Monday, November 10, 2008 - 14:00
1 hour (actually 50 minutes)
It is easy to ask for the number T(g,n) of (rooted) graphs with n edges on a surface of genus g. Bender et al gave an asymptotic expansion for fixed g and large n. The contant t_g remained missing for over 20 years, although it satisfied a complicated nonlinear recursion relation. The relation was vastly simplified last year. But a further simplification was made possible last week, thus arriving to Painleve I. I will review many trivialities and lies about this famous non-linear differential equation, from a post modern point of view.