School Seminars and Colloquia

From discrete surfaces and matrix models to topological recursions IV

Miscellaneous Seminar

by Nicholas Orantin


Institution: CERN Geneva
Date: Fri 26th March 2010
Time: 1:00 PM
Location: JH Michell Theatre, Richard Berry Building, The University of Melbourne

Abstract: This lecture shows how a Riemann surface arises from a matrix model as a branched cover with known periods of a holomorphic differential
over the Riemann surface. Random matrix models represent a wonderful
tool in the enumeration of random discrete surfaces of given topology.
These lectures will address three issues. I will first properly define the concept of formal matrix integral used to build generating functions of discrete surfaces. I will then show that the enumeration of all possible ways of removing one edge from such a surface gives a set of loop equations which can be solved by induction in terms of an algebraic curve characterizing the considered matrix model: the spectral curve.

For More Information: contact: Paul Norbury. email: p.norbury@ms.unimelb.edu.au