Monday, November 28, 2022
11/28/2022 - 3:00pm
Abstract: We will review the state of the art in fast algorithms for the solution of the heat equation in moving geometries, using integral equation methods. Such methods achieve optimal complexity and, in the homogeneous case, require the discretization of the space-time boundary alone. They achieve high order accuracy with suitable quadratures and are straightforward to implement adaptively in space-time. This set of tools has direct application to biophysical modeling, reaction-diffusion systems, and computational fluid dynamics.
11/28/2022 - 4:00pm
Approximate lattices in locally compact groups are approximate subgroups that are discrete and have finite co-volume. They provide natural examples of objects at the intersection of the theory of discrete subgroups of Lie groups, ergodic theory and additive combinatorics.
A central question arising from seminal work of Yves Meyer asks whether approximate lattices have an arithmetic origin. I will present a complete structure theorem for approximate lattices in linear algebraic groups in terms of bounded cohomology that, in particular, answers this question. I will pinpoint key instances where the interplay between additive combinatorics and other fields - e.g. ergodic theory and algebraic groups - is particularly fruitful.