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.

Our projects cover computational methods used in biology, chemistry, physics, finance and machine learning. They prepare applied and pure mathematicians for collaborative work with scientists and engineers and for doing a PhD in this area.

The curve shortening flow is a simple and beautiful example of a geometric heat flow, the family of equations which includes the Ricci flow used by Perelman to prove the Poincare conjecture as well as many other interesting examples.

Clifford algebras and Clifford modules; Spin structures and Dirac operators, their geometric properties, and some examples, possibly including Witten's proof of the positive mass theorem.

On a (compact) Riemannian manifold there is a natural differential operator on functions, the Laplacian. The eigenvalues of this operator are important invariants of the manifold, and there are many interesting results which relate the eigenvalues to other geometric quantities...

Higher arithmetic. The failure of unique factorization in generalized number systems. Integer and rational solutions to algebraic equations. Fermat's Last Theorem.

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.