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SUMMARY:Painlevé I and exact WKB: studying Stokes phenomenon analytically
  and numerically - Marcel Vonk (Universiteit van Amsterdam)
DTSTART:20221007T140000Z
DTEND:20221007T160000Z
UID:TALK182690@talks.cam.ac.uk
DESCRIPTION:I discuss recent work with Alexander van Spaendonck in which w
 e study the Stokes phenomenon of two-parameter solutions to the Painlev&ea
 cute\; I equation\, both analytically and numerically. On the analytical s
 ide we use the idea of isomonodromic deformation\, as studied by e.g. Take
 i and collaborators and Iwaki. We recover the exact expressions for the St
 okes data that were recently found by Baldino\, Schwick\, Schiappa and Veg
 a\, explain several ambiguities in relating parameter choices for transser
 ies solutions to actual Painlev&eacute\; transcendents\, and study the mon
 odromy of formal solutions. In the talk I also explain how one can numeric
 ally solve the Painlev&eacute\; I equation\, using ideas of Fornberg and W
 eideman\, to check analytic results in part of the full two-dimensional pa
 rameter space.
LOCATION:Seminar Room 2\, Newton Institute
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