The following seminar will be held as an activity of Web-seminar on Painlevé equations and related topics.
It is also an activity of Kobe Seminar on Integrable Systems.
Please register at the form. We will inform you the address of the zoom seminar.

Martin Klimeš (University of Zagreb)
Confluent approach to Fifth Painlevé equation

17:30--18:30 (JST) 12 May (Wed), 2021


The Fifth Painlevé equation (PV) is obtained from the Sixth one (PVI) by confluence. In principle, this allows to transfer knowledge from PVI to PV, however, to do this, one needs to be able to deal with divergence. For PVI a great deal of information can be obtained from its nonlinear monodromy group, the elements of which act on solutions by analytic continuation along loops, and which has a well known representation through the Riemann-Hilbert correspondence as an explicit action on the character variety of the (linear) monodromy data. For PV the analogical object is the ``nonlinear wild monodromy pseudogroup'' which expresses not only the nonlinear monodromy but also the nonlinear Stokes phenomenon at the singularity at infinity. The goal of the talk is to show how one can obtain the corresponding action of this pseudogroup on the "wild character variety" of the (linear) monodromy and Stokes data by studying the confluence. To do this I will try to explain how the confluence PVI -> PV works on both sides of the Riemann-Hilbert correspondence.

Kobe Seminar on Hypergeometric Systems: List of Seminer Talks (Oct 1995-Jul 2002)
Kobe Seminar on Integrable Systems: List of Seminar Talks (Sep 2002-)

q, q & q
Feb 19-21, 2020
Department of Mathematics, Kobe University
[HP, lecture notes(2020/5/20更新)]

Kobe Workshop on Integrable Systems and Painlevé Systems (Nov 23-25, 2005, Kobe) [ program Texsouce file , PDF file ]
Workshop on Elliptic Integrable Systems (Nov 8-11, 2004, Kyoto) [lecture notes]
Global Analysis of Painleve Equations (Oct 26-29, 1999, Kobe) [Japanese]
Workshop on Hypergeometric Systems in Kobe '99(Nov 30-Dec 3, 1999, Kobe) [Japanese]