This will be a reading project about a topic in representation theory determined by mutual interest. Possible topics include classical subjects such as representations of finite groups, semisimple Lie algebras, or quivers, or investigating more recent papers in the area depending on background. Prerequisite MATH2322.

A complex algebraic/analytic singularity is an amazingly intricate object from the point of view of topology. For example, intersecting a plane curve singularity with a unit sphere yields a knot that encodes important invariants of the singularity.

We will consider numerical methods to model tsunamis, flooding and debris flow.

White dwarfs are at the center of some of the most spectacular cataclysms in our Galaxy.

Seismic waves emanating from geophysical events propagate over hundreds to thousands of kilometers interacting with tectonic forces, geological structure, complicated topography and earthquake source processes on scales down to millimeters.

A notion of generalized solution for nonlinear partial differential equations, called viscosity solution has undergone considerable development in recent years.

The idea of this project would be to try to relate the outgoing wave emanating from the corner to properties of the incoming wave and and the link (ie circular cross-section) of the corner.

Wave packets in harmonic analysis

The idea of wavelets is to introduce useful bases for the Hilbert space. Useful means useful for harmonic analysis or PDE.

Well-posed and stable boundary conditions for bedload transport equation (the 2D Exner Equation)