Wednesday October 20th, 2021 | |
| Time: | 2:30 PM - 3:30 PM |
| Title: | The boundaries of the main hyperbolic component |
| Speaker: | Yusheng Luo, Stony Brook University |
| Abstract: | |
| Hyperbolic polynomials or rational maps form an open and conjecturally dense subset in the moduli space. A connected component is called a hyperbolic component. The topology of the hyperbolic compoennts has been studied extensively in various different settings. However, the boundaries of hyperbolic components and the interactions between different hyperbolic components remain very mysterious. In this talk, we will discuss how `quasi post-critically finite' degenerations of Blaschke products allows us to investigate these questions. In particular, we will use it to 1) classify geometrically finite polynomials on the boundary of the main hyperbolic component of degree d polynomials. 2) construct a self-bump on the boundary of the main hyperbolic component, and thus show the closure of the main hyperbolic component is not a manifold with boundary for degree > 3. | |