SCS: Sheehan Olver (Imperial)

Thursday Oct 29, 2026, 10:00 AM → 11:00 AM America/New_York

3rd floor classroom (162)

Title: Numerical Analysis Meets Representation Theory

Abstract: Representation theory tells us the ways symmetry can present itself, and building that information into discretisations of PDEs leads to trivial parallelisation with a substantial decrease in degrees of freedom. We will give a brief introduction to representation theory (for non-experts!), see how numerical linear algebra allows it to be used in a computationally efficient manner, and incorporate it into the construction of symmetry-adapted polynomial bases that enable parallelisation.  Applications include Maxwell’s equation in balls and cylinders and Schrödinger equation with multiple particles, where building in symmetry enables fast sparse spectral methods for PDEs in as many as 10 dimensions.

Bio: Sheehan works on spectral methods involving multivariate orthogonal polynomials with applications to partial and singular differential equations. Recently he has explored building ideas from representation theory into the construction of spectral methods to unlock parallelisation. He previously worked on the numerical solution of Riemann–Hilbert problems for which he was awarded the Adams Prize in 2012.