Geometric Recursion

We shall review the geometric recursion and its relation to topological recursion. In particular, we shall consider the target theory of continuous functions on Teichmüller spaces and we shall exhibit a number of classes of mapping class group invariant functions, which satisfies the geometric recursion. Many of these classes of functions are integrable over moduli spaces and we prove that these averages over moduli spaces satisfies topological recursion. The talk will end with some future perspectives of applications of geometric recursion. The construction of geometric recursion and the results relating it to topological recursion is joint work with Borot and Orantin.

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