|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