# Activities This Week

## Colloquium

### Ergodic theory and symplectic packing

*Jun 13, 14:30—15:30, 2023*,
**Math -101**

#### Speaker

**Misha Verbitsky** (*IMPA*)

#### Abstract

The group of diffeomorphisms acts on the space of symplectic structures on a given manifold. Taking a quotient by isotopies, we obtain the mapping class group action on the Teichmuller space of symplectic structures; the latter is a finite-dimensional manifold. The mapping class group action on the Teichmuller space is quite often ergodic, which leads to important consequences for symplectic invariants, such as symplectic packing problems. I would describe some of the problems which were solved using this approach. This is a joint work with Michael Entov.

## BGU Probability and Ergodic Theory (PET) seminar

### Random Permutations from Free Products

*Jun 15, 11:10—12:00, 2023*,
**-101**

#### Speaker

**Tomer Zimhoni** (*BGU*)

#### Abstract

Let $\Gamma=G_1*G_2*\dots *G_r$ be a free product of a finite number of finite groups and a finite number of copies of the infinite cyclic group. We sample uniformly at random an action of $\Gamma$ on $N$ elements. In this talk, we will discuss a few tools we developed to help answer some natural questions involving the configuration described above, such as: For $\gamma\in \Gamma$, what is the expected number of fixed points of $\gamma$ in the action we sampled? What is the the typical behavior of the cycle structure of the permutation corresponding to $\gamma$ etc.

This is a joint with Doron Puder.