Combinatorics Colloquium

Title:  New combinatorial identities derived from the theory of moduli of curves

Abstract: The standard multinomial coefficient recursion is of the form $\binom{n}{k_1,\ldots,k_m}=\sum_{i=1}^m \binom{n-1}{k_1,\ldots,k_{i-1},k_i-1,k_{i+1},\ldots,k_m}$, where $k_1+\cdots+k_m=n$.  We give new mysterious recursions coming from a computation on $\psi$ class products in the Chow ring of the moduli space $\overline{M}_{0,n}$ of n-pointed rational curves.  We also discuss the larger context in which these recursions can be generalized, to the "multicolored spaces", which are the largest class of compactifications of $M_{0,n}$ in which the $\psi$ class intersection numbers are necessarily positive.