International conference
Combinatorial Methods in Physics and Knot Theory

Dimitri ZVONKINE (Paris-7 Jussieu): Models of 2-dimensional gravity and enumeration of ramified coverings of the sphere

We explain why the enumeration of ramified coverings of the sphere provides a model of 2-dimensional gravity. We show how to obtain the values of observables of 2-dimensional gravity using the asymptotic of the number of ramified coverings. We also prove some combinatorial results concerning ramified coverings of the sphere. The algebra of power series generated by \sum q^n n^n/n! and \sum q^n n^{n-1}/n! plays an important role. It appears naturally in elementary graph enumeration problems, in the intersection theory on moduli spaces of stable curves, and in the enumeration of ramified coverings.