Quantization of Hitchin moduli space, Liouville theory,
and the (quantum) geometric Langlands correspondence
Joerg Teschner
The aim of my talk will be to elucidate the relations
between Liouville theory and the quantization of the
Hitchin moduli spaces. We will show that Liouville
theory unifies the quantization of the Hitchin
integrable system (Hitchin moduli space in complex
structure I) and the quantization of the isomonodromic
deformation equations (Hitchin moduli space in complex
structure J) in a suitable sense. The resulting picture
is closely related to the (quantization of the)
geometric Langlands correspondence.