# Eigenvalue Problems in the Complex Plane

*by Mark Sorrell*

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

*Date: Tue 25th August 2009*

*Time: 1:00 PM*

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

*Abstract*: I will introduce eigenvalue problems in the complex plane as a natural extension of eigenvalue problems on the real line. I will then work through an example of a particular eigenvalue problem, and the properties of asymptotic forms of its solution. The spectral determinants of these problems obey functional relations, analogous to ones occurring in some integrable systems, hence giving a concrete example of the Ordinary Differential Equation / Integrable Models correspondence (ODE/IM).

If time permits, we may make a short foray into the wacky world of PT-symmetry.

Good reference:

Patrick Dorey, Clare Dunning and Roberto Tateo, "The ODE/IM Correspondence", Journal of Physics A (Mathematical and Theoretical), 40(32):p205-p281, [hep-th/0703066].

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