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SUMMARY:Peter Miller (University of Michigan)
DTSTART:20220111T140000Z
DTEND:20220111T150000Z
DTSTAMP:20260422T201358Z
UID:CAvid/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/61/">R
 ational solutions of the Painlevé-IV equation with large parameters</a>\n
 by Peter Miller (University of Michigan) as part of CAvid: Complex Analysi
 s video seminar\n\nLecture held in N/A.\n\nAbstract\nThe Painlevé-IV equa
 tion has two families of rational solutions\, which can be represented in 
 terms of special polynomials called generalized Hermite polynomials and ge
 neralized Okamoto polynomials\, respectively.  The generalized Hermite pol
 ynomials have a convenient representation in terms of Hankel determinants 
 for a suitable weight and hence can be identified with norming constants f
 or certain pseudo-orthogonal polynomials.  This connection provides a path
  to the analysis of the generalized Hermite rationals when the parameters 
 are large\; however it is not known whether the generalized Okamoto polyno
 mials have a similar representation.  In this talk\, we explain how the is
 omonodromic approach places both families of rational solutions in terms o
 f special cases of the Riemann-Hilbert inverse monodromy problem for Painl
 evé-IV.  This allows techniques from steepest descent theory to be used t
 o analyze both families of rational solutions within a common analytical f
 ramework.  This is joint work with Robert Buckingham.\n
LOCATION:https://researchseminars.org/talk/CAvid/61/
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