21/07/2016, 16:20 — 17:00 — Amphitheatre Ea1, North Tower, IST
Marcel Vonk, University of Amsterdam

Two-Parameter Transseries for Painlevé I

The Painlevé I equation is one of the most studied non-linear ordinary differential equations. Its solutions have been constructed in many different frameworks, including numerics, perturbative series, resurgent transseries and transasymptotic expansions. Several of these approaches have also been related to each other in the literature, but mostly for a particular one-parameter transseries subfamily of solutions, and often only in restricted domains of the complex plane. Using resurgent transseries as a starting point, we show how this domain can be extended, which allows to study the famous pole fields in the Painlevé I solutions in much more detail. Moreover, our techniques can be extended to the full two-parameter family of Painlevé transseries solutions, and uncover interesting relations to modularity.

See also

R-vonk.pdf