Title: Resurgent Extrapolation and Summation: Painleve I
Speaker: Gerald Dunne (University of Connecticut)
Abstract: A generic and important problem in mathematical physics is to learn as much as possible about a function from limited input based on an expansion to some truncated order. This talk explores a new procedure, using methods of resurgent asymptotics, to reconstruct the tritronquee solution to the Painleve I equation in the entire complex plane, starting from just a finite number of coefficients of an asymptotic expansion along the positive real line. Combinations of Borel summation, conformal mapping, Pade approximation and continued fractions lead to remarkable precision throughout the complex plane, even into the tritronquee pole region. The larger goal is a new high-precision method of extrapolation and summation for general non-integrable problems. This study is also motivated by recent results concerning relations between Painleve connection problems and certain Heun ODE spectral problems.
