# Anush Tserunyan (McGill University)

Date

Friday November 18, 20222:30 pm - 3:30 pm

Location

Jeffery Hall, Room 234## Math & Stats Department Colloquium

**Friday, November 18th, 2022**

**Time:** 2:30 p.m. **Place:** Jeffery Hall, Room 234

**Speaker:** Anush Tserunyan (McGill University)

**Title:** A backward look at pointwise ergodic theorems

**Abstract:** Pointwise ergodic theorems provide a bridge between the global behaviour of the dynamical system and the local combinatorial statistics of the system at a point. Such theorems have been proven in dierent contexts, but typically for actions of (semi)groups on a probability space. Dating back to Birkho (1931), the rst known pointwise ergodic theorem states that for a measure-preserving ergodic (typically many-to-one) transformation T on a probability space, the mean of a function (its global average) is approximated by local averages at almost every point x over the sets fx, Tx, ..., Tnxg, intervals of T-future of x. Almost a century later, we turn Birkho's theorem backward, showing that the averages over trees of possible T-pasts also approximate the global average. This backward theorem for a single transformation surprisingly has applications to actions of free groups, yielding qualitatively new kinds of ergodic theorems for them. This is joint work with Jenna Zomback.

Dr. Tserunyan is an Assistant Professor in the Mathematics and Statistics Department at McGill University, and is a member of the Analysis lab at Centre de Recherches Mathematiques and of the Geometric Group Theory research group at McGill. Before this she was an Assistant Professor at the University of Illinois Urbana-Champaign. Dr. Tserunyan earned her PhD from the University of California Los Angeles under the advisement of Alexander S. Kechris (Caltech) and Itay Neeman (UCLA). She has held NSERC and NSF grants and has been a visiting fellow at the Bernoulli Center in Lausanne, Switzerland and the Institute Mittag-Leer in Djursholm, Sweden. Dr. Tserunyan is an editor for the Mathematical Logic Quaterly and the Archive for Mathematical Logic.

Rooted in logic and descriptive set theory, Tserunyan's research lies in the nexus of ergodic theory, measured group theory, countable Borel equivalence relations, and graph combinatorics.