Mathematics Colloquia and Seminars

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We will begin by briefly introducing the use of higher-order Fourier analysis in additive combinatorics for a general audience. In particular, we will introduce the inverse theorem for Gowers norms, and how it identifies a certain class of arithmetically-structured functions -- nilsequences -- as extremal objects for problems in arithmetic combinatorics. We will then discuss how the analysis of nilsequences on certain arithmetic patterns is easier than the general case, and discuss some recent ideas and developments in overcoming the difficulties that arise in general. Time permitting, we may discuss related results on the polynomial Szemer\'edi theorem.