On 9-10.12.2019 professor George Jorjadze (Free University of Tbilisi) gave the following lectures:

1. Deformations of 2d CFT
2. Liouville theory as a model of 2d gravity
3. Reflection amplitude in Liouville theory

Lectures on Liouville theory.pdf

Abstract of the talks
1. We analyze symmetries of 2-dimensional conforml field theories and their possible integrable deformations. We construct the T-bar T deformed Hamiltonian in a closed form for any 2d CFT and show its relation to string dynamics.

Abstract of the Lecture 1
2. We show that the Einstein-Hilbert action in 2d is degenerated and show that the constant curvature 2d manifolds in the conformal coordinates are described by the Liouville equation. We derive the general solution of the Liouville equation using its conformal symmetry. We then classify Liouville fields on a cylinder and describe their physical content.

Absract of the Lecture 2
3. We investigate scattering problem in Liouville theory and show that the S-matrix is non-trivial. We construct the Heisenberg operators for the Liouville field exponentials and calculate the reflection amplitude for the homogeneous Liouville field configurations.