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SUMMARY:Mikhail Hlushchanka (Utrecht University)
DTSTART:20220110T143000Z
DTEND:20220110T154500Z
DTSTAMP:20260423T021349Z
UID:BODS/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BODS/23/">Ca
 nonical decomposition of rational maps</a>\nby Mikhail Hlushchanka (Utrech
 t University) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nThe
 re are various classical and more recent decomposition results in mapping 
 class group theory\, geometric group theory\, and complex dynamics (which 
 include celebrated results by Bill Thurston). The goal of this talk is to 
 introduce a novel powerful decomposition of rational maps based on the top
 ological structure of their Julia sets. Namely\, we will discuss the follo
 wing result: every postcritically-finite rational map with non-empty Fatou
  set can be canonically decomposed into crochet maps (these have very "thi
 nly connected" Julia sets) and Sierpinski carpet maps (these have very "he
 avily connected" Julia sets). If time permits\, I will discuss application
 s of this result in various aspects of geometric group theory. Based on a 
 joint work with Dima Dudko and Dierk Schleicher.\n
LOCATION:https://researchseminars.org/talk/BODS/23/
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