# 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.