Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: On geometrically finite degenerations
Speaker: Yusheng Luo, University of Michigan
Date: February 22, 2021
Time: 18:00:00 Hours
Venue: via Zoom
Abstract: The Sullivan dictionary provides a conceptual framework for understanding the connections between dynamics of rational maps and Kleinian groups. In this talk, I will discuss some recent development of geometrically finite degenerations of rational maps motivated by the dictionary.
Title of Talk: On geometrically finite degenerations
Speaker: Yusheng Luo, University of Michigan
Date: February 22, 2021
Time: 18:00:00 Hours
Venue: via Zoom
Abstract: The Sullivan dictionary provides a conceptual framework for understanding the connections between dynamics of rational maps and Kleinian groups. In this talk, I will discuss some recent development of geometrically finite degenerations of rational maps motivated by the dictionary.
In particular, I will explain how to use this theory to understand the bumping structure of hyperbolic components and how to construct self-bumps, a phenomenon first discovered by McMullen on the Bers boundary and later generalized and studied by Bromberg, Anderson, Canary and McCullough.
I will also talk about how the analogues of a double limit theorem and Thurston’s compactness theorem can be deduced for this setting.