- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 13, 2016 - 11:05am for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Ernie Croot – Georgia Tech
- Organizer
- Anton Leykin
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_p^n 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 Z_4^n 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_p^n version (the original
context of the problem).