Canonical decomposition of rational maps

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• Mikhail Hlushchanka (Utrecht)
• Wednesday 03 May 2023, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

There 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 topological structure of their Julia sets. Namely, we will discuss 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 (these have very “heavily connected” Julia sets). If time permits, I will discuss applications of this result in various aspects of geometric group theory. Based on a joint work with Dima Dudko and Dierk Schleicher.

This talk is part of the Differential Geometry and Topology Seminar series.

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