Anand Pillay : Quasirandomness of definable subsets of definable groups in finite fields

Posted by Gabriel Conant , part of the Logic Seminar.

At

April 15, 2025, 3:30 p.m.

In

636 SEO

Abstract

We prove an "arithmetic" version of Tao's algebraic regularity lemma about graphs uniformly definable in finite fields. Namely with uniformly definable pairs $(G,A)$ ($G$ group, $A$ subset) in place of a graph. We make connections with Green's arithmetic regularity lemma for finite dimensional vector spaces over $F_p$, and results of Gowers on quasirandom groups. (Joint with Atticus Stonestrom.)