Exact values of exponential Følner functions and the Coulhon Saloff-Coste inequality (Bogdan Stankov, Lyon 1)

23.11.2021 10:30 – 11:30

The Følner function of a group is defined on positive integers as the smallest size of a Følner set, the boundary of which is at most 1/n of its size. Its values are finite if and only if the group is amenable. It can be thought of as encoding "how amenable a group is". The functions obtained on the same group by different generating sets are distinct, but asymptotically equivalent. Numerous results on Følner functions are known, however only up to asymptotic equivalence. In this talk, we will consider fixed generating sets and obtain (to our knowledge) the first results on the exact values of exponential Følner functions. We will present possible applications, in particular to the Coulhon Saloff-Coste inequality - in terms of whether its constants can be improved. The inequality in question provides, as a corollary, a lower bound for the Følner function. In a joint work with Christophe Pittet we obtain, for amenable groups of exponential growth, an explicit expression of the optimal multiplicative constant in the Coulhon and Saloff-Coste inequality. We prove that the optimal value over all groups for that constant is between 1 and 2.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Groupes et géométrie"

entrée libre