MSc, MA, & PhD defences
Organizer: The Graduate Program Assistant
Upcoming defence
TBA
Past defences
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:  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:  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.