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

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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.