Mathematical logic seminar - Oct 2 2012

Time: 12:00 - 13:20

Room: Wean Hall 7201

Speaker:     Jason Rute    
Department of Mathematical Sciences
Carnegie Mellon University

Title: Applications of Ultrafilters to Ergodic Theory and Additive Combinatorics


It is well known that results in Ergodic Theory can be used to prove results in Additive Combinatorics.  An example is Szemeredi’s Theorem: A set of natural numbers of positive upper density contains arbitrarily long arithmetic progressions. In this survey talk I will explain how one can use limits along nilpotent ultrafilters to generalize such results.  This is a lecture I will be giving as part of a workshop on Ergodic Theory and Additive Combinatorics.  No knowledge of Ergodic Theory or Additive Combinatorics is required. I will present the necessary background.