| Résume | The Analytic Langlands Correspondence (ALC) combines elements of the geometric Langlands correspondence with
harmonic analysis. It builds on the geometric Langlands correspondence constructed by Beilinson and Drinfeld
relating a certain class of connections on Riemann surfaces called opers to the D-modules on Bun_G defined
by the quantization of Hitchin's integrable system, G being a reductive algebraic group. According to the ALC,
the D-modules on Bun_G admitting solutions which are square-integrable with respect to a natural scalar product
are related to opers having holonomy which is conjugate to a real form of the Langlands dual group to G. It
thereby describes the solution to the spectral problem defined by the quantization of Hitchin's integrable
system in geometric terms.
The goal of my talk will be to introduce to the conjectures called Analytic Langlands Correspondence, to
outline some proof strategies proposed in the literature, and to summarize the state of the art. |
