Séminaire Géométrie et groupes discrets

A Mathematical Approach to Liouville Conformal Field Theory on Riemann Surfaces

by Prof. Colin Guillarmou (CNRS & Université Paris-Saclay)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Conformal field theory is a vast subject intensively studied in theoretical physics since the 80s. In this talk I will explain how one can use probabilistic methods, analytic methods and tools from Teichmüller spaces and the geometry of Riemann surfaces to construct rigorously (in the mathematical sense) an important conformal field theory in dimension 2, called the Liouville conformal field theory. This theory is a theory of random Riemannian metrics on surfaces and its correlation functions can be computed explicitly and decomposed into two quantities: the so-called structure constant (the 3 point function on the sphere) and the Virasoro conformal blocks. The conformal blocks are holomorphic functions of the moduli of surfaces linked to the representation theory of the Virasoro algebra.

This is based on joint works with Kupiainen, Rhodes and Vargas, and an ongoing work with the same authors together with Baverez.


IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.


Organized by

Fanny Kassel