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SUMMARY:Isomonodromy and the accessory parameter problem for conformal map
 s - Bruno Carneiro da Cunha (Universidade Federal de Pernambuco)
DTSTART:20230728T133000Z
DTEND:20230728T140000Z
UID:TALK202834@talks.cam.ac.uk
DESCRIPTION:A classical result in complex analysis relates the uniformizin
 g map of a given simple domain to the ratio of solutions of a second order
  ordinary differential equation of the Fuchsian type. Despite its simplici
 ty\, the usefulness of this relation to the actual construction of the map
  has been hindered by the problem of fixing the parameters of the equation
  given the geometrical information of the domain. In this talk we will out
 line a solution for this problem for simply-connected domains bounded by a
 rcs of circles\, as well as present the new type of special functions invo
 lved in the solution\, the semi-classical conformal block. We will illustr
 ate the technique by considering a few examples numerically.\nThis work wa
 s done in collaboration with Tiago Anselmo\, Salman Abarghouei Nejad\, Rho
 dri Nelson and Darren Crowdy
LOCATION:Seminar Room 1\, Newton Institute
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