# Introduction to associated linear problems for Painleve equations

*by Chris Ormerod*

*Institution:*Mathematics and Statistics Dept, The University of Melbourne

*Date: Tue 20th October 2009*

*Time: 1:00 PM*

*Location: Room 107, Richard Berry Building, The University of Melbourne*

*Abstract*: One may consider a system integrable if it is solvable via a system of associated linear problems, called Lax pairs. One may derive a representation of the fundamental group of the complex plane with holes punched in it from a system of differential equations. This representation is called the monodromy representation. All the Lax pairs for the Painleve equations are equivalent to conditions required so that some monodromy representation is preserved. We shall give an elementary introduction to these classical concepts and the theory behind monodromy preserving deformations and present some simple cases of this theory.

*For More Information:* contact: Chris Ormerod. email: C.Ormerod@ms.unimelb.edu.au