Carlo Pagano, University of Glasgow and Max Planck Institute for Mathematics (Bonn)

January 15th, 2021 4:00-5:00 pm CET

Title : On the statistics of number fields, integral points and Arakelov ray class groups

Abstract : I will present new results coming from a novel approach to Malle’s conjectures (in its strong form): this is a joint work with Peter Koymans. If time allows, I will also survey recent works on the statistics of the solvability, respectively the failure of weak approximation, for integral points on conics and the distribution of Arakelov ray class groups of quadratic fields: this covers joint works (past and in progress) with Alex Bartel, Peter Koymans and Efthymios Sofos. During the talk I will highlight the natural connections between these subjects.