Ernest Schimmerling

Mathematical logic seminar - November 14, 2006

Time: 12 - 1:20 p.m.

Room: Wean Hall 5304

Speaker: Henry Towsner
Graduate Student
Department of Mathematical Sciences
Carnegie Mellon University

Title: Unwinding Szemeredi's theorem

Abstract:     Szemeredi's Theorem states that any dense enough subset of the integers contains arbitrarily long arithmetic progressions. The proof using the techniques of ergodic Ramsey theory is generally considered the simplest, and allows some generalizations not currently proven by other techniques; unfortunately, the proof is also non-constructive, giving no quantitative bounds at all on the result. I will present some of the key steps in the ergodic proof and discuss the extraction of a constructive analog.