Quantisation of the Hitchin system and the analytic Langlands program

The first part of the series of lectures will review the CFT-based approach to the geometric Langlands Correspondence pioneered by Beilinson and Drinfeld, and how this approach is related to the quantisation of the Hitchin system. The subject of the second part will be a strengthening of the geometric Langlands Correspondence called analytic Langlands correspondence following Etingof, Frenkel and Kazhdan. We will outline an approach to the analytic Langlands program based on the quantisation of the integrable structure of the Hitchin system which is beingdeveloped in joint work with Duong Dinh, and discuss the relation to the work of Etingof, Frenkel and Kazhdan