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Geometry and Topology Seminar

Friday, February 17, 2023
4:00pm to 5:00pm
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Online Event
Boundedness problems in conformal dynamics
Yusheng Luo, Institute for Mathematical Sciences, Stony Brook University,

In 1980s, Thurston's formulated the geometrization conjecture for 3-manifolds, and proved the hyperbolization theorem. The keys to Thurston's proof are two bounded results for certain deformation spaces of Kleinian groups. In early 1990s, motivated by Thurston's boundedness theorem and the Sullivan dictionary, McMullen conjectured that certain hyperbolic components of rational maps are bounded.

In this talk, I will start with a historical discussion on a general strategy of the proof of Thurston's boundedness theorem. I will then explain how a similar strategy could work for rational maps, and discuss some recent breakthrough towards McMullen's boundedness conjecture.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit