School of Mathematical Sciences
Monday, November 4, 2013
Schreiber 006, 12:15
An inverse theorem for the Gowers norms in finite field geometries
Abstract: Inverse theorems play a central role in modern additive combinatorics.
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