# Manchester Geometry Seminar 2013/2014

**Thursday 10 October 2013. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm*
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Topological Recursion in Matrix Models

Leonid Chekhov (Steklov Mathematical Institute and Loughborough University)

`chekhov@mi.ras.ru`

Matrix models are integrals over (usually Hermitian) $N\times N$ matrices weighted
by some potential function. In spite of their simplicity they manifest
both conformal symmetries and integrability properties, and some of these
models are related to geometry (notably the Kontsevich matrix integral is
the generating function for intersection indices on Riemann surfaces with
marked points). In my talk I will concentrate on the method of
"topological recursion" originated in papers by L. Ch., B. Eynard, and
N. Orantin, which allows constructing a consistent $1/N$-expansion for
integrals over Hermitian $N\times N$ matrices with arbitrary potentials in terms
of algebro-geometrical quantities related to the spectral curve of the
corresponding model. This method was proved to be universal as it has been
successfully applied to solving a variety of models of theoretical physics
and mathematics. I will also briefly describe the results of a recent
paper by L. Ch., B. Eynard and S. Ribault in which this method was
generalized to the case of quantum Liouville theory.