Forthcoming events in this series


Wed, 19 Sep 2007
15:00
L3

Hankel determinant formulae for the Painlevé

Dr M. Mazzocco
Abstract
In this talk I'll explore the meaning of the Hankel determinant formula for the general solutions of the Painleve' equations both from the analytic and the geometric point of view. I'll start with the simple example of PII and I'll show how the generating function for the Hankel determinant satisfies two Riccati equations. These linearize into the Jimbo-Miwa-Ueno isomonodromic deformation problem. Indeed this occurs for all the Painleve' equations PII,..,PVI and it is due to the link between their solutions and the infinite Toda lattice equation. I'll then explore the geometric meaning of the Hankel determinants by looking at the (suitably defined) spectral curve of the Toda lattice equation.
Wed, 19 Sep 2007
14:15
L3

Monodromy evolving deformations and Halphen-type

Dr Y. Ohyama
Abstract
Chakravarty and Ablowitz (PRL vol.76 p.857, 1996). showed that a fifth-order equation arizing from the Bianchi IX system can be described asmonodromy evolving (non-preserving) deformations. In my talk, we will show that general Halphen-type systems, which comes from generic DH-IX systems, can be represented as monodromy evolving deformations.