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Nilsequences on general patterns
Algebraic Geometry and Number Theory| Speaker: | Daniel Altman -- postponed, Stanford University |
| Location: | 2112 MSB |
| Start time: | Thu, Feb 20 2025, 1:10PM |
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 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 pattern of interest is not flag.