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…
Uniform a priori bounds for neutral renormalization. Variation II: -ql Siegel maps
Dzmitry Dudko, Yusheng Luo, Mikhail Lyubich
We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to -quadratic-like Siegel maps. In this form, the bounds are compatible with the -quadratic…
Sierpinski carpet hyperbolic components of disjoint type are bounded
Dzimitry Dudko, Yusheng Luo
We establish certain uniform a priori bounds for hyperbolic components of disjoint type. As an application, we will prove that Sierpinski carpet hyperbolic components of disjoint t…