EVENT DETAILS AND ABSTRACT

Title: Sets of single recurrence and combinatorial number theory
Speaker: Hoàng Lê
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Abstract:

A set $H$ of positive integers is said to be intersective if for any dense subset $A$ of the integers, $H \cap (A-A) \neq \emptyset$. Thanks to Furstenberg's correspondence principle, intersective sets are one and the same as sets of Poincare recurrence in ergodic theory. I will give a survey on intersective sets and in particular their connection with equidistribution theory via what is known as van der Corput sets. I will also discuss the function field setting, in which the integers are replaced by the polynomial ring $\mathbf{F}_q[t]$. The talk includes joint works with Yu-Ru Liu and Michael Kelley.