Algorithms, Combinatorics and Optimization Seminar Ernie Croot
Georgia Tech
Title: New Applications of the Polynomial Method to Problems in Combinatorics

Abstract: In this talk I will discuss some new applications of the polynomial method to some classical problems in combinatorics, in particular the Cap-Set Problem. The Cap-Set Problem is to determine the size of the largest subset A of F_pⁿ having no three-term arithmetic progressions, which are triples of vectors x,y,z satisfying x+y=2z. I will discuss an analogue of this problem for Z₄ⁿ and the recent progress on it due to myself, Seva Lev and Peter Pach; and will discuss the work of Ellenberg and Gijswijt, and of Tao, on the F_pⁿ version (the original context of the problem).

Date: Thursday, March 2, 2017
Time: 3:30 pm
Location: Wean Hall 8220