The following seminar will be held as an activity of Webseminar 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

17:3018:30 (JST) 12 May (Wed), 2021


Abstract: 



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 RiemannHilbert 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 RiemannHilbert correspondence.


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