Invitations to Mathematics - Caroline Terry

August 26, 2020
Wednesday, October 21, 2020 - 4:10pm to 5:40pm
Zoom (email anthony.69@osu.edu for link)
photo of Caroline Terry

Title: On the structure of stable subsets of finite abelian groups

Speaker: Caroline Terry

Abstract: The arithmetic regularity lemma for $\mathbb{F}_p^n$ (first proved by Green in 2005) states that given $A\subseteq {F}_p^n$, there exists $H\leq {F}_p^n$ 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 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.

Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for two credit hours of Math 6193 with Professor Nimish Shah.

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