Group actions with spectral gap on surfaces
20.30 SR 2.058
Spectral gap is an important rigidity property for group actions with various applications. One of these applications is the construction of families of expander graphs. I will explain a new class of actions with spectral gap on surfaces of arbitrary genus. These are the first examples of actions with spectral gap on surfaces of genus g > 1. I will also explain some of the surprising large-scale geometric features of the expander families constructed from these actions. This is joint work with Goulnara Arzhantseva, Dawid Kielak, and Damian Sawicki.