Thurston theory in complex dynamics: a tropical perspective

Abstract: A rational function in one complex variable defines a branched covering from Riemann sphere $\mathbb{CP}^1$ 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 $\mathbb{CP}^1$? 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.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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