Aranka Hru拧kov谩 (Weizmann Institute of Science)
Title: Asymptotically commuting measures share the Furstenberg-Poisson boundary
Abstract: In classical harmonic analysis, Poisson and Dirichlet studied what form do harmonic functions on the unit ball of R^d take. The 20th century reworked this question in the setting of groups. Furstenberg showed that for every (locally compact second countable) topological group G and a Borel probability measure \mu on G, there is a measure space (B,\nu), called the Poisson boundary -- in analogy to the boundary of the unit ball --, which gives a natural representation for all \mu-harmonic functions on G. I will review and explain the foundational results and then talk about joint work with Yair Hartman and Omer Segev in which we give conditions for probability measures \mu_1 and \mu_2 to share the Poisson boundary.
We will gather for teatime in the lounge after the talk and then we will go for dinner with Aranka.