Publications and Pre-prints:
Universality of the Basilica (joint work with Yusheng Luo and Mahan Mj).
On topology and singularities of quadrature domains (joint work with Rashmita).
Antiholomorphic correspondences and mating II: Shabat polynomial slices (joint work with Mikhail Lyubich and Jacob Mazor).
Correspondences on hyperelliptic surfaces, combination theorems, and Hurwitz spaces (joint work with S. Viswanathan).
Uniformization of tongues in Double Standard Map family and variation of maximal chaotic sets (joint work with Kuntal Banerjee and Anubrato Bhattacharyya).
Teichmüller spaces, polynomial loci, and degeneration in spaces of algebraic correspondences (joint work with Yusheng Luo and Mahan Mj).
A general dynamical theory of Schwarz reflections, B-involutions, and algebraic correspondences (joint work with Yusheng Luo and Mikhail Lyubich).
Mating parabolic rational maps with Hecke groups (joint work with Shaun Bullett, Luna Lomonaco, and Mikhail Lyubich).
Algebraic correspondences and Schwarz reflections: Where rational dynamics meets Kleinian groups (joint work with Luna Lomonaco), to appear in the Proceedings of the ICM 2026.
Simultaneous Uniformization and Algebraic Correspondences (joint work with Mahan Mj), to appear in New Aspects of Teichmüller Theory, Adv. Stud. Pure Math.,
Mathematical Society of Japan, Tokyo, 2025.
Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz reflections, and correspondences (joint work with Mikhail Lyubich), to appear in Algebraic,
Complex, and Arithmetic Dynamics, edited by Mattias Jonsson and Laura DeMarco, Simons Symposia, Springer, 2025.
Matings, holomorphic correspondences, and a Bers slice (joint work with Mahan Mj), J. Éc. polytech. Math., 12:1445--1502, 2025.
David extension of circle homeomorphisms, welding, mating, and removability (joint work with Mikhail Lyubich, Sergei Merenkov, and Dimitrios Ntalampekos), Mem. Amer. Math. Soc., vol. 313, no. 1588, pp. v+110, 2025.
Schwarz reflections and the Tricorn (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), Ann. Inst. Fourier (Grenoble), 75:1987-2100, 2025.
Antiholomorphic correspondences and mating I: realization theorems (joint work with Mikhail Lyubich and Jacob Mazor), Comm. Amer. Math. Soc., 4:495–547, 2024.
Dynamics of Schwarz reflections: the mating phenomena (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), Ann. Sci. École Norm. Sup. (4), 56:1825–1881, 2023.
The Sullivan dictionary and Bowen-Series maps (joint work with Mahan Mj), EMS Surv. Math. Sci., 10:179-221, 2023.
Combining rational maps and Kleinian groups via orbit equivalence (joint work with Mahan Mj), Proc. London Math. Soc. (3), 126:1740-1809, 2023.
On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections (joint work with Russell Lodge, Mikhail Lyubich, and Sergei Merenkov), Conform. Geom. Dyn., 27:1-54, 2023.
On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps (joint work with Russell Lodge and Yusheng Luo), Geom. Funct. Anal., 32:1428-1485, 2022.
Combination theorems in groups, geometry and dynamics (joint work with Mahan Mj), in In the tradition of Thurston II (edited by K. Ohshika and A. Papadopoulos), pp 331–383, Springer, 2022.
Discontinuity of straightening in antiholomorphic dynamics: II (joint work with Hiroyuki Inou), Int. Math. Res. Not. IMRN, 2022(9):6948–6990, 2022.
Circle packings, kissing reflection groups and critically fixed anti-rational maps (joint work with Russell Lodge and Yusheng Luo), Forum Math. Sigma, vol. 10, e3, 2022.
Bers slices in families of univalent maps (joint work with Kirill Lazebnik and Nikolai Makarov), Math. Z., 300:2771-2808, 2022.
Univalent polynomials and Hubbard trees (joint work with Kirill Lazebnik and Nikolai Makarov), Trans. Amer. Math. Soc., 374:4839-4893, 2021.
Schwarz reflections and anti-holomorphic correspondences (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), Adv. Math., 385:107766, 2021.
Discontinuity of straightening in antiholomorphic dynamics: I (joint work with Hiroyuki Inou), Trans. Amer. Math. Soc., 374:6445-6481, 2021.
Invisible Tricorns in real slices of rational maps (joint work with Russell Lodge), Discrete Contin. Dynam. Systems, 41:1755-1797, 2021.
On the support of the bifurcation measure of cubic polynomials (joint work with Hiroyuki Inou), Math. Ann., 378:1-12, 2020.
A rigidity result for some parabolic germs (joint work with Luna Lomonaco), Indiana Univ. Math. J., 67:2089-2101, 2018.
Antiholomorphic perturbations of Weierstrass zeta functions and Green's function on tori (joint work with Konstantin Bogdanov, Khudoyor Mamayusupov, and Dierk Schleicher), Nonlinearity, 30:3241-3254, 2017.
Parabolic arcs of the Multicorns: real-analyticity of Hausdorff dimension, and singularities of Per_n(1) curves, Discrete Contin. Dynam. Systems, 37:2565-2588, 2017.
On Multicorns and Unicorns II: bifurcations in spaces of antiholomorphic polynomials (joint work with Shizuo Nakane, and Dierk Schleicher), Ergodic Theory Dynam. Systems, 37:859-899, 2017.
Rational parameter rays of the Multibrot sets (joint work with Dominik Eberlein, and Dierk Schleicher), in Dynamical Systems, Number Theory and Applications (World Scientific), 49-84, 2016.
Non-landing parameter rays of the Multicorns (joint work with Hiroyuki Inou), Invent. Math., 204:869-893, 2016.
Orbit portraits of unicritical antiholomorphic polynomials, Conform. Geom. Dyn., 19:35-50, 2015.
In preparation:
Accelerated Bowen-Series maps and matings (joint work with Yusheng Luo and Mahan Mj).
On Bers boundary correspondences and geometric limits (joint work with Yusheng Luo and Mahan Mj).
PhD thesis: