School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

Hebrew University

Inverse theorems play a central role in modern additive combinatorics.

Abstract:

Typically, such theorems involve recovering some structure given a measurement

that is biased away from random behavior. The Gowers uniformity norms Uk measure

a certain kind of psuedorandmness: a Uk uniform set in a vector space over a finite

field contains roughly the same number of linear configurations as one would expect

in a random subset of the same density. The inverse conjecture for the Gowers norms

concerns the structure of sets which deviate from this type of random behavior; it

predicts that such subsets will have non trivial correlation with low degree polynomials

(degree smaller than k). We will describe how one can use ergodic theoretic techniques

to settle this conjecture.

Coffee will be served at 12:00 before the lecture

at Schreiber building 006