Abstract:
Liouville Conformal Field Theory (LCFT) was introduced by A. Polyakov in 1981 in the context of string theory and two dimensional quantum gravity and subsequently it has reappeared in various contexts of physics and mathematics such as 4 dimensional Yang-Mills theory of quantum Teichmuller theory. I will review in this talk a probabilistic formulation of LCFT and show that it satisfies the geometric axioms of Conformal Field Theory due to Graeme Segal. Then I explain how this leads to an expression for the correlation functions of LCFT in terms of simple data: the structure constants and spectrum of the theory. Joint work with C. Guillarmou, R. Rhodes and V. Vargas.
Biography:
Antti Kupiainen received his PhD from Princeton and has been a professor at Rutgers and presently at Helsinki. His work covers several topics in mathematical physics from constructive field theory, statistical mechanics and disordered systems to turbulence and most recently Liouville quantum gravity.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai