Matrix models for partitions, plane partitions and topological vertex formulae
by Bertrand Eynard (via video)
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.
For More Information: contact: Paul Norbury. email email@example.com