12:30 pm, Monday, 27th November
We will begin by 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 arithmetic 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 arithmetic pattern of interest is not flag.
University of Michigan
Monday 27 November 2023, 12.30 pm
RC-1043 (Anita B. Lawrence Center)