Groups

Ramon van Handel surveys recent progress on constructing graphs, manifolds and groups with optimal spectral gaps, which control how rapidly random walks explore a structure. The talk describes a polynomial method that proves optimality in new settings and connects these developments to longstanding questions about the prevalence of optimal gaps.

Justin Chen introduces groups as collections of actions and explains their relationship to symmetry. The discussion uses accessible examples to show the power of abstraction, then considers the challenges of explaining group theory to non-specialists. Chen also reflects on his experience communicating mathematics and his plans for further study.