Title: An analytic version of stable arithmetic regularity
Abstract: In 2011, Malliaris and Shelah proved a strong form of Szemeredi's regularity lemma for the class of "stable graphs", which are graphs omitting a certain special subgraph called a ``half-graph". A group theoretic analogue of their result for finite abelian groups was later obtained by Terry and Wolf using Fourier analytic methods from additive combinatorics. A suitable generalization to arbitrary finite groups was then proved by myself, Pillay, and Terry using model theoretic methods. This talk will focus on an analytic analogue of stability defined for functions, rather than graphs. Roughly speaking, the main result of the talk says that if G is amenable, then any stable function on G is almost constant on all translates of a unitary Bohr neighborhood in G of bounded complexity. The proof of this result uses ingredients from topological dynamics and continuous model theory. I will also explain how this result leads to a short proof of Bogolyubov’s Lemma for arbitrary amenable groups. This is joint work with Anand Pillay.
Zoom info:
Topic: Gabriel Conant talk
Time: Feb 6, 2024 04:00 PM Central Time (US and Canada) Join Zoom Meeting
https://illinois.zoom.us/j/83060349769?pwd=bm9GSkNCWnFIS04xVmN1aGI3RmJDdz09
Meeting ID: 830 6034 9769
Password: 379800
