The Mysteries of Liouville Theory (Antti Kupiainen, University of Helsinki)

21.03.2019 16:15

A. Polyakov introduced Liouville Conformal Field theory (LCFT) in 1981 as a way to put a natural measure on the set of Riemannian metrics over a fixed two dimensional manifold. Ever since, the work of Polyakov has echoed in various branches of physics and mathematics, ranging from string theory to probability theory through geometry.
In the context of 2D quantum gravity models, Polyakov’s approach is conjecturally equivalent to the scaling limit of Random Planar Maps and through the Alday-Gaiotto-Tachikava correspondence LCFT is conjecturally related to certain 4D Yang-Mills theories.
Through the work of Dorn,Otto, Zamolodchikov and Zamolodchikov and Teschner LCFT is believed to be to a certain extent integrable. I will review a probabilistic approach to LCFT based on Kahane's theory of Gaussian Multiplicative Chaos developed together with David, Rhodes and Vargas. In particular this has recently led to proof of an integrability conjecture on LCFT, the celebrated DOZZ formula, in a joint work with Rhodes and Vargas.

PS. The Colloquium will be followed by an aperitif

Lieu

Room 17

Organisé par

Section de mathématiques

Intervenant-e-s

Antti Kupiainen, University of Helsinki

entrée libre

Classement

Catégorie: Colloque