# Modularity and Moduli Spaces (19w5210)

## Organizers

(University of Arizona)

(Imperial College London)

(University of Chicago)

David Savitt (Johns Hopkins University)

## Description

The Casa Matemática Oaxaca (CMO) will host the "Modularity and Moduli Spaces" workshop in Oaxaca, from October 20, 2019 to October 25, 2019.

The year 2019 will mark the 25th anniversary of the resolution of Fermat's Last Theorem, as well as the 20th anniversary of the proof that all elliptic curves over the rational numbers are modular. The many mathematical ideas that were introduced in these celebrated results have blossomed in the intervening years, leading to the development of entire areas of research in the contemporary arithmetic of automorphic forms: potential automorphy theorems, the $p$-adic Langlands program, and the weight part of Serre's conjecture for higher rank groups, just to name some of them.

This workshop brings together leading and emerging experts in these several areas, to take stock of the current state of developments in them, and to chart a course for future progress.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT