Sharp relations between growth and isoperimetry in vertex-transitive graphs, and applications in probability
16th December 2020, 2:30 pm – 3:30 pm
Romain Tessera and I have an ongoing project to study various geometric aspects of vertex-transitive graphs of polynomial growth. In particular, building on work of Breuillard & Green & Tao, Trofimov, and Coulhon & Saloff-Coste, we recently obtained certain sharp isoperimetric inequalities in such graphs. These have in turn led to the resolution of some long-standing probabilistic conjectures (some in joint work with Tessera, some in joint work with Tom Hutchcroft). In this talk I will give a broad overview of the project and some of its applications, and go into detail on some of the underlying group-theoretic techniques.