Oct 26 2020

# Logic Seminar: A backward ergodic theorem and its forward implications, by Jenna Zomback

October 26, 2020

4:00 PM - 4:50 PM

Zoom

Chicago, IL

## Calendar

Jenna Zomback (UIUC): A backward ergodic theorem and its forward implications

A pointwise ergodic theorem for the action of a transformation $T$ on a probability space equates the global property of ergodicity of the transformation to its pointwise combinatorics. Our main result is a backward (in the direction of $T^{-1}$) ergodic theorem for countable-to-one probability measure preserving (pmp) transformations $T$. 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. This is joint work with Anush Tserunyan.

## Contact

Filippo Calderoni

Oct 21, 2020

Oct 21, 2020