# $p$-adic Cohomology and Arithmetic Applications (17w5118)

## Organizers

(Imperial College London)

Tomoyuki Abe (Kavli Institute for the Physics and Mathematics of the Universe)

(University of California, San Diego)

## Description

The Banff International Research Station will host the "$p$-adic Cohomology and Arithmetic Applications" workshop from October 1st to October 6th, 2017.

The subject of the conference, $p$-adic cohomology, is a perfect example of the sort of synthesis in pure mathematics which has been dominating the subject in its most modern period. It is the study of rather discrete objects, systems of polynomial congruences, using methods of analysis, the theory of continuous change, while the language of the subject is topology, a modern area of mathematics developed to study properties of geometric objects which do not change under deformations or distortions. In its goals the area has been brilliantly successful: for example it was used as a key ingredient in the proof of Fermat's last theorem, and it is continued to be used in the subject which provided the proof for this famous old conjecture, namely the Langlands program. In addition to its theoretical success the subject also provided important solution-counting algorithms for systems of polynomial congruences, and hence has a potentially large role in cryptography in the future. The workshop will concentrate on the rapid development in the foundations of the subject, and its applications to some central and outstanding conjectures in arithmetic. By hosting this conference we will give experts in the area the opportunity to present their last results on these questions, and encourage an exchange that can only drive forward this exciting and rapidly developing subject.

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 disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng 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).