Logic Seminar

Anush TserunyanMcGill University
A backward ergodic theorem and its forward implications (part 1)

Friday, October 9, 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 one of the talk, we will give a general overview of the known pointwise ergodic theorems for pmp actions of f.g. groups, culminating in our result. If time permits, we will hint at the main (backward) ergodic theorem for a single transformation that underlies the aforementioned result for group actions. This is joint work with Jenna Zomback.