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SUMMARY:Canonical decomposition of rational maps
DTSTART:20250411T091500Z
DTEND:20250411T101500Z
DTSTAMP:20260504T201300Z
UID:indico-event-14169@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mikhail Hlushchanka (University of Amsterdam)\n\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 powerful decomposition of rational maps based on the topologic
 al structure of their Julia sets. Namely\, we will discuss the following r
 esult: every postcritically-finite rational map with non-empty Fatou set c
 an be canonically decomposed into crochet maps (these have very "thinly co
 nnected" Julia sets”) and Sierpinski carpet maps (these have very "heavi
 ly connected" Julia sets). If time permits\, I will discuss applications o
 f this result in various aspects of geometric group theory. Based on a joi
 nt work with Dima Dudko and Dierk Schleicher.\n\nhttps://indico.math.cnrs.
 fr/event/14169/
URL:https://indico.math.cnrs.fr/event/14169/
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