Higher Expansion, Representation Stability and Minimal Submanifolds

Attend this 57-minute conference talk exploring the intersection of higher expansion, representation stability, and minimal submanifolds in geometric topology. Learn about k-expander families of Riemannian manifolds, where k-waists are bounded below by positive multiples of their volume, meaning any map to k-dimensional space has fibers with volume comparable to the ambient space. Discover how Gromov's challenging problem of constructing bounded-geometry examples for k greater than 1 was initially solved through cosystolic expander CW-complexes that satisfy systems of isoperimetric inequalities in mod 2 cohomology. Explore recent developments showing how non-abelian generalizations of cosystolic expansion prove representation stability by demonstrating that approximate homomorphisms between groups are close to true ones. Examine a novel approach to non-abelian higher expansion using minimal submanifolds and the geometry of locally symmetric spaces, based on joint research with Ben Lowe, presented by Mikolaj Fraczyk from Jagiellonian University as part of the ZhengTong Chern-Weil Symposium.