Explore diverse mathematical research projects at ANU's Mathematical Sciences Institute. Engage in areas like algebra, geometry, computational mathematics, and astrophysics, addressing complex real-world challenges. Contact your supervisor for further discussion and ideas.
Displaying 31 - 45 of 65 project(s).
The aim of the project is to learn about equivariant stable homotopy theory, and go through as much of the Hill, Hopkins and Ravenel proof as possible.
Magnetic equilibrium and particle orbit modelling of the OpenStar Dipole
Open for Honours, Masters, MPhil, PhD, Summer scholar students
The LASSO and penalized likelihood methods have become an extremely hot topic in statistics over the past decade, as they offer a computationally efficient method of variable selection particularly in high dimensional situations.
operator theoretic aspects of quantum field theory
computational problems in vector-valued modular forms
tensor categories and functorial conformal field theories
Open for Honours, Masters, PhD, Summer scholar students
Population genetics deals with the evolution of genomes as a result of the drift of point mutations throughout a population over long timescales.
A model category is a category with some extra structure which makes it possible to do homotopy theory.
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.
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 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.
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.
Open for Honours, Masters, PhD, Summer scholar students
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.
Open for Bachelor, Honours, Masters, PhD students
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.
Open for Bachelor, Honours, Masters, Summer scholar students
