Mathematics Colloquia and Seminars

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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.