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Institute for the Physics and Mathematics of the UniverseWPI

IPMU Komaba Seminar

Lecturer: Shinobu Hikami (The University of Tokyo)
Date: June 2, 2008, 17:00 - 18:30
Place: Room 002, Mathematical Sciences Building, Komaba Campus, The University of Tokyo
Title: Intersection theory from duality and replica
Abstract: Kontsevich's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on N by N matrices and N-point functions of k by k matrices, plus the replica method, familiar in the theory of disordered systems, allows one to recover Kontsevich's results on the intersection numbers, and to generalize them to other models. This provides an alternative and simple way to compute intersection numbers with one marked point, and leads also to some new results. This is a joint work with E. Brezin (Comm.Math. Phys. in press, arXiv:0708.2210).
Note: This seminar is organized by Institute for the Physics and Mathematics of the Universe (IPMU) and Graduate School of Mathematical Sciences, The University of Tokyo.
IPMU Komaba Seminar Web Page