# A stable arithmetic regularity lemma in finite abelian groups

• Caroline Terry (University of Chicago)
• Thursday 14 February 2019, 14:30-15:30
• MR12.

Abstract: The arithmetic regularity lemma for Fpn (first proved by Green in 2005) states that given $A\subseteq \F_pn$, there exists $H\leq \F_pn$ of bounded index such that $A$ is Fourier-uniform with respect to almost all cosets of $H$. In general, the growth of the index of $H$ is required to be of tower type depending on the degree of uniformity, and must also allow for a small number of non-uniform elements. Previously, in joint work with Wolf, we showed that under a natural model theoretic assumption, called stability, the bad bounds and non-uniform elements are not necessary. In this talk, we present results extending this work to stable subsets of arbitrary finite abelian groups. This is joint work with Julia Wolf.

This talk is part of the Combinatorics Seminar series.