Baptiste Louf: Counting Ising maps in every genus

Abstract:

We consider the Ising model on combinatorial maps (i.e. graphs on surfaces), more precisely we obtain a (polynomial time) algorithm to compute the partition function of Ising triangulations of a surface of genus g with 2n triangles. The main tools we use are equations coming from the KP hierarchy (a set of integrable PDEs which first arose in mathematical physics) and a correspondence between Ising maps and bipartite maps. 

Joint work with Mireille Bousquet-Mélou and Ariane Carrance