Ergodic Theory / Probability Seminar - Sebastian Donoso

November 26, 2018
Thursday, December 6, 2018 - 3:00pm to 4:00pm
Math Tower 154
Ergodic Theory/Probability Seminar

Title: Quantitative multiple recurrence in ergodic theory

SpeakerSebastian Donoso (Universidad de O'Higgins)

Abstract: In this talk I will survey recent development of the multiple recurrence problem in ergodic theory. For a probability space $(X,\mathcal{X},\mu)$ and measure preserving transformations $T_1,\ldots,T_d$, the problem is to study the largeness of the set of $n\in \mathbb{N}$ such that \[ \mu(A\cap T_1^{-a_1(n)}A\cap \cdots \cap T_d^{-a_d(n)}A) > F(\mu(A)) \] where $a_1,\ldots,a_d$ take integer values on the integers and $F$ is a suitable function. I will mention key results and comment on the problem for commuting transformations, linear and polynomial functions $a_i$. I plan to provide some proofs that rely on combinatorial constructions.

Seminar URLhttp://u.osu.edu/ergodictheory/

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