![Daniel Altman](/sites/default/files/styles/news_and_events_image/public/2024-08/img_5016.jpeg?h=e0a70c89&itok=AEu2h7Yx)
Daniel Altman
Stanford University
Title
Nilsequences on general additive patterns
Abstract
We will begin by briefly introducing the use of higher-order Fourier analysis in additive combinatorics for a general audience. In particular, we will discuss the arithmetic regularity lemma and how it identifies a certain class of arithmetically-structured functions -- nilsequences -- as extremal objects for problems in additive combinatorics. We will then discuss how it has recently come to light that the analysis of nilsequences on certain additive patterns -- those which satisfy a certain algebraic criterion known as the flag condition -- is easier than the general case, and discuss some recent ideas and developments in overcoming the difficulties that arise when the additive pattern of interest is not flag.