Operator algebras seminar
Sven Raum (Stockholm University)
: From Poisson boundaries to proximal boundaries
AbstractIn the first part of my talk I will explain results in group theory published in 2019 by Frisch-Tamuz-Vahidi Ferdowsi and Frisch-Hartman-Tamuz-Vahidi Ferdowsi, respectively. The first result says that a countable discrete group is icc (infinite conjugacy classes) if and only if it admits a faithful proximal boundary. This result yielded a characterisation of groups that are strongly amenable in Glasner's sense. The second result says that a countable discrete group is icc if and only if it admits a faithful Poisson boundary. This result yielded a characterisation of so-called Choquet-Deny groups. In the second part of my talk, I will explain how to construct a faithful proximal boundary of a countable discrete group, given the existence of a faithful Poisson boundary. This provides a new and technically simpler proof for Frisch-Tamuz-Vahidi Ferdowsi's result on proximal boundaries.
*This is joint work with Matthew Kennedy and Guy Salomon