8 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…
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…
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…
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 \p…
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…
Tight contact structures on hyperbolic homology 3-spheres
Mahan Mj, Balarka Sen
We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many disti…
Cubulating Drilled bundles over graphs
Mahan Mj, Biswajit Nag
We start with a Gromov-hyperbolic surface bundle over a graph, and drill out essential simple closed curves from fibers to obtain a drilled bundle . We prove that for such d…
Indiscrete Common Commensurators
Jingyin Huang, Mahan Mj
We develop a framework for common commensurators of discrete subgroups of lattices in isometry groups of CAT(0) spaces. We show that the Greenberg-Shalom hypothesis about discreten…