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Isomonodromic tau-functions on Hurwitz spaces and their applications

Date: 
Tuesday 22nd November 2005 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 

We discuss Jimbo-Miwa tau-functions corresponding to Riemann-Hilbert problems with quasi-permutation monodromy groups; these tau-functions are sections of certain line bundles on Hurwitz spaces. We show how to compute these tau-functons explicitly in terms of theta-functions and discuss their applications in several areas: large N expansion in Hermitian matrix models, Frobenius manifolds, determinants of laplacians over Riemann surfaces and conformal factor of Ernst equation.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons