Local and Global Langlands Duality

This is the continuation of the previous talk. After recalling the Hitchin system, I will briefly explain that it is a completely integrable system. Next, I will explain what kind of duality one expects for the singular fibers of the Hitchin system. I will briefly talk about upgrading the "geometric" duality to a derived equivalence (I will define the derived category).

Then I will explain how the Langlands duality for Hitchin systems can be deformed to obtain the formulation of the "geometric Langland duality for GL(n)" due to Beilinson and Drinfeld. If time permits, I will talk about generalizations from GL(n) to arbitrary reductive groups.