# Matrix models for partitions, plane partitions and topological vertex formulae

#### by Bertrand Eynard (via video)

Institution: CEA-Saclay, Paris
Date: Fri 16th April 2010
Time: 1:00 PM
Location: JH Michell Theatre, Richard Berry Building, The University of Melbourne

Abstract: VIDEO lecture recorded at IST Lisbon on 10/11/2009

Speaker: Bertrand EYNARD (CEA-Saclay, Paris)

Gromov-Witten invariants can be computed by topological vertex formulae, which are written as sums over partitions or plane partitions. We will show how to rewrite sums over partitions as matrix integrals, along the lines of 0804.0381[math-ph] (conifold), 0905.0535[math-ph] (framed vertex), 0810.4944[math-ph] (Seiberg-Witten), and then for general toric CY 3-folds. As a consequence, since matrix models satisfy the topological recursion, then, automatically, the Gromov-Witten invariants also satisfy the topological recursion attached to the matrix model's spectral curve. Then, we compute the matrix model's spectral curve, and we will show that it coincides (modulo symplectic transformations) with the mirror spectral curve. This proves the "remodeling the B-model proposal" for all toric geometries. We will also present some further developments of these methods.