The polynomial method: more results and open questions

Computer Science/Discrete Mathematics Seminar II
Topic:The polynomial method: more results and open questions
Speaker:Jordan Ellenberg
Affiliation:University of Wisconsin
Date:Tuesday, January 17
Time/Room:11:35am - 1:00pm/S-101
Video Link:https://video.ias.edu/csdm/2017/0117-JordanEllenberg

This will be a bit of a "grab bag" talk where I discuss some results and open questions in combinatorial geometry which are either approachable by the polynomial method or which I hope are approachable by the polynomial method! I will talk about some subset of:
  • subsets of $\mathbb F_p^n$ which have large intersection with a $k$-plane in every direction (joint work with D. Erman)
  • subsets of $\mathbb F_p$ with many arithmetic progressions
  • applications of the Croot-Lev-Pach technique to subsets of $\mathbb Z/N \mathbb Z$ with no 3-term arithmetic progression
Relevant papers: