Speaker: Atticus Stonestrom
University of Notre Dame
Will give a Logic Seminar entitled:
An arithmetic algebraic regularity lemma
Abstract: I will discuss a joint work with Anand Pillay, in which we give an "arithmetic" version of Tao's "algebraic regularity lemma" for graphs definable in finite fields; in particular we show that, if $F$ is a finite field, and $G$ is a definable group in $F$ and $D\subseteq G$ a definable subset, both of bounded complexity, then $G$ has a definable normal subgroup $H$ of bounded complexity and index such that, for any cosets $V,W$ of $H$, the bipartite graph $(V,W,xy^{-1}\in D)$ is quasirandom. I will largely discuss the result's statement and the broader context for it, including Tao's original theorem and other arithmetic regularity results in the literature.
Date: 04-15-2025
Time: 2:00 pm
Location: 125 Hayes-Healy Bldg