# NCMW - Introduction to the p-adic local Langlands program

## Venue: Indian Institute of Technology, Jammu

## Dates: 17 Sep 2024 to 25 Sep 2024

**Convener(s)**

Name: |
Prof. Eknath Ghate | Dr. Arvind Kumar |

Mailing Address: |
Senior Professor, School of Mathematics, Tata Institute of Fundamental Research Homi Bhabha Road Mumbai, 400 005, India |
Assistant Professor Indian Institute of Technology Jammu NH-44, PO Nagrota, Jagti Jammu and Kashmir, 181221, India |

Email: |
eghate at math.tifr.res.in | arvind.kumar at iitjammu.ac.in |

One of the main discoveries of the last century is that there is an intimate connection between algebra and analysis. More precisely there is a deep connection between n-dimensional representations of Galois groups of local fields and representations of matrix groups, such as the general linear group of size n over such fields. The simplest case is the case

n = 1: this is local class field theory, which is often taught at graduate school. The local Langlands program extends this connecion to n > 1 and has been the focus of attention of many mathematicians worldwide over the past half-century.

The current workshop aims to introduce the audience to some topics in the local Langlands program. The courses will start at an elementary level and attempt to reach some research topics. A particular emphasis will be placed on covering recent developments in the p-adic and mod p local Langlands program discovered by Breuil, Berger, Colmez and Paskunas about two decades ago. There will also be invited talks by experts in related aspects of Number Theory.