Speaker: Sabyasachi Mukherjee, TIFR Mumbai
November 29, 2024 04:00 PM
- 05:00 PM
Abstract:
Various connections and philosophical analogies exist between two branches of conformal dynamics; namely, rational dynamics on the Riemann sphere and actions of Kleinian groups. In an attempt to study these common features in a unified framework, we construct combinations/matings of complex polynomials and Fuchsian groups realized as iterated algebraic correspondences. This gives rise to 'products' of Teichmüller spaces of genus zero orbifolds and parameter spaces of polynomials inside the space of algebraic correspondences, which allows one to see these objects through a common lens. We will discuss compactifications of such copies of Teichmüller spaces, and end with a host of open questions. (Based on joint works with Yusheng Luo, Mikhail Lyubich, and Mahan Mj.)