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Fourier transforms and solving linear equations

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If you have a question about this talk, please contact Anton Evseev.

Additive combinatorics is a subject in which one often uses techniques from unexpected areas of mathematics in order to solve simple-to-state problems. An example of this is the use of Fourier analysis in dealing with solutions to linear equations in sets of integers. The aim of this talk is to describe some of these basic techniques, including some of the Fourier analysis and some of the oft-used averaging methods. We will focus in particular on how such techniques may be used to prove Roth’s theorem on arithmetic progressions. If time permits, we will also describe a cute link with evaluating some Dirichlet series.

This talk is part of the Junior Algebra and Number Theory seminar series.

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