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Graduate Seminar

Andrew Zucker
Carnegie Mellon University
Title: Ramsey theorems via ultrafilters

Abstract: In this talk, we will investigate the notion of partition regularity. Loosely speaking, a family of sets is partition regular if by taking any member of the family and breaking it into finitely many pieces, some piece contains another member of the family. There is often some difficulty in proving that a given family is partition regular; theorems of this sort include Ramsey's theorem. We will investigate a slick method of proving that certain families are partition regular by introducing the notion of an ultrafilter and constructing ultrafilters which "describe" the family in question.

Date: Tuesday, January 17, 2017
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on Youtube: https://youtu.be/ti22yZexBgw