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Enumeration of planar graphs by matrix integrals

Thursday 10th April 2008 - 09:30 to 10:15
INI Seminar Room 1

We apply matrix integrals to combinatorially defined functions (not to the functions of the traces) and express: The number of graphs embeddable in the plane as the matrix integral of an ice-type partition function; the number of the directed cycle double covers as the matrix integral of an Ihara-Selberg-type function. The asymptotic analysis of the integrals remains a challenging open problem.

(joint work with Mihyun Kang)

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