Logic Seminar

Jenna ZombackUniversity of Illinois, Urbana-Champaign
A backward ergodic theorem and its forward implications (part 2)

Friday, October 16, 2020 - 3:00pm
Zoom meeting 931 1107 7941

In this two-part talk, we discuss and prove a backward (inverse) ergodic theorem for countable-to-one probability measure preserving (pmp) Borel transformations. We discuss various examples of such transformations, including the shift map on Markov chains, which yields a new (forward) pointwise ergodic theorem for pmp actions of finitely generated countable groups, as well as one for the (non-pmp) actions of free groups on their boundary. In part two of the talk, we state the backward ergodic theorem and derive from it the ergodic theorem for pmp actions of f.g. countable groups. We will then discuss some ingredients that go into the proof of the backward ergodic theorem. This is joint work with Anush Tserunyan.