The branches of number theory most directly related to automorphic forms have seen enormous progress over the past five years.  Techniques introduced since 2008 have made it possible to prove many new arithmetic applications. The purpose of the current workshop is to drow the attention of young students or researchers to new questions that have arisen in the course of bringing several chapters in the Langlands program and related algebraic number theory to a close. We will focus especially on some precise questions of a geometric nature, or whose solutions seem to require new geometric insights.  A graduate level in Number Theory is expected.

This two-week workshop will be devoted to the following subjects: Automorphy lifting theorems, p-adic local Langlands program, Characters of categorical representations and Hasse-Weil zeta function. During the first week, the lecturers present an open question and related mathematical objects. The first  exercice  sessions serve to direct the participants to an appropriate subject depending on their level. During the second week, the lecturers give some more advanced lectures on the field.

For eligibility and how to apply, see the Summer Graduate Workshop homepage