Growth, isoperimetry and resistance in vertex-transitive graphs (Matthew Tointon, Cambridge)

30.10.2018 10:30

A famous result of Varopoulos says that if the simple random walk on an infinite Cayley graph is recurrent then its balls grow sub-cubically.
Combined with Gromov's celebrated polynomial growth theorem, this in turn implies the underlying group has a finite-index subgroup isomorphic to either Z or Z^2. These results generalise to infinite vertex-transitive graphs by work of Trofimov and Saloff-Coste.
In this talk I will discuss an ongoing project with Romain Tessera in which, amongst other things, we provide analogues of these results for finite graphs. Highlights will include a technique to reduce various questions about (not necessarily finite) vertex-transitive graphs to questions about Cayley graphs, and a bound on resistance in finite vertex-transitive electric networks conjectured by Benjamini and Kozma in 2002.

Lieu

Room 623, Séminaire "Groupes et Géométrie"

entrée libre