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SUMMARY:Nonlinear Riemann-Hilbert Problems: History\, Results and Question
 s - Elias Wegert (Technische Universität Bergakademie Freiberg)
DTSTART:20230725T133000Z
DTEND:20230725T140000Z
UID:TALK202783@talks.cam.ac.uk
DESCRIPTION:In my opinion the (general) Riemann-Hilbert problem (RHP) is T
 HE fundamental boundary value problem in complex analysis. It comprises th
 e well-known linear boundary and transmission problems of Riemann-Hilbert 
 type\, but also conformal mapping and conformal welding and has interrelat
 ions with singular integral equations\, Toeplitz operators\, Wiener-Hopf f
 actorization\, and extremal problems in geometric function theory.\nThough
  many aspects of the problem are by now fairly well understood\, the probl
 em has not yet received the attention it deserves. A main aim of the talk 
 is to stimulate the interest of the young generation in this fascinating t
 opic and to encourage further research in theory and applications of RHPs.
 This includes the development of universal numerical methods and a direct 
 proof of the existence of solutions via an extremal principle that general
 izes Caratheodory's principle for conformal mappings.
LOCATION:Seminar Room 1\, Newton Institute
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