# Student projects

We have a wide range of potential research topics. They range from short term PhB projects, to year long Honours and graduate projects and three year PhD projects.

Contact your supervisor for further discussion and ideas.

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.

#### Student intake

Open for Honours, Masters, PhD, Summer scholar students

#### Group

#### People

- Matthew Hole, Supervisor

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.

#### Student intake

Open for Bachelor, Honours, Masters, PhD students

#### Group

#### People

- Anand Deopurkar, Supervisor

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.

#### Student intake

Open for Bachelor, Honours, Masters, Summer scholar students

#### Group

#### People

- Matthew Hole, Supervisor