Alexander Its (Indianapolis)
A conformal block approach to the connection problem
of the third Painleve equation
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
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
for the usual Riemann-Hilbert isomonodromy method. In the talk, the
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.