at the university level is indicative of some previous difficulties with mathematics which in turn can be linked to negative affect towards math. The conjecture was that motivation would be lacking among this group of students but that a class that is taught from a motivational standpoint would result in better attitudes towards math. Based on an a priori profile of motivational characteristics of the students in the course, the hypothetical student, the course was taught with the aim of improving motivation. Observations, course evaluations, a questionnaire and a survey were used to: (1) create a profile of observed motivational characteristics, the realistic student, and (2) to describe the effect of the course on student motivation. It was found that a classroom that addressed students’ needs for autonomy, competence and relatedness, promoted an understanding of why a procedure was used (rather than just how to apply the procedure), and that at all times respected the dignity of students, was motivational. In this classroom, the students reported improved affect towards mathematics across the dimensions of emotions, attitudes, beliefs and values. 
Title:  The Minimizer of Dirichlet Integral 
Speaker:  Mr. Ruomeng Lan (M.Sc.) 
Date:  Wednesday, March 21, 2012 
Time:  11:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  In this thesis, we consider the minimizer of the Dirichlet integral, which is used to compute the magnetic energy. We know that the Euler equations describe a motion of an inviscid incompressible fluid. We show that the infimum of the Dirichlet integral, by the action of areapreserving diffeomorphisms, is a stream function corresponding to some velocity field, which is a solution to the stationary Euler equation. According to this result, we study the properties and behaviors of the steady incompressible flow numerically. We utilize three distinct numerical methods to simulate the minimizer of the Dirichlet integral. In all cases the singularity formation was observed. Every hyperbolic critical point of the original function gives rise to a singularity of the minimizer. 
Title:  Heuristic Results for Ratio Conjectures of LE(1, χ) 
Speaker:  Mr. Jungbae Nam (M.Sc.) 
Date:  Thursday, January 12, 2012 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  Let LE(s, χ) be the HasseWeil Lfunction of an elliptic curve E defined over Q and twisted by a Dirichlet character χ of order k and of conductor fχ. Keating and Snaith introduced the way to study Lfunctions through random matrix theory of certain topological groups. Conrey, Keating, Rubinstein, and Snaith and David, Fearnley, and Kisilevsky developed their ideas in statistics of families of critical values of LE(1, χ) twisted by Dirichlet characters of conductors ≤ X and proposed conjectures regarding the number of vanishings in their families and the ratio conjectures of moments and vanishings which are strongly supported by numerical experiments. In this thesis, we review and develop their works and propose the ratio conjectures of moments and vanishings in the family of LE(1, χ) twisted by Dirichlet characters of conductors fχ ≤ X and order of some odd primes, especially 3, 5, and 7 inspired by the connections of Lfunction theory and random matrix theory. Moreover, we support our result on the ratio conjectures of moments and vanishings of the families for some certain elliptic curves by numerical experiments. 
Title:  Analysis of the Dynamic Traveling Salesman Problem with Different Policies 
Speaker:  Mr. Santiago Ravassi (M.Sc.) 
Date:  Thursday, December 8 , 2011 
Time:  1:30 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We propose and analyze new policies for the traveling salesman problem in a dynamic and stochastic environment (DTSP). The DTSP is defined as follows: demands for service arrive in time according to a Poisson process, are independent and uniformly distributed in a Euclidean region of bounded area, and the time service is zero; the objective is to reduce the time the server visits all the present demands for the first time. We start by analyzing the nearest neighbour (NN) policy since it has the best performance for the dynamic vehicle routing problem (DTRP), a closely related problem to the DTSP. We further introduce the random start policy whose efficiency is similar to that of NN, and we observe that when the random start policy is delayed, it behaves as the DTRP with NN policy. Finally, we introduce the partitioning policy and show that it reduces the expected time demands are swept from the region for the first time relative to other policies. 
Title:  On Existence and Stability of Absolutely Continuous Invariant Measures in Some Chaotic Dynamical Systems 
Speaker:  Mr. Peyman Eslami (Ph.D.) 
Date:  Friday, September 9, 2011 
Time:  10:30 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Title:  Parameter Estimation in a TwoDimensional Commodity 
Speaker:  Ms. Wenxi Liu (M.Sc.) 
Date:  Wednesday, August 31, 2011 
Time:  2:00 p.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  We consider the problem of estimating the parameters of an unobservable model for the spot price of a commodity. Using the observable timeseries of the termstructure of futures prices and a filterbased implementation of the expectation maximization (EM) algorithm, we calculate the maximum likelihood parameter estimates (MLEs). New finitedimensional filters are derived that allow the EM algorithm to be implemented without calculating Kalman smoother estimates. The method is applied to a twofactor commodity price model. 
Title:  Theory and Applications of Generalized Linear Models in Insurance 
Speaker:  Mr. Jun Zhou (Ph.D.) 
Date:  Monday, August 29, 2011 
Time:  10:00 a.m. 
Location:  LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) 
Abstract:  (Click here to view) 
Speaker: Mr. Oscar Quijano Xacur (M.Sc.)
Date: Tuesday, August 23, 2011
Time: 1:30 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Property and Casualty Premiums Based on Tweedie Families of Generalized Linear Models
Abstract: We consider the problem of estimating accurately the pure premium of a property and casualty insurance portfolio when the individual aggregate losses can be assumed to follow a compound Poisson distribution with gamma jump size. The Generalized Linear Models (GLMs) with a Tweedie response distribution are analyzed as a method for this estimation. This approach is compared against the standard practice in the industry of combining estimations obtained separately for the frequency and severity by using GLMs with Poisson and gamma responses respectively. We show that one important difference between these two methods is the variation of the scale parameter of the compound Poissongamma distribution when it is parametrized as an exponential dispersion model. We conclude that both approaches need to be considered during the process of model selection for the pure premium.
Speaker: Mr. Petr Zorin (M.Sc.)
Date: Tuesday, August 23, 2011
Time: 11:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: The Discrete Spectra of Dirac Operators
Abstract: A single particle is bound by an attractive central potential and obeys the Dirac equation in d dimensions. The Coulomb potential is one of the few examples for which exact analytical solutions are available. A geometrical approach called 'the potential envelope method' is used to study the discrete spectra generated by potentials V(r) that are smooth transformations V(r) = g(1/r) of the soluble Coulomb potential. When g has definite convexity, the method leads to energy bounds. This is possible because of the recent comparison theorems for the Dirac equation. The results are applied to study softcore Coulomb potentials used as models for confined atoms. The estimates are compared with accurate eigen values found by numerical methods.
Speaker: Ms. Anne Mackay (M.Sc.)
Date: Monday, August 22, 2011
Time: 1:00 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Pricing and Hedging EquityLinked Products Under Stochastic Volatility Models
Abstract: Equityindexed annuities (EIAs) are becoming increasingly interesting for investors as market volatility increases. Simultaneously, they represent a higher risk for insurers, which amplifies the need for hedging strategies that perform well when index returns present unexpected changes in their volatility. In this thesis, we introduce hedging strategies that aim at reducing the risk of the financial guarantees embedded in EIAs.
We first derive closedform expressions for the price and the Greeks of a pointtopoint EIA under the Heston model, which assumes stochastic volatility. To do so, we rely on the similarity between the payoff of a European call option and that of the EIA. We use the Greeks to develop dynamic hedging strategies that aim at reducing equity and volatility risk. Using Monte Carlo simulations to derive the distribution of the resulting hedging errors, we compare the performance of hedging strategies that use the Greeks derived under the Heston model to other strategies based on Greeks developed under BlackScholes.
We show that, when the market is Hestonian, the performance of hedging strategies developed in a BlackScholes framework are significantly affected by the calibration of the model and the volatility risk premium. We further show that the performance of a simple delta hedging strategy using Heston Greeks is also reduced by the presence of a volatility risk premium, and that this performance can be improved by incorporating gamma or vega hedging to the strategy. We conclude by recommending the use of a deltavega hedging strategy to reduce model calibration and volatility risk.
Speaker: Ms. Mengjue Tang (M.Sc.)
Date: Tuesday, July 26, 2011
Time: 10:30 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: A Comparison of Two Nonparametric Density Estimators in the Context of Actuarial Loss Model
Abstract: In this thesis, I will introduce two estimation methods for estimating loss function in actuarial science. Both of them are related to nonparametric density estimation (kernel smoothing). One is deriving from kernel smoothing which is called semiparametric transformation kernel smoothing while another one derives from Hille's lemma and perturbation idea which is quite similar to kernel smoothing. As the increasing frequently used of nonparametric density estimation in many areas, actuaries are more likely to use this kind of simple method when doing decisionmaking. There are now existing many nonparametric density estimation methods, but which one is better? In order to compare the two methods which are introduced in this thesis, I conduct simulation study on both of them and try to find out which one is preferable and easier to apply. Also the second method which derives from Hille's lemma gives us a new idea about how to estimate loss function when we are doing decisionmaking in actuarial science.
Speaker: Mr. Ramin Okhrati (Ph.D.)
Date: Monday, July 25, 2011
Time: 10:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Credit Risk Modeling under Jump Processes and under a Risk MeasureBased Approach
Abstract: (Click here to view)
Speaker: Ms. Li Ma (Ph.D.)
Date: Monday, June 27, 2011
Time: 2:00 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Generalized FeynmanKac Transformation and Fukushima's Decomposition for Nearly Symmetric Markov Processes
Abstract: (Click here to view)
Speaker: Ms. Yasmine Raad (M.Sc.)
Date: Wednesday, June 22, 2011
Time: 10:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Comparison theorems for the principal eigenvalue of the Laplacian
Abstract: We study the Faber  Krahn inequality for the Dirichlet eigenvalue problem of the Laplacian, first in $\mathbb{R}^N$, then on a compact smooth Riemannian manifold $M$. For the latter, we consider two cases. In the first case, the compact manifold has a lower bound on the Ricci curvature, in the second, the integral of the reciprocal of an isoperimetric estimator function of the Riemannian manifold is convergent. In all cases, we show that the first eigenvalue of a domain in $\mathbb{R}^N$, respectively $M$, is minimal for the ball of the same volume, respectively, for a geodesic ball of the same relative volume in an appropriate manifold $M^\ast$. While working with the isoperimetric estimator, the manifold $M^\ast$ need not have constant sectional curvature. In $\mathbb{R}^N$, we also consider the Neumann eigenvalue problem and present the Szeg\"o  Weinberger inequality. In this case, the principal eigenvalue of the ball is maximal among all principal eigenvalues of domains with same volume.
Speaker: Mr. Alexandre Laurin (M.Sc.)
Date: Friday, April 1, 2011
Time: 1:30 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: On Duncan's characterization of McKay's monstrous E_8
Abstract: McKay's Monstrous $E_8$ observation has provided further evidence, along with the evidence provided by the study of Monstrous Moonshine, that the Monster is intimately linked with a wide spectrum of other mathematical objects and, one might even say, with the natural organization of the universe. Although these links have been observed and facts about them proved, we have yet to understand exactly where and how they originate. We here review a set of conditions, due to Duncan, imposed on arithmetic subgroups of $PSL2(R)$ that return McKay's Monstrous $E_8$ diagram. The purpose is to compare these with Conway, McKay and Sebbar's (CMS) conditions that return the complete set of Monstrous Moonshine groups in order to gain some insight on their meaning. By way of doing this review of Duncan's conditions, we will also review and elaborate on Conway's method for understanding groups like $\Gamma_0(N)$.
Speaker: Mr. Jun Li (Ph.D.)
Date: Monday, November 29, 2010
Time: 1:30 p.m.
Room: H 762 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)
Title: Some Contributions to Nonparametric Estimation of Density and Related Functionals for Biased Data
Abstract: Length biased sampling as a special case of biased sampling occurs naturally in many statistical applications. One aspect regarding length biased data in which people are interested is estimating the underlying true density with the observed samples. Since most length biased data are nonnegative, the true density has a support with a nonnegative finite end point. The current proposed kernel density estimators with symmetric kernels may have large bias at the lower boundary. In this thesis, we propose some new smooth density estimators with weights generating from Poisson distribution or nonnegative asymmetric kernels for length biased data to take care of the edge effect. Besides density estimators, we also consider smooth estimators of distribution function and functions related to distribution and density function, such as hazard function and mean residual life function. Our methods are easily to extend to the general biased data as well.
Speaker: Ms. Di Xu (M.Sc.)
Date: Friday, November 26, 2010
Time: 10:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: The Range Time for Jump Diffusion with TwoSided Exponential Jumps
Abstract: The range time for a stochastic process is the stopping time when the difference between its running maximum and running minimum first exceeds a certain level. It has been studied by several authors for random walks and diffusion processes. In this presentation we consider a jump diffusion process with twosided exponential jumps. By a martingale approach, we first solve the twosided exit problem for this jump diffusion process. Using solutions to the exit problem, we then obtain several results concerning the range time related to joint distributions for the jump diffusion.
Speaker: Ms. Janine Bachrachas (M.Sc.)
Date: Monday, November 22, 2010
Time: 1:30 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: On the Mean Curvature Flow
Abstract: We present a selfcontained expository review on the mean curvature flow for smooth embedded hypersurfaces in the (n+1)dimensional Euclidean space. We start by addressing the short time existence of solutions to the flow, followed by the long time existence in the case of compact convex hypersurfaces and entire graphs. Although the results presented here are part of the classical literature originated in the 80’s, we derive all necessary calculations and gather the simplest possible approach in view of later developments of the area.
Speaker: Ms. Yafang Wang (Ph.D.)
Date: Friday, October 29, 2010
Time: 3:30 p .m.
Room: LB 9214 (Concordia University, Hall Building, 1400 de Maisonneuve Blvd. W.)
Title: The Distribution of the Discounted Compound PHRenewal Process
Abstract: The family of phasetype (PH) distributions has many useful properties such as closure under convolution and mixtures, as well as rational Laplace transforms. PH distributions are widely used in applications of stochastic models such as in queuing systems, biostatics and engineering. They are also applied to insurance risk, such as in ruin theory. In this thesis, we extend the work of Wang (2007), that discussed the moment generating function (mgf) of discounted compound sums with PH interarrival times under a nonzero net interest rate. Here we focus on the distribution of the discounted compound sums. This represents a generalization of the classical risk model for which the net interest rate is zero. A differential equation system is derived for the mgf of a discounted compound sum with PH interarrival times and any claim severity if its mgf exists. For some PH interarrival times, we can further simplify this differential equation system. If the matrix is order of 2, an ordinary differential equation is developed for PH interarrival times. By inverting the corresponding Laplace transforms, the density functions and cumulative distribution functions are also obtained. In addition, the series and transformation methods for solving differential equations are discussed, when the mean of interarrival times is small. Applications such as stoploss premiums, and risk measures such as VaR and CTE are investigated. These are compared for different interarrival times. Some numerical examples are given to illustrate the results. Finally asymptotic results have been discussed, when the mean interarrival time goes to zero. We obtain normality to approximate compound renewal processes. The asymptotic normal distribution is also derived for the discounted compound renewal sum at a fixed time.
Speaker: Mr. Xinghua Zhou (M.Sc.)
Date: Thursday, September 2, 2010
Time: 10:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Stochastic Flow and FBSDE Approaches to Quadratic Term Structure Models
Abstract: We study the stochastic flow method and ForwardBackward Stochastic Differential Equation (FBSDE) approach to Quadratic Term Structure Models (QTSMs). Applying the stochastic flow approach, we get a closed form solution for the zerocoupon bond price under a onedimensional QTSM. However, in the higher dimensional cases, the stochastic flow approach is difficult to implement. Therefore, we solve the ndimensional QTSMs by implementing the FBSDE approach, which shows that the zerocoupon bond price under QTSM provided some Riccati type equations have global solutions.
Speaker: Ms. Wenxia Li (M.Sc.)
Date: Friday, August 27, 2010
Time: 10:30 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Optimal Surrender and Asset Allocation Strategies for EquityIndexed Insurance Investors
Abstract: Equityindexed annuity (EIA) products is getting more and more popular since first introduced in 1995. An EIA investor may consider surrendering the contract before maturity and invest in the stock index in order to earn the full stock growth. We consider an EIA policyholder who seeks the optimal surrender strategy and asset allocation strategy after surrender in order to maximize his expected discounted utility at the maturity of the contract or his time of death, whichever comes first. The optimal value functions satisfy HamiltonJacobiBellman equations from which the optimal strategies are derived.
Speaker: Mr. Ferenc Balogh (Ph.D.)
Date: Tuesday, July 20, 2010
Time: 11:00 a.m.
Room: H 443 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)
Title: Orthogonal Polynomials, Equilibrium Measures and Quadrature Domains Associated with Random Matrix Models
Abstract: Motivated by asymptotic questions related to the spectral theory of complex random matrices, this work focuses on the asymptotic analysis of orthogonal polynomials with respect to quasiharmonic potentials in the complex plane. The ultimate goal is to develop new techniques to obtain strong asymptotics (asymptotic expansions valid uniformly on compact
subsets) for planar orthogonal polynomials and use these results to understand the limiting behavior of spectral statistics of matrix models as their size goes to infinity. For orthogonal polynomials on the real line the powerful RiemannHilbert approach is the main analytic tool to derive asymptotics for the eigenvalue correlations in Hermitian matrix models. As yet, no such method is available to obtain asymptotic information about planar orthogonal polynomials, but some steps in this direction have been taken. The results of this thesis concern the connection between the asymptotic behavior of orthogonal polynomials and the corresponding equilibrium measure. It is conjectured that this connection is established via a quadrature identity: under certain conditions the weakstar limit of the normalized zero counting measure of the orthogonal polynomials is a quadrature measure for the support of the equilibrium measure of the corresponding twodimensional electrostatic variational problem of the underlying potential. Several results are presented on equilibrium measures, quadrature domains, orthogonal polynomials and their relation to matrix models. In particular, complete strong asymptotics are obtained for the simplest nontrivial quasiharmonic potential by a contour integral reduction method and the RiemannHilbert approach, which confirms the above conjecture for this special case.
Speaker: Mr. Farhat Abohalfya (Ph.D.)
Date: Tuesday, May 11, 2010
Time: 1:00 p.m.
Room: H 443 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)
Title: On RGspaces and the Space of Prime dideals in C(X)
Abstract: Let A be a commutative semiprime ring with identity. Then A has at least two epimorphic regular extensions namely, the universal epimorphic regular extension T(A), and the epimorphic hull H(A). We are mainly interested in the case of C(X), the ring of realvalued continuous functions defined on a Tychonoff space X. It is a commutative semiprime ring with identity and it has another important epimorphic regular extension namely, the minimal regular extension G(X). In our study we show in chapter 5 that the spectrum of the ring H(A) with the spectral topology is homeomorphic to the space of the prime ξideals in A with the patch topology. In the case of C(X), the spectrum of the epimorphic hull H(X) with the spectral topology is homeomorphic to the space of prime dideals in C(X) with the patch topology.
A Tychonoff space X which satisfies the property that G(X) = C(Xδ) is called an RGspace. We shall introduce a new class of topological spaces namely the class of almost kBaire spaces, and as a special case of this class we shall have the class of almost Baire spaces. We show that every RGspace is an almost Baire space but it need not be a Baire space. However, in the case of RGspaces of countable pseudocharacter, RGspaces have to be Baire spaces. Furthermore, in this case every dense set in RGspaces has a dense interior.
The Krull zdimension and the Krull ddimension will play an important role to determine which of the extensions H(X) and G(X) has the form of a ring of realvalued continuous functions on some topological space. In [31] the authors gave some techniques to prove that there is no RGspace with infinite Krull zdimension, but there was an error that we found in the proof of theorem 3.4. In this study, we will give an accurate proof which applies to many spaces but the general theorem will remain open. And we will use the same techniques to prove that if C(X) has an infinite chain of prime dideals then H(X) cannot be isomorphic to a ring of realvalued continuous functions.
Speaker: Ms. Noushin Sabetghadam Haghighi (Ph.D.)
Date: Thursday, April 8, 2010
Time: 3:00 p.m.
Room: LB 649 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: On Larcher Subgroups and Fourier Coefficients of Modular Forms
Abstract: This work consists of two parts, both revolving around Monstrous moonshine. First we compute the signature of Generalized Larcher subgroups. These subgroups were first introduced by Larcher to prove his result about the cusp widths of any congruence subgroup. They also played a significant role in the classification of torsionfree low genus congruence subgroups. In the second part, we establish universal recurrence formulae satisfied by the Fourier coefficients of meromorphic modular forms on moonshinetype subgroups.
Speaker: Ms. Huan Yi Li (M.Sc.)
Date: Wednesday, April 7 , 2010
Time: 10:30 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Analyzing EquityIndexed Annuities Using LeeCarter Stochastic Mortality Model
Abstract: Equityindexed annuity (EIA) insurance products have become more and more popular since being introduced in 1995. Some of the most important characteristics of these products are that they allow the policyholders to benefit from the equity market’s potential growth and ensure that the principals can grow with a minimum guaranteed interest rate. In this thesis, we show how to derive the closedform pricing formula of a pointtopoint (PTP) financial guarantee, using the BlackScholes framework. Furthermore, the PTP equityindexed annuity is discussed in details as well. We will show how to construct the replicating portfolio for both the PTP financial guarantee and the PTP equityindexed annuity. Because in the real financial market, companies cannot trade continuously, which violates the assumptions of the completemarket, the replicating portfolio will generate hedging errors. The distributions of the present values hedging errors for both the financial guarantee and EIA will be shown. In addition, the distribution of the present values of hedging errors will be showed. We will talk about the impacts on the hedging errors caused by the stochastic mortality rates in the end of the thesis.
Speaker: Mr. Colin Grabowski (M.Sc.)
Date: Wednesday, March 31 , 2010
Time: 11:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Local Torsion on Elliptic Curves
Abstract: Let E be an elliptic curve over Q. Let p be a prime of good reduction for E. We say that p is a local torsion prime if E has ptorsion over Qp, and more generally, we say that p is a local torsion prime of degree d if E has ptorsion over an extension of degree d of Qp.
We study in this thesis local torsion primes by presenting numerical evidence, and by computing estimates for the number of local torsion primes on aver age over all elliptic curves over Q.
Speaker: Mr. Amir Reza RajiKermany (Ph.D.)
Date: Thursday, February 4, 2010
Time: 10:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Mathematical Models for Interactions Among Evolutionary Forces in Finite and Infinite Populations
Abstract: Mathematical modeling in population genetics plays an important role in understanding the effects of different evolutionary forces on the evolution of populations. The complexity of these models increases as we include more factors affecting the genetic composition of the population under consideration. In this thesis, we focus on interactions among evolutionary forces in finite and infinite populations. In the first part of the thesis we study the effect of migration between two populations of equal sizes with mutations occurring between two alleles at the locus under study.
Stochastic changes in the frequencies of one of the alleles in the population is described by a twodimensional diffusion process. The stationary distribution of this process is characterized by identifying the joint moments under the stationary measure. The second part of this thesis is devoted to studying the effect of recombination on the distribution of types in an infinite haploid population with selection and mutation. In particular, we study the frequency of an allele promoting recombination in such a population. The dynamics of this system are studied in a deterministic framework where the distribution of types is described by a system of ordinary differential equations. We provide numerical solutions to this system. Our results suggest that even if there is no epistatic interaction among loci under selection, an increased rate of deleterious mutations provides a sufficient condition for recombination to be favored in the population.
Speaker: Mr. Zhaoyang Wu (M.Sc.)
Date: Monday, January 25, 2010
Time: 11:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Predicting Stock Index Based on Grey Theory, Arima Model and Wavelet Methods
Abstract: In this thesis, we develop a new forecasting method by merging traditional statistical methods with innovational nonstatistical theories for the purpose of improving prediction accuracy of stock time series. The method is based on a novel hybrid model which combines the grey model, the ARIMA model and wavelet methods. First of all, we improve the traditional GM (1, 1) model to the GM (1, 1, u, v) model by introducing two parameters: the grey coefficient u and the grey dimension degree v. Then we revise the normal GARMA model by merging the ARMA model with the GM (1, 1, u, v) model. In order to overcome the drawback of directly modeling original stock time series, we introduce wavelet methods into the revisedARMA model and name this new hybrid model WGARMA model. Finally, we obtain the WPGARMA model by replacing the wavelet transform with the wavelet packets decomposition. To keep consistency, all the proposed models are merged into a single model by estimating parameters simultaneously based on the total absolute error (TAE) criterion. To verify prediction performance of the models, we present case studies for the models based on the leading Canadian stock index: S&P/TSX Composite Index on the daily bases. The experimental results give the rank of predictive ability in terms of the TAE, MPAE and DIR metrics as following :WPGARMA,WGARMA,GARMA,GM(1,1,u,v),ARIMA.
Speaker: Mr. Radu Gaba (Ph.D.)
Date: Tuesday, September 15, 2009
Time: 11:00 a.m.
Room: H 769 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)
Title: On Fontaine Sheaves
Abstract: In this thesis we focus our research on constructing two new types of Fontaine sheaves, Armax and Amax in the third chapter and the fourth one respectively and in proving some of their main properties, most important the localization over small affines. This pair of new sheaves plays a crucial role in generalizing a comparison isomorphism theorem of Faltings for the ramified case. In the first chapter we introduce the concept of padic Galois representation and provide and analyze some examples. The second chapter is an overview of the Fontaine Theory. We define the concept of semilinear representation and study the period rings introduced by Fontaine while understanding their importance in classifying the padic Galois representations.
Speaker: Ms. Klara Kelecsenyi (Ph.D.)
Date: Thursday, September 3, 2009
Time: 2:00 p.m.
Room: H 760 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)
Title: Popularization of Mathematics as Intercultural Communication – An Exploratory Study
Abstract: Popularization of mathematics seems to have gained importance in the past decades. Besides the increasing number of popular books and lectures, there are national and international initiatives, usually supported by mathematical societies, to popularize mathematics. Despite this apparent attention towards it, studying popularization has not become an object of research; little is known about how popularizers choose the mathematical content of popularization, what means they use to communicate it, and how their audiences interpret popularized mathematics. This thesis presents a framework for studying popularization of mathematics and intends to investigate various questions related to the phenomenon, such as:
 What are the institutional characteristics of popularization?
 What are the characteristics of the mathematical content chosen to be popularized?
 What are the means used by popularizers to communicate mathematical ideas?
 Who are popularizers and what do they think about popularization?
 Who are audience members of a popularization event?
 How audience members interpret popularization?
The thesis presents methodological challenges of studying popularization and suggests some ideas on the methods that might be appropriate for further studies. Thus it intends to offer a first step for developing suitable means for studying popularization of mathematics.
Speaker: Mr. Jeremy Porter (M.Sc.)
Date: Thursday, September 3, 2009
Time: 11:00 a.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: On a Conjecture for the Distributions of Primes Associated with Elliptic Curves
Abstract: For an elliptic curve E and fixed integer r, Lang and Trotter have conjectured an asymptotic estimate for the number of primes p bounded by x such that the trace of Frobenius equals r. Using similar heuristic reasoning, Koblitz has conjectuerd an asymptotic estimate for the number of primes p bounded by x such that the order of the group of points of E over the finite field of prime characteristic p is also prime. These estimates have been proven correct for elliptic curves “on average”; however, beyond this the conjectures both remain open.
In this thesis, we combine the condition of Lang and Trotter with that of Koblitz to conjecture an asymptotic for the number of primes p bounded by x such that both the order of the group of points of E over the finite field of characteristic p is prime, and the trace of Frobenius equals r. In the case where E is a Serre curve, we will give an explicit construction for the estimate. As support for the conjecture, we will also provide several examples of Serre curves for which we computed the number of primes p bounded by large x such that the order of the group of points of E over the finite field of characteristic p is prime and the trace of Frobenius equals r, and compared this count with the conjectured estimates.
Speaker: Ms. Valerie Hudon (Ph.D.)
Date: Friday, August 28, 2009
Time: 10:30 a.m.
Room: AD 324 (Concordia University, Administration Building, 7141 Sherbrooke Street W.)
Title: Study of the Coadjoint Orbits of the Pointcare Group in 2 + 1 Dimensions and Theiry Coherent States
Abstract: The first main objective of this thesis is to study the orbit structure of the (2+1)Poincaré group (the symmetry group of relativity in two space and one time dimensions) by obtaining an explicit expression for the coadjoint action. From there, we compute and classify the coadjoint orbits. We obtain a degenerate orbit, the upper and lower sheet of the twosheet hyperboloid, the upper and lower cone and the onesheet hyperboloid. They appear as twodimensional coadjoint orbits and, with their cotangent planes, as fourdimensional coadjoint orbits. We also confirm a link between the fourdimensional coadjoint orbits and the orbits of the action of SO(2,1) on the dual of R^(2,1).
The second main objective of this thesis is to use the information obtained about the structure to induce a representation and build the coherent states on two of the coadjoint orbits, namely the upper sheet of the twosheet hyperboloid and the upper cone. We obtain coherent states on the hyperboloid for the principal section. The Galilean and the affine sections only allow us to get frames. On the cone, we obtain a family of coherent states for a generalized principal section and a frame for the basic section.
Speaker: Mr. Baohua He (M.Sc.)
Date: Friday, August 21, 2009
Time: 2:00 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Smoothing Parameter Selection for a New Regression Estimator for NonNegative Data
Abstract: In this thesis, crossvalidation based smoothing parameter election technique is applied to Chaubey, Laib and Sen’s (2008) estimator, which is a new regression estimation for nonnegative random variables. The estimator is based on a generalization of Hille's lemma and a perturbation idea. A second order expansion for mean squared error (MSE) of the estimator is derived and the theoretical optimal values of the smoothing parameters are discussed and calculated. Simulation results and graphical illustrations on the new estimator comparing with Fan's (1992, 2003) local linear regression estimators are provided.
Speaker: Ms. Tamanna Howlader (Ph.D.)
Date: Friday, June 19, 2009
Time: 1:30 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: WaveletBased Noise Reduction of CDNA Microarray Images
Abstract: Microarray experiments have greatly advanced our understanding of how genes function by enabling us to examine the activity of thousands of genes simultaneously. In cDNA microarray experiments, information regarding gene activity is extracted from a pair of red and green channel images. These images are often of poor quality since they are corrupted with noise arising from different sources, including the imaging system itself. Inferences based on noisy microarray images can be highly misleading. Many noise reduction algorithms have been proposed for natural images. Among these various methods, those that have been developed in the wavelet transform domain are found to be most successful. Unfortunately, the existing waveletbased methods are not very efficient for reducing noise in cDNA microarray images because they are only capable of processing the red and green channel images separately. In doing so, they ignore the correlation that exists between the wavelet coefficients of the images in the two channels. This thesis deals with the problem of developing novel waveletbased methods for reducing noise in cDNA microarray images for the purpose of obtaining accurate information regarding gene activity. Two types of wavelet transforms have been used. The proposed methods use joint statistical models that take into account the interchannel dependencies for estimation of the noisefree images of the two channels. The performance of the proposed methods is compared with that of other methods through extensive experimentations which are carried out on a large set of microarray images. Results show that the new methods lead to improved noise reduction performance and more accurate estimation of the level of gene activity. Thus, it is expected that these methods will play a significant role in improving the reliability of results obtained from real microarray images.
Speaker: Ms. Yuliya Klochko (Ph.D.)
Date: Monday, May 4, 2009
Time: 9:30 a.m.
Room: LB 646 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Genus One Polyhedral Surfaces, Spaces of Quadratic Differentials On Tori and Determinants of Laplacians
Abstract: This thesis presents a formula for the determinant of the Laplacian on an arbitrary compact polyhedral surface of genus one. The formula generalizes the wellknown RaySinger result for a flat torus. A special case of flat conical metrics given by the modulus of a meromorphic quadratic differential on an elliptic curve is also considered. We study the determinant of the Laplacian as a functional on the moduli space of meromorphic quadratic differentials with L simple poles and L simple zeroes and derive formulas form variations of this functional with respect to natural coordinates on this space. We also give a new proof of Troyanov's theorem stating the existence of a conformal flat conical metric on a compact Riemann surface of arbitrary genus with a prescribed divisor of conical points.
Speaker: Ms. Olga Veres (Ph.D.)
Date: Wednesday, April 8, 2009
Time: 12:15 p.m.
Room: H 771 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)
Title: On the Complexity of Polynomial Factorization Over Padic Fields
Abstract: Let p be a rational prime and Φ (x) be a monic irreducible polynomial in Zp[x]. Based on the work of Ore on Newton polygons (Ore, 1928) and MacLane's characterization of polynomial valuations (MacLane, 1936), Montes described an algorithm for the decomposition of the ideal pOK over an algebraic number field (Montes, 1999). We give a simplified version of the Montes algorithm with a full Maple implementation which tests the irreducibility of Φ (x) over Qp. We derive an estimate of the complexity of this simplified algorithm in the worst case, when Φ (x) is irreducible over Qp. We show that in this case the algorithm terminates in at most O((deg Φ)^3+epsilon v_p(disc Φ)^2+\epsilon) bit operations. Lastly, we compare the "oneelement" and "twoelement" variations of the Zassenhaus "Round Four" algorithm with the Montes algorithm.
Speaker: Ms. Nadia Hardy (Ph.D.)
Date: Friday, April 3, 2009
Time: 2:30 p.m.
Room: LB 9214 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)
Title: Students’ Models of the Knowledge to be Learned About Limits in College Level Calculus Courses. The Influence of Routine Tasks and the Role Played By Institutional Norms
Abstract: This thesis presents a study of instructors' and students' perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I have analyzed these perceptions from an anthropological perspective combining elements of the Anthropological Theory of Didactics, developed in mathematics education, with a framework for the study of institutions  the Institutional Analysis and Development framework  developed in political science. The analysis of these perceptions is based on empirical data: final examinations from the past six years (20012007), used in the studied College institution, and specially designed interviews with 28 students. While a model of the instructors' perceptions could be formulated mostly in mathematical terms,
a model of the students' perceptions had to include an eclectic mixture of mathematical, social, cognitive and didactic norms. The analysis that I carry out shows that these students' perceptions have their source in the institutional emphasis on routine tasks and on the norms that regulate the institutional practices. Finally, I describe students' thinking about various tasks on limits from the perspective of Vygotsky's theory of concept development. Based on the 28 interviews that I have carried out, I will discuss the role of institutional practices on students' conceptual development.