# 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 Hardyâ€“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.