Logic Seminar
Caroline Terry
Maryland
A stable arithmetic regularity lemma in finite abelian groups
Abstract: The arithmetic regularity lemma for $\mathbb{F}_p^n$ (first proved by Green in 2005) states that given $A\subseteq \mathbb{F}_p^n$, there exists $H\leq \mathbb{F}_p^n$ 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 stability theoretic assumption, the bad bounds and non-uniform elements are not necessary. In this talk, we present results extending these results to stable subsets of arbitrary finite abelian groups. This is joint work with Julia Wolf.
Tuesday September 4, 2018 at 3:30 PM in 427 SEO