On Liouville quantum field theory on Riemann surfaces


We will discuss some joint work with Rhodes and Vargas on defining a 2 dimensional conformal field theory through path integral (via probabilistic methods) on Riemann surfaces of genus g>1, and we describe the behaviour of the partition function on the moduli space of Riemann surfaces using analysis and hyperbolic geometry (Teichmüller theory). This allows to show the convergence of Polyakov partition function which appeared in 2d gravity.


  •  Colin Guillarmou
    Colin Guillarmou , Université Paris-Sud