With roots over a century old in the work of mathematicians such as Fatou and Julia, complex dynamics has experienced a resurgence over the past 40 years, capturing the popular imagination but also attracting the attention of a growing number of Fields medalists. Part of the appeal is its diverse connections to abstract algebra, algebraic geometry, geometric topology, measure theory, and other fields. The first half of this course will develop the basic theory of iteration of rational functions: local models for periodic points, classification of Fatou components, hyperbolicity. The second part will emphasize recent outward-facing developments, including research questions related to Milnor-Thurston kneading theory, group theory, and Thurston’s characterization theorem for rational maps. 

 

This course is intended for students with a basic understanding of analysis and complex analysis, and will be based in part on “Iteration of Rational Functions” by Alan Beardon.

 

Registration:

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