EVENT DETAILS AND ABSTRACT

Title: On sets of pointwise topological recurrence
Speaker: Daniel Glasscock
Speaker Info: University of Massachusettes, Lowell
Brief Description:
Special Note:
Abstract:

Recurrence of points and sets is a central topic in dynamics that has, for the last half century, found numerous applications in combinatorics and additive number theory. “Sets of topological recurrence” – integer times at which any open set is guaranteed to return to itself under a continuous map of a compact metric space – are well studied. In this talk, we will discuss the class of “sets of pointwise topological recurrence,” integer times at which any point is guaranteed to return to a neighborhood of itself. This class is markedly different from its set analogue: all sets of pointwise topological recurrence are combinatorially large and “good” for multiple set recurrence, for example. We will explain these facts and some of the anticipated combinatorial and number-theoretic connections. This talk is based on ongoing joint work with Anh Le (University of Denver).