Boundedness problems in conformal dynamics

Seminar on Algebraic and Complex Dynamics

About the Seminar

More information about the seminar can be found at:

https://ywfan-math.github.io/ADCD.html

Abstract

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.

Speaker

I am a Milnor Lecturer at IMS, Stony Brook University. I was a postdoc assistant professor at University of Michigan, Ann Arbor. I got my PhD from Harvard University in 2019, advised by Curtis McMullen.

My research is in dynamics and geometry, especially the dynamics of rational maps on the Riemann sphere, the corresponding moduli space, and its interplays with Kleinian groups, hyperbolic geometry, Teichmuller theory and Berkovich dynamics.

Home page

sites.google.com/view/yushengmath