Birational Kleinian groups

Yuan Zhao

I will present a classification result concerning a generalization of Kleinian groups to complex dimension two. It is first based on a detailed understanding of dynamics of automorphisms/birational transformations on complex surfaces. I will start from an introduction to birational dynamics on algebraic surfaces; the key object is an infinite dimensional hyperbolic space on which every transformation acts. Then I will explain briefly how to combine surface dynamics with Kahler groups, holomorphic foliations to attack the problem. At last I will focus on a unsolved case in the classification that leads to a dynamical problem on infinite dimensional Teichmüller spaces.

http://scgp.stonybrook.edu/video_portal/video.php?id=4562

Simons- Program: Renormalization and universality in Conformal Geometry, Dynamics, Random Processes, and Field Theory