Florent Baudier: On the coarse rigidity of Roe-type algebras

Data: sexta-feira, 11 de março de 2022, às 9h30.

Formato híbrido: Sala B143 IME. Google meet:  meet.google.com/wmd-srcj-kbc

Florent Baudier (Texas A&M)

Título: On the coarse rigidity of Roe-type algebras

Resumo:  The classical Banach-Stone theorem states that if two spaces of continuous functions on some compact Hausdorff spaces are isometric as Banach spaces, then the topological spaces they are built on must be homeomorphic. Therefore spaces of continuous functions are topologically rigid. In this talk we will discuss a similar problem in the context of coarse geometry for certain $C^*$-algebras that we can associate to metric spaces, namely uniform Roe algebras and some variants of those. These algebras introduced by Roe in the mid 90's are fundamental in noncommutative geometry and appear in certain coarse versions of the Baum-Connes conjecture. We will show how a Lyapunov-type result for vector measures was used to shed some new light on the coarse rigidity problem for Roe-type algebras. This is a joint work with B. de Mendonça Braga, I. Farah, A. Khukhro, A. Vignati, and R. Willett.