Dmitrii Zakharov, Massachusetts Institute of Technology

Abstract

For a given prime p and a dimension n, the Erdos-Ginzburg-Ziv problem asks about the smallest number s such that any subset in F_p^n of size s contains p vectors with zero sum. We drastically improve previous upper bounds in the case when p is fixed and n is large. In particular, we overcome a certain 'multicolor' barrier of the slice rank method for this problem which appears in many applications of the slice rank polynomial method. The proof combines the slice rank method with a generalization of the Balog-Szemeredi-Gowers Theorem due to Borenstein and Croot.

Joint work with Lisa Sauermann.

See: https://sites.google.com/view/rutgersdmseminar