Doron Puder, Tel Aviv University

Matrix integrals, graphs on surfaces, and mapping class group.

Since the 1970's, physicists and mathematicians who study random matrices in the GUE or GOE models are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new aspect of this theory: for random matrices sampled from the classical groups U(n), O(n), or Sp(n). The group structure of these matrices allows us to go further and find surprising algebraic quantities hidden in the values of these integrals. The talk will be aimed at a wide audience, and all notions will be explained. Based on joint work with Michael Magee (Durham).