A stable arithmetic regularity lemma in finite abelian groups
Analysis and Geometry Seminar
29th May 2018, 3:00 pm – 4:00 pm
Howard House, 2nd Floor Seminar Room
The arithmetic regularity lemma for Fpn (first proved by Green in 2005) states that given A ⊆ Fpn, there exists H ≤ Fpn 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.