|Jul 29, 2014
The Langlands correspondence is a deep statement relating number theory and harmonic analysis in a rather unexpected way. It is still largely conjectural for number fields but a lot is known for function fields, not least because one has more algebro-geometric tools over a function field. The geometric Langlands program is in a sense even further simplification by working over the complex number C. The goal of this introductory talk is to state the best hope conjecture of geometric Langlands program from a natural context in terms of categorical harmonic analysis. One should note that we only aim to give some idea of the subject and in particular the version of the conjecture we will see in the talk is known to be wrong.