I will discuss how random curves appearing in critical models, probability theory, and complex geometry are related to evident and hidden algebraic content in CFT.

I will discuss how random curves appearing in critical models, probability theory, and complex geometry are related to evident and hidden algebraic content in CFT.

In the context of the probabilistic construction of Liouville CFT, we prove the irreducibility of highest-weight representations of the Virasoro algebra on the Kac table. Joint with Baojun Wu.

In these lectures, we will review the probabilistic construction of Liouville CFT. We will explain the Segal axioms for CFTs and how they can be implemented in Liouville CFT with the construction of amplitudes. Gluing amplitudes then allows us to identify the Hamiltonian of the Liouville CFT and to provide a representation of the Virasoro algebra in the Hilbert space of Liouville theory. We...

In these lectures, we will review the probabilistic construction of Liouville CFT. We will explain the Segal axioms for CFTs and how they can be implemented in Liouville CFT with the construction of amplitudes. Gluing amplitudes then allows us to identify the Hamiltonian of the Liouville CFT and to provide a representation of the Virasoro algebra in the Hilbert space of Liouville theory. We...

Tau function not only is the essential object in the study of integrable system in mordern mathematics but also plays important role in physics; they correspond to the (chiral) conformal blocks. I will talk about our work on an application of tau function to study the physics, which is to prove a special limit of the conjectured topological string/ spectral theory (TS/ST) correspondence. I...

I will review a recently developed approach to studying integrability in

CFT based on affine Yangian symmetry. I will focus on the derivation of

Bethe's ansatz equations for the spectrum of integrals of motion.

We shall explain how to construct conformal blocks on Riemann surfaces for Liouville CFT from the probabilistic representation of Segal amplitudes in Liouville theory and the diagonalisation of the Hamiltonian done using analytic methods.

This is based on several joint works with Baverez, Kupiainen, Rhodes, Vargas.