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UID:20251019T001428EDT-2603WWF4hs@132.216.98.100
DTSTAMP:20251019T041428Z
DESCRIPTION:Title: Holomorphic motions\, conformal welding and capacity\n	Ab
 stract: The notion of a holomorphic motion was introduced by Mane\, Sad an
 d Sullivan in the 1980's\, motivated by the observation that Julia sets of
  rational maps often move holomorphically with holomorphic variations of t
 he parameters. Even though the original motivation for their study came fr
 om complex dynamics\, holomorphic motions have found over the years to be 
 of fundamental importance in other related areas of Complex Analysis\, suc
 h as the theory of Kleinian groups and Teichmuller theory for instance. Ho
 lomorphic motions also played a central role in the seminal work of Astala
  on distortion of dimension and area under quasiconformal mappings. In thi
 s talk\, I will first review the basic notions and results related to holo
 morphic motions\, including quasiconformal mappings and the (extended) lam
 bda lemma. I will then present some recent results on the behavior of loga
 rithmic capacity and analytic capacity under holomorphic motions. As we wi
 ll see\, conformal welding (of quasicircle Julia sets) plays a fundamental
  role. This is joint work with Tom Ransford and Wen-Hui Ai.\n\n \n\nFor zo
 om seminar log info please contact dmitry.jakobson [at] mcgill.ca\n
DTSTART:20200515T183000Z
DTEND:20200515T193000Z
SUMMARY:Malik Younsi (Hawaii)
URL:/mathstat/channels/event/malik-younsi-hawaii-32210
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