UBC Math Department Colloquium: Sheehan Olver

In this talk we see how representation theory can be used in numerical methods for partial differential equations (PDEs) and how numerics can give more efficient methods for computational problems in representation theory. In particular, we will see that representation theory tells us the ways symmetry can present itself, and building that information into discretisations of PDEs leads to trivial parallelisation. We will also see that numerical linear algebra can be used to construct a polynomial time algorithm for decomposing representations of the symmetric group. Finally, we discuss potential application of the ideas to Schrödinger equation with multiple particles.