# From discrete surfaces and matrix models to topological recursions III

This is the third lecture in a series which will take place this semester each Friday 1-3pm

*by Nicholas Orantin*

*Institution:*

*Date: Fri 19th March 2010*

*Time: 1:00 PM*

*Location: JH Mitchell Theatre, Richard Berry Building, The University of Melbourne*

*Abstract*: This lecture focuses on manipulating discrete surfaces and interpreting this in terms of matrix integrals. 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