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math.DS2026
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…
math.DS2026
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…
math.DS2026
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…