Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Thu, 25 Apr 2024
16:00
Lecture Room 4, Mathematical Institute

The leading constant in Malle's conjecture

Dan Loughran
(University of Bath)
Abstract

A conjecture of Malle predicts an asymptotic formula for the number of number fields with given Galois group and bounded discriminant. Malle conjectured the shape of the formula but not the leading constant. We present a new conjecture on the leading constant motivated by a version for algebraic stacks of Peyre's constant from Manin's conjecture. This is joint work with Tim Santens.

Thu, 02 May 2024
16:00
Lecture Room 4, Mathematical Institute

Twisted correlations of the divisor function via discrete averages of $\operatorname{SL}_2(\mathbb{R})$ Poincaré series

Jori Merikoski
(University of Oxford)
Abstract

The talk is based on joint work with Lasse Grimmelt. We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with high uniformity in the modulus. It is obtained by using spectral methods of $\operatorname{SL}_2(\mathbb{R})$ automorphic forms to study Poincaré series over congruence subgroups while keeping track of interactions between multiple orbits. This approach offers increased flexibility over the widely used sums of Kloosterman sums techniques. We give applications to correlations of the divisor function twisted by periodic functions and the fourth moment of Dirichlet $L$-functions on the critical line.