Kavli IPMU Komaba Seminar

過去の記録 ~03/04次回の予定今後の予定 03/05~

開催情報 月曜日 16:30~18:00 数理科学研究科棟(駒場) 002号室
担当者 河野 俊丈


16:30-18:00   数理科学研究科棟(駒場) 002号室
池田 暁志 氏 (東京大学大学院数理科学研究科)
The correspondence between Frobenius algebra of Hurwitz numbers
and matrix models (JAPANESE)
[ 講演概要 ]
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.