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Thurston Theory and Application: Pt I

[HYBRID WORKSHOP] Introductory Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables February 08, 2022 - February 17, 2022

February 08, 2022 (10:45 AM PST - 11:45 PM PST)
Speaker(s): Dzmitry Dudko (Stony Brook University)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Thurston Theory And Application: Pt I


Thurston's theorem states that a post-critically finite branched self-covering of a sphere is combinatorially equivalent to a rational map if and only if it does not admit a certain kind of topological obstruction. The proof of the theorem uses iteration on the Teichmueller space, the so-called Thurston pullback map, to find an invariant complex structure. In the obstructed (and non-parabolic) case, the map diverges to the stratum at infinity associated with the canonical obstruction of the map. We will review properties of the Thurston pullback map and discuss its relation to the twisting problem of branched self-coverings of the sphere and other applications.

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Thurston Theory And Application: Pt I

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