Matrix models and statistical mechanical models on random geometries
by Alex Lee
Abstract: Partition functions involving integrations over matrices, also known as matrix models, can describe statistical mechanical systems where the underlying geometry is allowed to fluctuate. Recently, Eynard and Orantin developed a method for solving such systems on surfaces of arbitrary Euler characteristic. Their theory has since been applied to a number of well-known systems including the Ising, Potts and O(N) loop models and has also found applications in other areas of mathematics.
In this talk, I will give a basic introduction to the theory of matrix models with particular emphasis on the 1-matrix model, which describes discrete random surfaces, and the 2-matrix model, describing the Ising model on random geometries. I will show how such systems are generated from a perturbative expansion of the matrix integral, along with a few simple rules, and also how the partition functions of the models are calculated. Finally, I will mention some of the challenges encountered when trying to solve more complicated matrix models such as the Potts model and loop models.
For More Information: contact: Mark Sorrell. email: firstname.lastname@example.org