# Past Mathematical Physics Seminar

26 September 2007
16:15
H. Sakai
Abstract
• Mathematical Physics Seminar
26 September 2007
15:00
Peter Clarkson
Abstract
• Mathematical Physics Seminar
26 September 2007
14:15
Y. Ohyama
Abstract
• Mathematical Physics Seminar
19 September 2007
16:15
Dr H. Sakai
Abstract
• Mathematical Physics Seminar
19 September 2007
15:00
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.
• Mathematical Physics Seminar
19 September 2007
14:15
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.
• Mathematical Physics Seminar
19 May 2006
12:00
Leonid Chekhov
Abstract
• Mathematical Physics Seminar