# Geometric Aspects of $p$-adic Automorphic Forms (14frg207)

## Organizers

Ana Caraiani (Princeton Univeristy)

(University of Oregon)

(California Institute of Technology)

## Description

The Banff International Research Station will host the "Geometric aspects of $p$-adic automorphic forms" workshop from October 26 to November 2.

Over the past two decades, there has been a spectacular amount of progress in the Langlands program, leading to the resolution of major open questions such as Fermat's Last Theorem, the Sato-Tate conjecture and Serre's conjecture. In addition, there have been recent breakthroughs in the field, such as the work of Harris-Lan-Taylor-Thorne and Scholze associating Galois representations to classes in the cohomology of locally symmetric spaces for $GL_n$.
All of these developments have depended crucially on being able to $p$-adically interpolate automorphic forms. Questions about $p$-adic automorphic forms are intertwined with questions about the geometry of Shimura varieties. As there has been a lot of recent progress in the field of $p$-adic geometry, we propose to investigate the possible consequences this may have for $p$-adic automorphic forms and for the classical and $p$-adic Langlands programs.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides 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 is located at The Banff Centre in Alberta and 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).