Description:

Title: Infinite patterns in large sets of integers

Abstract: Since Szemeredi's Theorem and Furstenberg's proof thereof using ergodic theory, ergodic methods have been used to show the existence of numerous patterns in sets of integers with positive upper density. These tools have led to uncovering new patterns that occur in any sufficiently large set of integers, but until recently all such patterns have been finite. This talk will be an overview of our resolution of questions and conjectures of Erdos on infinite configurations in sets with positive upper density. This is joint work with Joel Moreira, Florian Richter, and Donald Robertson.