Alexander Its (Indianapolis)
A conformal block approach to the connection problem
of the third Painleve equation
Abstract:
In the recent series of papers of O. Gamayun, N. Igorov, O.
Lisovyy, A. Shchechkin, J. Teschner, and Yu. Tykhyy a novel approach to
the analysis of the Painleve equations has been suggested. The method
is based on the Virasoro conformal block representation of the relevant
tau-functions, and it allows, in particular, to evaluate the constant
term in
the asymptotics of the Painleve VI tau-function. It should be
mentioned that the evaluation
of the constant terms in the asymptotics of tau-fucntions is a very
serious challenge
for the usual Riemann-Hilbert isomonodromy method. In the talk, the
conformal
block technique will be extended to the case of the third Painleve
equation. A new feature which needs to be taken care of is the presence
of the irregular singularities in the problem.
This is the joint work with O. Lisovyy and Yu. Tykhyy.