Circle Packings, Kissing Reflection Group and Critically Fixed Anti-rational Maps
Time: 2021-04-07
Published By: He Liu
Speaker(s): Yusheng Luo (Stony Brook University)
Time: 09:00-10:00 April 12, 2021
Venue: Online
Circle packings appear frequently in the studies of dynamics, geometry. One can naturally associate a reflection group to a finite circle packing, generated by reflections along the corresponding circles. In this talk, we will establish an explicit correspondence between such reflection groups with anti-holomorphic maps of the Riemann sphere where all the critical points are fixed. We will explore the correspondence both in the dynamical plane and the parameter spaces. In particular, we will explain how the analogue of Thurston’s compactness theorem for acylindrical hyperbolic 3-manifold holds for critically fixed anti-rational maps.
We will also brief discuss some open questions motivated by the correspondence.
Zoom ID: 677 2262 6461
Password: 304728
