Colloquium: Tuesday, January 28, 2020. Speaker: Yair Hartman (BGU). Title: “Which groups have bounded harmonic functions?”.
Place: Room 614 in the Education & Sciences Building
Bounded harmonic functions on groups are closely related to random walks on groups. It has long been known that all virtually nilpotent groups are “Choquet-Deny groups”: these groups cannot support non-trivial bounded harmonic functions. Equivalently, their Furstenberg-Poisson boundary is trivial, for any random walk. I will present a recent result where we complete the classification of discrete countable Choquet-Deny groups, proving a conjecture of Kaimanovich-Vershik. We show that any finitely generated group which is not virtually nilpotent, is not Choquet-Deny. Surprisingly, the key here is not the growth rate, but rather the algebraic infinite conjugacy class property (ICC). This is joint work with Joshua Frisch, Omer Tamuz and Pooya Vahidi Ferdowsi.
Tea will be served before the talk (at 13:50).