

6th International Workshop on Combinatorics of Moduli Spaces, Cluster Algebras, and Topological Recursion
June 4, 2018 17:00–17:40, Moscow, Higher School of Economics






Generalisations of the HarerZagier recursion for 1point functions
Norman Do^{} 
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Abstract:
n their work on Euler characteristics of moduli spaces of curves, Harer and Zagier proved a recursion to enumerate gluings of a 2dgon that result in an orientable genus g surface. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: How large is the family of problems for which these socalled 1point recursions exist? In joint work with Anupam Chaudhuri, we prove the existence of 1point recursions for a class of enumerative problems that have Schur function expansions. In particular, we recover the HarerZagier recursion, but our methodology also applies to the enumeration of dessins d’enfant, to monotone Hurwitz numbers, and more. On the other hand, we prove that there is no 1point recursion that governs simple Hurwitz numbers. Our results are effective in the sense that one can explicitly compute particular instances of 1point recursions. We conclude with a brief discussion of relations between 1point recursions and the theory of topological recursion
Language: English

