5 papers
Combining cusped triangle groups with Blaschke products: commensurable matings
Yusheng Luo, Mahan Mj, Sabyasachi Mukherjee
In this note, we construct algebraic correspondences as matings of Fuchsian -triangle groups with Blaschke products. Combined with the results of [MM25], this proves…
Teichmüller spaces, polynomial loci, and degeneration in spaces of algebraic correspondences
Yusheng Luo, Mahan Mj, Sabyasachi Mukherjee
We develop an analog of the notion of a character variety in the context of algebraic correspondences. It turns out that matings of certain Fuchsian groups and polynomials are cont…
Universality of the Basilica
Yusheng Luo, Mahan Mj, Sabyasachi Mukherjee
We establish universality of the fat Basilica Julia set in conformal dynamics in the following sense: is quasiconformally equivalent to the fat Ba…
Simultaneous Uniformization and Algebraic Correspondences
Mahan Mj, Sabyasachi Mukherjee
We prove a generalization of Bers' simultaneous uniformization theorem in the world of algebraic correspondences. More precisely, we construct algebraic correspondences that simult…
Landing rays and ray Cannon-Thurston maps
Rakesh Halder, Mahan Mj, Pranab Sardar
In this paper, we describe a procedure to construct pairs of hyperbolic groups with the following properties. 1) Every geodesic ray in converges to a point $ξ_γ\in…