Some background on the geometric Langlands correspondence
The talk will be an extension of a preparational talk in the Friday-Bourbaki seminar, with only aim to give some background on the geometric Langlands correspondence.
The question started out with an arithmetic question and part of the recent progress has relied on a very fruitful exchange of ideas between arithmetic and geometric perspectives, that finally allowed Gaitsgory and Raskin to deduce results for the original correspondence in the case of function fields from an abstract looking categorical result. It is quite beautiful that the abstract looking statement can be used to deduce a classical statement on automorphic functions.
The different settings involved mean that if you either like arithmetic questions or complex geometry you might appreciate some aspects of this and I will try to explain some of the more elementary ideas that serve as starting point to translate between these languages.