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DTSTART:19700329T010000
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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Canonical decomposition of rational maps - Mikhail
  Hlushchanka (Utrecht)
DTSTART;TZID=Europe/London:20230503T160000
DTEND;TZID=Europe/London:20230503T170000
UID:TALK199360AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/199360
DESCRIPTION:There are various classical and more recent decomp
 osition results in mapping class group theory\, ge
 ometric group theory\, and complex dynamics (which
  include celebrated results by Bill Thurston). The
  goal of this talk is to introduce a novel powerfu
 l decomposition of rational maps based on the topo
 logical structure of their Julia sets. Namely\, we
  will discuss the following result: every postcrit
 ically-finite rational map with non-empty Fatou se
 t can be canonically decomposed into crochet maps 
 (these have very "thinly connected" Julia sets”) a
 nd Sierpinski carpet maps (these have very "heavil
 y connected" Julia sets). If time permits\, I will
  discuss applications of this result in various as
 pects of geometric group theory. Based on a joint 
 work with Dima Dudko and Dierk Schleicher.
LOCATION:MR13
CONTACT:Oscar Randal-Williams
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