Document 10485246

Virgil Pierce Associate Professor University of Texas-­‐Pan American April 14, 2015 OSB A327 12:30pm TITLE: Random triangulations of genus g surfaces ABSTRACT: The generating function of polygonizations of oriented surfaces is a tau-­‐function of the Toda lattice hierarchy and a partition function for an ensemble of random matrices. Tau-­‐functions are generating function for solutions of integrable hierarchies of PDEs, and in this case satisfy the well known KP hierarchy of equations. We exploited these facts to derive solutions to the enumeration problem of polygonizations partitioned by the genus of the surface for some special cases. Results can be checked by enumerating these triangulations using algorithms which check all possible configurations. An alternative approach is to utilize algorithms which randomly sample configurations. We will examine the connections between this random sampling approach and the explicitly known results for the generating functions we have found.