Mathematical Physics Seminar

"We give an overview of the ideas and techniques relating these seemingly different subjects. I will start from the classical examples, such as enumeration of triangulations by means of one matrix model and counting of colored graphs (Ising model on planar graphs), and explain its relation to integrability and algebraic curves. I will metion the matrix model of dually weighted graphs (counting graphs with weighted valences of both vertices and faces). The solution uses the GL(N) character expansion method. I will also explain the relation of random graphs and matrix models to random surfaces, 2D quantum gravity and toy models of strings."