Astronomers are often faced with the problem of constructing models for systems which are not fully constrained by observational data.

Morse theory is a branch of differential topology. Equipping a manifold with a generic real-valued function allows one to use differential techniques to study fundamental topological properties of the manifold.

Learn some basic game theory and read some of Nobel prizewinner John Nash's classic papers on the subject.

The efficient solution of the Navier Stokes equation provides many challenges. Of particular interest is the efficient description and implementation of free boundaries.

Non-commutative geometry and its application to physics.

This project would involve learning about the linear and nonlinear heat equations, understanding the literature about blowup, and analysing some interesting examples in detail possibly involving new forms of blow up that have yet been fully described.

The student will read some books or papers at the interface between number theory and algebraic geometry and meet regularly with me to discuss them.

The modelling of high dimensional data sets pose a particular challenge both for approximation and the parallel implementation. In this project we investigate the parallelization of sparse grid methods.

The goal of this project is to compute the particle orbits in a MRxMHD equilibrium with fully 3D field and quantify the impact of the islands and chaos to particle confinement.

The polarised radiative transfer equations consist of four coupled first order differential equations in the four Stokes parameters which describe the radiation field.

Echelle spectroscopy (here Hamilton echelle at the Lick Observatory 3m telescope) of short period evolved binaries is the key to understanding the origin of cataclymic variables.

Proof-calculi for Propositional Non-classical Logics

In this project we rederive and implement a recently published quantum algorithm for the Vlasov-Maxwell system of equations in Q#, a quantum computation platform.

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.