

Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
January 14, 2015 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 404 (8 Gubkina)






Hurwitz numbers, Belyi pairs, Grothendieck dessins d'enfant, and matrix models
L. O. Chekhov^{} 
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Abstract:
Belyi pairs are functions mapping Riemann surfaces of genus $g$ on the
complex projective line with branchings at a fixed number of points (at
three points for the case of original Belyi pairs and Grothendieck's
dessins d'enfant corresponding to these pairs). We construct the matrix
model describing this situation and more general models describing the
case of $n$ branching points. All these models are tau functions of the KP
hierarchy and upon some constraints on their generating functions their
solutions can be attained using the topological recursion technique.

