Event Title: OR
Speaker Last Name:    OR
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Mathematics Colloquium


Date:  Tuesday, January 14, 2014

Title:  Parabolic Blowups, and a new entry in the Sullivan Dictionary

Abstract:  Sullivan proposed a dictionary relating 1-dimensional complex dynamics on one side and 3-dimensional hyperbolic geometry on the other. I will propose a new entry in the dictionary: 1) Parabolic implosion, as developed by Douady, Lavaurs, Shishikura, Buff, and many others on the dynamics side, and 2) Geometric limits, non-local connectivity of parameter spaces, and ``bumponomics'', as developed by Thurston, Kerckhoff, Bromberg, Canary and many others, on the hyperbolic geometry side. I propose to relate both topics using the notion of parabolic blowups, which explain many of the features observed in both fields.

Speaker:  John Hubbard
Institution:  Cornell University


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