4 papers
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…
On topology and singularities of quadrature domains
Rashmita, Sabyasachi Mukherjee
We prove a linear upper bound for the number of singular points on the boundary of a quadrature domain, improving a previously known quadratic bound due to Gustafsson \cite{Gus88}.…
Antiholomorphic correspondences and mating II: Shabat polynomial slices
Mikhail Lyubich, Jacob Mazor, Sabyasachi Mukherjee
We study natural one-parameter families of antiholomorphic correspondences arising from univalent restrictions of Shabat polynomials, indexed by rooted dessin d'enfants. We prove t…
Correspondences on hyperelliptic surfaces, combination theorems, and Hurwitz spaces
Sabyasachi Mukherjee, S. Viswanathan
We construct a general class of correspondences on hyperelliptic Riemann surfaces of arbitrary genus that combine finitely many Fuchsian genus zero orbifold groups and Blaschke pro…