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Mathematical Physics Seminar

Resurgent Extrapolation: Painleve I

Gerald Dunne - University of Connecticut 

Location:  Hill 705
Date & time: Thursday, 31 October 2019 at 12:00PM - 1:00PM

Abstract:  I describe some recent work developing new extrapolation and summation techniques using ideas from resurgent asymptotics. The motivation is both physical and mathematical: given a finite number of terms in a perturbative expansion (typically asymptotic), how much physical information can be extracted? This very practical physics question is surprisingly rich mathematically. Pade approximation combined with conformal mapping yields dramatically better extrapolations, because it takes advantage of the underlying resurgent structure. As an example: for the Painleve I equation, a modest number of terms in the asymptotic expansion about infinity leads to a remarkably accurate extrapolation throughout the complex plane, even across non-linear Stokes transitions into the pole region.

This is based on recent and ongoing work with Ovidiu Costin.


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