### Thurston theory in complex dynamics: a tropical perspective

Geometry and Topology Seminar

21st May 2024, 2:00 pm – 3:00 pm

Fry Building, 2.04

A rational function in one complex variable defines a branched covering from Riemann sphere CP^1 to itself. In the 1980s, William Thurston proved a theorem addressing the question: which branched coverings of the topological sphere S^2 are (suitably equivalent to) rational functions on CP^1? Thurston’s theorem is still central in one-variable complex and arithmetic dynamics.

Tropical geometry is a field in which polyhedral geometry and combinatorics are used to describe degenerations in algebraic geometry. There are connections with geometric group theory; for example, Culler-Vogtmann Outer Space is closely related to the space of tropical curves.

I will introduce Thurston’s theorem and describe a connection with tropical geometry.

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