**Title:** Topological recursion and enumerative geometry (note unusual time)

**Speaker:** GaĆ«tan Borot

**Speaker Info:** Max-Planck Institute for Mathematics, Bonn

**Brief Description:**

**Special Note**:

**Abstract:**

I will present the formalism of the blobbed topological recursion, that computes the general solution of a set of loop equations. The outcome is a sequence[wof germs of forms in_{g,n}]_{g,n}nvariables on a curve, indexed by integersgand n and defined from some initial data by recursion on2g-2+n>0. This construction enjoys many properties : representation ofwas integrals over Deligne-Mumford moduli space_{g,n}M, variational formulae under infinitesimal deformations of the initial data, and a property of symplectic invariance. I will describe some applications of this theory in enumerative geometry of surfaces, and in computation of all-order asymptotic expansions in matrix models._{g,n}This is partly based on joint works with Eynard, Orantin, and ongoing work with Shadrin.

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