May 18: Konstantin Aleshkin

Title: Liouville quantum gravity and integrable systems

Abstract:

Correlation numbers of 2d Liouville quantum gravity are defined as integrals of certain products of conformal blocks over moduli spaces of punctured curves and are quite challenging to compute directly. The other major approaches to 2d quantum gravity: topological gravity, and matrix models are much better understood. The connection between the topological gravity and matrix models is established by the Witten conjecture and its generalizations. In the talk I will speculate on the connection of the Liouville gravity and the other two approaches.