### DIMACS - Graduate Student Combinatorics Seminar

Title: Van der Waerden's theorem

Speaker: ** Kellen Myers**, Rutgers University

Date: Wednesday, April 1, 2009 12:00pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
In 1927, B.L. van der Waerden proved the theorem that bears his name: for given integers r and k, there exists an N so that any r-coloring of the integers 1 through N contains a monochromatic arithmetic progression of length k. Proof of this theorem will be presented, as well as an explanation of the sorts of bounds on N (w.r.t r and k) that are known. I will also discuss, if time permits, generalizations and related ideas, including the Hales-Jewett theorem and Szemeredi's theorem. If there is any extra time, I will also present an interesting new combinatorial proof of a famous conjecture of Fermat.