Title: Totally a Combinatorics Talk
Speaker: Keith Frankston, Rutgers University
Date: Wednesday, November 18, 2015 12:10pm
Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ
This is definitely not a talk on ultrafilters and the Stone-Cech compactification of the natural numbers and their use in proving Hindman's theorem. Hindman's theorem (also known as the finite sums theorem) is a result from infinite Ramsey theory which states that any finite coloring of the natural numbers contains an infinite subset B of one of the colors such that the sum of any finite selection of elements of B is in the same color class. We will prove this result through the introduction of a bizarre binary operation on ultrafilters with the property that the existence of any idempotent element will allow us to construct such a B given any choice of coloring.