We construct explicit representations of Virasoro algebra from Markov semigroups quantizing flows of holomorphic vector fields, and we use this to compute the scattering matrix explicitly and to define rigorously and study the conformal blocks for certain conformal field theories with central charge c>25 and continuous spectrum.
This is joint work with G. Baverez, A. Kupiainen, R. Rhodes and V. Vargas.