115 Robert Buckingham

Robert Buckingham (University of Cincinnati, USA) // Asymptotics of Rational Painlevé V Functions // Abstract: The Painlevé functions are a family of ordinary differential equations with myriad applications to mathematical physics and probability. The rational solutions of these equations have drawn attention for the remarkable geometric structure of their zeros and poles. We study the family of rational solutions of the Painlevé-V equation built from Umemura polynomials. We derive a new Riemann-Hilbert representation and use it to obtain the boundary of the pole region and the large-degree behavior in the pole-free region. This is joint work with Matthew Satter of the University of Cincinnati.