# Group actions/dynamics seminar: Sebastián Donoso (University of O'Higgins, Chile) Quantitative multiple recurrence for two and three transformations

In this talk I will provide some counter-examples for quantitative multiple recurrence problems for systems with more than one transformation.  For instance, I will show that there exists an ergodic system $(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that  $\mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell}$  for every $n \in \mathbb{N}$.  The construction of such a system is based on the study of big'' subsets of $\mathbb{N}^2$ and $\mathbb{N}^3$  satisfying combinatorial properties.   This a joint work with Wenbo Sun.

## Date:

Thu, 25/05/2017 - 10:00 to 11:00

Ross 70