The project involves comparing different numerical schemes and testing those schemes with real data.

Reading some classics in commutative algebra and algebraic geometry based on the student's interest and level of preparation. Readings can range from introductory to more advanced (intersection theory, toric varieties, birational geometry). Expected background: MATH3345 and beyond.

Recent development of a flowing MHD model for a rotating, collisional plasma column discovered the intriguing prediction of opposite axial acceleration of the plasma ions in the subsonic and supersonic regimes. This project would examine the regime above, below, and through the shock.

Current research topics in representation theory and related areas explored via computer algebra systems.

Dirichlet's theorem on primes in an arithmetic progression, Riemann zeta function, distribution of prime numbers.

For people involved in the Mathematical Modelling and Computation program, research opportunities exist in formulation of fault-tolerant numerical schemes, implementation of fault-tolerant schemes on supercomputers, simulation of hardware failure events on ultrascale supercomputers, and application of these techniques to scientific computing.

Scattering theory is about properties of solutions of the eigenfunction equation, usually closely related to the Laplacian.

Describe the theoretical properties of methods based on machine learning to solve forward, inverse and operator design problems associated with partial differential equations.

Sensitivity analysis is an important tool in evaluating model behaviour and assessing which parameters are significant, as well as the interactions between parameters.

Shaping value of information to real world conditions in water decision making

Spectral sequences in algebraic topology

I am interested in using a multi-parameter study of invariants from algebraic topology to do statistical shape analysis. The goal is to quantitatively compare geometric objects such as a set of bones, tumours, leaves, bird beaks, etc. I have both theory and application projects.

The symmetries of a manifold are described by its mapping class group, and the mapping class group (MCG) of a surface is a particularly important object.

The basic problem is to understand under what conditions it is possible to find a convex surface of prescribed Gauss curvature which also satisfies some boundary conditions.

Symplectic vortice and Hamiltonian Gromov-Witten theory.