Wednesday July 16th, 2025 | |
| Time: | 2:15 PM - 3:15 PM |
| Title: | Beyond the Punctured Sphere: Mating Fuchsian Groups with Power Maps |
| Speaker: | Yusheng Luo, Cornell University |
| Abstract: | |
The matings of the modular group and a quadratic polynomials, first introduced by Penrose and Bullet, has inspired a broad program to explore the dynamical correspondences between Kleinian groups and rational maps. While there has been a lot of recent new developments on these construction, all known examples of such matings involve essentially punctured sphere groups. In this talk, I want to explain an on-going project with Mahan Mj and Sabya Mukherjee on extending these results to other groups. I will explain that any non-compact Fuchsian group can be virtually mated with a power map via a David homeomorphism; and any compact Fuchsian group can be virtually quasiconformally mated with a power map - possibly excluding compact triangle groups. The talk will go through various examples to illustrate the construction. I will also discuss some prospects and obstacles for an algebraic description of such matings. | |