IPMU Komaba Seminar

Speaker: Akishi Ikeda (The University of Tokyo)
Title: The correspondence between Frobenius algebra of Hurwitz numbers and matrix models
Date (JST): Mon, Apr 26, 2010, 16:30 - 18:00
Place: Room 002, Mathematical Sciences Building, Komaba Campus
Abstract: The number of branched coverings of closed surfaces are called Hurwitz numbers. They constitute a Frobenius algebra structure, or two dimensional topological field theory. On the other hand, correlation functions of matrix models are expressed in term of ribbon graphs (graphs embedded in closed surfaces).

In this talk, I explain how the Frobenius algebra structure of Hurwitz numbers are described in terms of matrix models. We use the correspondence between ribbon graphs and covering of S^2 ramified at three points, both of which have natural symmetric group actions.

As an application I use Frobenius algebra structure to compute Hermitian matrix models, multi-variable matrix models, and their large N expansions. The generating function of Hurwitz numbers is also expressed in terms of matrix models. The relation to integrable hierarchies and random partitions is briefly discussed.