|Computer Science/Discrete Mathematics Seminar I|
|Topic:||Topology of Norms Defined by Systems of Linear forms|
|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.