Computer Science/Discrete Mathematics Seminar II

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:

• https://arxiv.org/abs/1502.03736