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SUMMARY:Two optimization problems of the Loewner energy
DTSTART:20260515T133000Z
DTEND:20260515T150000Z
DTSTAMP:20260523T230800Z
UID:indico-event-16570@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Yilin Wang (ETH Zürich)\n\nSéminaire d'Analyse\nA 
 Jordan curve on the Riemann sphere can be encoded by its conformal welding
  homeomorphism\, which is a circle homeomorphism. I will explain that this
  correspondence should be viewed as a canonical correspondence between a J
 ordan curve in the boundary of hyperbolic 3-space H3 and a positive curve 
 on the boundary of AdS3 space.\nThe Loewner energy measures how far a Jord
 an curve is away from being a circle or\, equivalently\, how far its weldi
 ng homeomorphism is away from being Möbius. It arises as the action of ra
 ndom curves SLE\, Kähler potential of Weil-Petersson universal Teichmüll
 er space\, Fredholm determinant of Grunsky operator\, free energy of Coulo
 mb gas on a Jordan curve\, and a renormalized volume of H3\, etc. All thes
 e links refer to either the curve description or the welding description o
 f the Loewner energy.\nI will discuss two optimizing problems for the Loew
 ner energy\, one under the constraint for the curve to pass through n give
 n points on the Riemann sphere and the other under the constraint for the 
 welding curve to pass through n given points in the boundary of AdS3. Thes
 e two problems exhibit many symmetries that are poorly understood\, but do
  suggest that the Loewner energy sits right in the middle of two perspecti
 ves (curve/welding).\n========\nPour être informé des prochains séminai
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 ps du message vide.\n\nhttps://indico.math.cnrs.fr/event/16570/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/16570/
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