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SUMMARY:Isomonodromic tau functions\, the constructive approach to conform
 al maps\, and black holes. - Bruno Carneiro da Cunha (Universidade Federal
  de Pernambuco)
DTSTART:20190911T090000Z
DTEND:20190911T100000Z
UID:TALK129382@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Recent developments on the relation between the Riemann-Hilber
 t problem and the representation theory of Virasoro algebras allowed for e
 xplicit expansions of the isomonodromic tau functions in terms of conforma
 l blocks. In this talk I will describe how these expansions can be used to
  constructively solve the connection problem of ordinary differential equa
 tions of the Fuchsian type.  The simplest non-trivial case of 4 regular si
 ngular points (the Heun equation) -- as well as a particular confluent lim
 it -- are solved by generic Painlev&eacute\; transcendents of the sixth an
 d fifth type. On the formal side\, these relations allow us to conjecture 
 an interpretation of the zeros of the tau functions in the general case. O
 n the application side\, the explicit expansions are useful for high preci
 sion numerical calculations of the accessory parameters of conformal maps\
 , as well as the determination of (quasi)-normal modes of metric vibration
 s for a variety of black hole backgrounds in general relativity.  <br> <br
 > Co-authors include: T. Anselmo\, J.-J. Barrag&aacute\;n-Amado\, J. P. Ca
 valcante\, R. Nelson\, D. Crowdy and E. Pallante.
LOCATION:Seminar Room 1\, Newton Institute
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