### DIMACS - Graduate Student Combinatorics Seminar

Title: Some Algebraic Combinatorics

Speaker: **Arran Hamm**, Rutgers University

Date: Wednesday, October 13, 2010 12:10pm

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

Abstract:
In this talk we will discuss the Chevalley-Warning Theorem and Combinatorial Nullstellensatz (two algebraic theorems) and their applications to combinatorial problems. The Cauchy-Davenport Theorem states that if we have two nonempty subsets, A and B, of Z_p for p prime, then |A+B| is at least the minimum of |A|+|B|-1 and p. We'll see an algebraic proof using CN and extend to a few related problems.
If time permits, we'll discuss the formerly-known-as Kemnitz Conjecture."

Lunch will be provided.