EVENT DETAILS AND ABSTRACT

Title: Multiple recurrence along sparse sequences over thick sets
Speaker: Joel Moreira
Speaker Info: Northwestern University
Brief Description:
Special Note: Midwest Dynamical Systems Conference
Abstract:

Multiple recurrence results in probability preserving systems (i.e., higher order versions of Poincare's recurrence theorem) were first studied by Furstenberg in 1977. He obtained a multiple recurrence theorem and moreover showed that the set of return times is syndetic, i.e., has bounded gaps, thus partially extending Khintchine's recurrence theorem. Multiple recurrence has since been established along polynomial sequences and more general classes of sequences; however, for most non polynomial sequences the set of return times is no longer syndetic. In this talk I will describe joint work with Bergelson and Richter showing that for a wide class of sequences, the set of return times has nice combinatorial properties and, in particular is thick, i.e., contains arbitrarily long intervals of integers.