Speaker
Ivan Kostov
Description
We study a two-matrix model which generates the higher-genus Fuss--Catalan numbers as the coefficients of its $1/N$-expansion. The genus-$g$ Fuss-Catalan number counts the number of ways to obtain a genus-$g$ surface by identifying the edges of a $pn$-gone via $p$-valent hyperedges. For $p=2$ our model reduces to the the Gaussian matrix model which generates the higher genus Catalan numbers. We obtain an explicit formula for the higher genus $p$-Fuss-Catalan numbers which generalises the Harer-Zagier formula for $p>2$.