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.
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and where the social distancing is not possible;
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