Geometric Analysis and Topology Seminar

---

Minimal submanifolds, higher expanders, and waists of locally symmetric spaces

Speaker: Ben Lowe, University of Chicago

Location: Warren Weaver Hall 512

Date: Friday, February 7, 2025, 11 a.m.

Synopsis:

Gromov initiated a program to prove statements of the following form: Suppose we are given two simplicial complexes X and Y, where X is “complicated” and Y is lower dimensional. Then any map f: X-> Y must have at least one "complicated” fiber.  In this talk I will describe various results of this kind for compact locally symmetric spaces, that are proved by bringing new tools into the picture from minimal surface theory and representation theory. Much of the talk will be focused on octonionic hyperbolic manifolds, the case where our approach seems to work best. If time permits I will also discuss some applications to systolic geometry, global fixed point statements for actions of higher rank lattices on contractible CAT(0) simplicial complexes, and/or non-abelian higher expansion and branched cover stability.  Based on joint work with Mikolaj Fraczyk.