Talk information

Date: Sunday, May 24, 2026
Time: 10:10–11:00
Place: Schreiber 309
Speaker: Tomer Milo (Tel Aviv University)
Title: On the Gowers Inverse problem over finite fields

Abstract:

The Gowers inverse problem informally states that the only polynomials which have a large $U^d$ norm (called the uniformity norm, or Gowers norm, of order $d$) are the ones which correlate non-trivially with some polynomial of degree smaller than $d$. While this problem is essentially solved, quantitative bounds on the size of the correlation in terms of the magnitude of the norm remain elusive.

The $PGI(d)$ problem (Polynomial Gowers inverse) states that the correlation should be polynomial in the magnitude of the $U^d$ norm. The case of degree $d$ polynomials for the $U^d$ norm is classically obtained as an application of the `partition-versus-analytic rank’ problem for multilinear forms. In this talk, we present a (nearly) polynomial bound for polynomials of degree $d+1$ - the next open case.

The work presented is a joint work with Guy Moshkovitz.