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In this talk, I will review the notion of modular functor and explain how one use it to defines bundles over the compactified moduli space of Riemann surfaces. The Chern classes of these bundles turn out to define Cohomological field theories. I will explain how this implies that they can be computed by an inductive procedure called topological recursion. One of the motivating example is the study of the so-called Verlinde bundle associated to Wess-Zmino-Witten Conformal field theories.
Based on a joint work with Andersen and Borot