Available research projects
Opportunity for collaboration
Faculty members frequently lead research projects that offer students the chance to contribute and gain valuable experience. Project descriptions vary widely, creating a diverse range of opportunities.
Ways to participate
- Are you a faculty member looking to share a research project? Submit details through the Faculty Research Project Proposals form.
- Are you a student looking to explore topic for a project? Complete Student Research Project Proposals form. You will be connected with relevant professors.
Available research projects
Research in Spectral Theory and Geometric Analysis
Professor: Alexey Kokotov
Description: Spectral characteristics of non-orientable Mandelstam diagrams. Asymptotics of determinats of pseudolaplacians. Self-adjoint extensions with interaction of conical points. Spinors on polyhedrons of higher genus.
Geometric explorations of curves of surfaces
Professor: Alina Stancu
Description: Investigations into a special type of curves or surfaces following an introduction into differential or convex geometry.
Mathematical Logic and Set Theory
Professor: Assaf Shani
Description: Some possible directions: foundations of mathematics; the measure problem and Set Theory; classification problems in mathematics and Descriptive Set Theory; Fractal Dimension and Complexity Theory; and, Dynamical Systems and Chaos.
Applications linear algebra in data science
Professor: Fred E. Szabo
Contact for details.
Optimal financial risk management strategies with reinforcement learning
Professor: Frédéric Godin
Contact for details.
Harmonic analysis originated with the study of Fourier series
Professor: Galia Dafni
Description: Harmonic analysis originated with the study of Fourier series and Fourier transforms, but now also includes the study of wavelets, with many applications in signal and image processing. Interesting questions connect harmonic analysis to analysis on metric spaces, fractals, geometric measure theory, graph theory, group theory, number theory and partial differential equations. Duration: Summer research or 1 semester honours project. Summer projects may be funded by an award.
Algebra and Number Theory
Professor: Giovanni Rosso
Description: Galois Theory; p-adic numbers; and, elliptic curves.
Extracting system-level information from data
Professor: Jason Bramburger
Description: How do we understand the dynamics of a system if we only have data from it? Can we predict beyond just what we see in the data? This stream incorporates machine learning and dynamical systems analysis to learn differential equations from data, extrapolate beyond the training set, identify important features of the system, and control the output.
Pattern formation on random networks
Professor: Jason Bramburger
Description: Collective behaviour over networks of interacting agents is ubiquitous. The question is: can we predict patterns of synchronization when we can only describe the network structure probabilistically? This project brings together graph theory, probability and statistics, and dynamical systems to understand how patterns form on random networks.
Determinants in infinite dimensions: Fredholm determinants
Professor: Marco Bertola
Description: Reference: "Trace Ideals and their applications", by Barry Simon.
Prerequisites: linear algebra and functional analysis (464). Duration: 1 semester (scalable).
Orthogonal polynomials and applications
Professor: Marco Bertola
Description: Reference: Orthogonal polynomials and random matrices: a Riemann-Hilbert approach, Deift, P. A. Prerequisite: all 300-level done. Duration: 1 semester
Fuchsian groups and hyperbolic geometry
Professor: Marco Bertola
Description: Reference: (for example) The geometry of Discrete Groups (A. F. Beardon). Duration: 1 semester.
Various topics in Analysis and Partial Differential Equations
Professor: Maria Ntekoume
Description: Such as Fourier analysis and dispersive PDEs, nonlinear shock waves, solitons. Paid position. Duration: 1 semester honours project or summer research.
Assessment of climate change risk on natural catastrophes
Professor: Mélina Mailhot
Description: Measuring and quantifying risk and uncertainty rising from climate change on insurable extreme risks.
Experimental combinatorics
Professor: Nadia Lafrenière
Contact for details.
Genetic programming
Professor: Patrice Gaillardetz
Description: Evaluating equity-linked products using genetic programming. Pricing and hedging financial securities in incomplete markets.
Iterated Function Systems and related fractals
Professor: Pawel Gora
Contact for details.
Commutative algebra
Professor: Robert Raphael
Description: Commutative algebra; the Cohen Seidenberg theorems; the spectrum of a commutative ring; and topics in point set topology.
Nonlinear Optimization and Control Theory
Professor: Ronald Stern
Description: Basic theory of Nonsmooth Analysis with applications to Nonlinear Optimization and Control Theory.
Data Science and Computational Mathematics
Professor: Simone Brugiapaglia
Description: Dr. Brugiapaglia offers to co-supervise honours projects in the areas of data science and computational mathematics. Projects can be theory-oriented (e.g., involving the theoretical analysis of state-of-the-art algorithms), computationally-oriented (e.g., the implementation of new computational methods and numerical tests on synthetic or real-world data), or a mix of both. Specific areas of interest include deep learning, compressed sensing, numerical approximation methods, and their applications. Duration: 1 semester.
Impact of climate change on natural disaster costs
Professor: Yang Lu
Description: Because of the climate change, the frequency of natural disasters might be evolving. This could mean an increasing expected risk, and/or more and more uncertainties. Using sophisticated time series techniques, we try to better predict the trend of natural disasters, and quantify the uncertainty around these predictions. General field interest: statistics, actuarial mathematics, financial mathematics
Impact of climate change on natural disaster costs
Professor: Yogendra P. Chaubey
Description: This is a broad area in density estimation and covers Bernstein polynomial estimators and special attention may be given to circular density through transformation.