Title: Topological recursion and enumerative geometry (note unusual time)
Speaker: Gaëtan Borot
Speaker Info: Max-Planck Institute for Mathematics, Bonn
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 [wg,n]g,n of germs of forms in n variables on a curve, indexed by integers g and n and defined from some initial data by recursion on 2g-2+n>0. This construction enjoys many properties : representation of wg,n as integrals over Deligne-Mumford moduli space Mg,n, 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.Date: Tuesday, September 23, 2014
This is partly based on joint works with Eynard, Orantin, and ongoing work with Shadrin.