Combinatorics Seminar: Additive structure of sets of Fourier coefficients

Seminar | April 10 | 12:10-1 p.m. | 939 Evans Hall

 Thomas Bloom, University of Bristol

 Department of Mathematics

The collection of large Fourier coefficients of a function, whether they be called `major arcs' or the `large spectrum', are one way of representing the linearly structured component of a function, and as such plays an important role in many problems in additive combinatorics, analytic number theory, theoretical computer science, and beyond. In this talk I will discuss some results concerning what kind of additive structure such sets can have, and how this structure can be exploited to improve density increment arguments.