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SUMMARY:Canonical decomposition of rational maps - Mikhail Hlushchanka (Ut
 recht)
DTSTART:20230503T150000Z
DTEND:20230503T160000Z
UID:TALK199360@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:There are various classical and more recent decomposition resu
 lts in mapping class group theory\, geometric group theory\, and complex d
 ynamics (which include celebrated results by Bill Thurston). The goal of t
 his talk is to introduce a novel powerful decomposition of rational maps b
 ased on the topological structure of their Julia sets. Namely\, we will di
 scuss the following result: every postcritically-finite rational map with 
 non-empty Fatou set can be canonically decomposed into crochet maps (these
  have very "thinly connected" Julia sets”) and Sierpinski carpet maps (t
 hese have very "heavily connected" Julia sets). If time permits\, I will d
 iscuss applications of this result in various aspects of geometric group t
 heory. Based on a joint work with Dima Dudko and Dierk Schleicher.
LOCATION:MR13
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