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Higher genus Catalan numbers and the Eynard-Orantin recursionAlgebra & Discrete Mathematics
|Speaker: ||Motohico Mulase, UC Davis|
|Location: ||2112 MSB|
|Start time: ||Tue, May 1 2012, 2:10PM|
The Catalan numbers have many different
definitions, and accordingly, many different
generalizations. In this talk we present
a generalization from the point of view of
map enumeration. We derive a simple
recursion equation that is a straightforward
extension of the Catalan recursion formula.
The Laplace transform of this equation
is equivalent to the Eynard-Orantin recursion
formula, which is a universal B-model
formalism that appears in the Remodeling
Conjecture in topological string theory/Gromov-Witten
theory. The higher genus Catalan numbers give the
dimensions of algebras defined by modifying
the construction of the Temperley-Lieb algebras.
The talk is based on my joint papers with
Dumitrescu, Safnuk, Sorkin, and others.