BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yilin Wang (MIT\, USA) DTSTART:20210928T130000Z DTEND:20210928T140000Z DTSTAMP:20260422T201115Z UID:CAvid/49 DESCRIPTION:Title: L oewner-Kufarev energy and foliations by Weil-Petersson quasicircles\nb y Yilin Wang (MIT\, USA) as part of CAvid: Complex Analysis video seminar\ n\nLecture held in N/A.\n\nAbstract\nWe use Loewner-Kufarev equation to de scribe evolutions of univalent functions and introduce an energy on the dr iving measure\, called Loewner-Kufarev energy. We show that when this ener gy is finite\, the boundaries of the evolving image domains are Weil-Peter sson quasicircles which form a foliation of the Riemann sphere. Weil-Peter sson quasicircles are studied in Teichmuller theory\, geometric function t heory\, and string theory by both mathematicians and physicists. More than 20 equivalent definitions of this class of Jordan curves are discovered s o far. In particular\, it is characterized as the class of curves having f inite Loewner energy which was also introduced recently. Furthermore\, we show that the Loewner-Kufarev energy is dual to the Loewner energy and exh ibits remarkable symmetries. Both energies and their duality result are in spired by ideas from the probabilistic theory of Schramm-Loewner evolution s. This is a joint work with Fredrik Viklund (KTH).\n\nReferences: \n\nThe Loewner-Kufarev energy and foliations by Weil-Petersson quasicircles\nFre drik Viklund\, Yilin Wang (2020)\nhttps://arxiv.org/abs/2012.05771\n LOCATION:https://researchseminars.org/talk/CAvid/49/ END:VEVENT END:VCALENDAR