# A Schroedinger equation for Catalan numbers

*by Professor Motohico Mulase*

*Institution:*University of California, Davis

*Date: Tue 5th March 2013*

*Time: 12:05 PM*

*Location: Russell Love Theatre, Richard Berry building*

*Abstract*: In this talk I will present a stationary Schroedinger equation that is obtained by the geometric quantization of the mirror symmetric dual of the Catalan numbers. Unexpectedly, the asymptotic expansion of a particular solution of this equation knows not only about the Catalan numbers and their higher-genus generalizations, but also the Euler characteristic of the moduli space of smooth pointed curves, the Witten-Kontsevich theory of intersection numbers on the compactified moduli space of stable curves, and the number of lattice points on these moduli

spaces. This is a concrete mathematical theorem that gives an evidence for the amazing physics conjecture that predicts the existence of a Schroedinger-type equation for many topological enumeration problems, including quantum knot invariants. The talk is aimed at an introduction to this exciting new development by many mathematicians and physicists.