Pure Maths Colloquium: Sean Prendiville

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: Purdie Theatre C
When: Mar 17 2022 @ 16.00
Video: Link (internal)
Speaker: Sean Prendiville Lancaster University
Title: Additive combinatorics, Diophantine problems and Fourier analysis

Fourier analysis has proved a fundamental tool in analytic and combinatorial number theory, usually in the guise of the Hardy–Littlewood circle method. When applicable, this method allows one to asymptotically estimate the number of solutions to a given Diophantine equation with variables constrained to a given finite set of integers. I will survey recent work extending the range of applicability of Fourier methods, with a focus on nonlinear problems in additive combinatorics.