Topology of Norms Defined by Systems of Linear forms

Computer Science/Discrete Mathematics Seminar I
Topic:Topology of Norms Defined by Systems of Linear forms
Speaker:Pooya Hatami
Affiliation:University of Chicago
Date:Monday, May 7
Time/Room:11:15am - 12:15pm/S-101

Gowers' uniformity norms are defined by average of a function over specific sets of linear forms. We study norms that are similarly defined by a system of linear forms. We prove that for bounded complex functions over $F_p^n$, each such norm is equivalent to a Gowers' uniformity norm. To do this we prove direct and inverse theorems for norms defined by a system of linear forms. Joint work with Shachar Lovett.