tbranzov

An ICMS seminar talk by Mladen Dimitrov, University of Lille

Abstract: An amazing feature of the p-adic L-functions is their ability to live in families, thus their laws are governed by the geometry of p-adic eigenvarieties. In this lecture we will illustrate this philosophy through examples coming from classical modular forms and the Coleman-Mazur eigencurve.

A seminar talk by Marta Pieropan, Utrecht University

Abstract: In joint work with Damaris Schindler we develop a new version of the hyperbola method for counting rational points of bounded height that generalizes the work of Blomer and Brüdern for products of projective spaces. The hyperbola method transforms a counting problem into an optimization problem on certain polytopes. For rational points on subvarieties of toric varieties, the polytopes have a geometric meaning that reflects Manin's conjecture, and the same holds for counts of Campana points of bounded height. I will present our results as well as some general heuristics.

The talk aims to review the progress in the study of higher rank P-and Q-polynomial association schemes, starting with the foundational concepts and recent advancements as outlined in the referenced papers. It will provide explicit examples of multivariate P-and Q-polynomial association schemes and explore the implications of these developments. The discussion will draw from multiple sources, including recent significant contributions by Bernard et al. and Crampé et al., and will conclude with speculations on future directions for research in this area.

This talk is based on the two joint papers with Hirotake  Kurihara (Yamaguchi University), Da Zhao (East China University of Science  and Technology) and Yan Zhu (Shanghai University for Science and Technology).