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 nonconstructive, 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. 