Publications and Pre-prints:
Antiholomorphic dynamics: topology of parameter spaces and discontinuity of straightening, PhD thesis, Jacobs University Bremen, 2015.
Orbit portraits of unicritical antiholomorphic polynomials, Conformal Geometry and Dynamics of the AMS, 19:35-50, 2015.
Non-landing parameter rays of the Multicorns (joint work with Hiroyuki Inou), Inventiones Mathematicae, 204:869-893, 2016.
Rational parameter rays of the Multibrot sets (joint work with Dominik Eberlein, and Dierk Schleicher), Dynamical Systems, Number Theory and Applications (World Scientific), 49-84, 2016.
On Multicorns and Unicorns II: bifurcations in spaces of antiholomorphic polynomials (joint work with Shizuo Nakane, and Dierk Schleicher), Ergodic Theory and Dynamical Systems, 37:859-899, 2017.
Parabolic arcs of the Multicorns: real-analyticity of Hausdorff dimension, and singularities of Per_n(1) curves, Discrete and Continuous Dynamical Systems-A, 37:2565-2588, 2017.
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.
A rigidity result for some parabolic germs (joint work with Luna Lomonaco), Indiana University Mathematics Journal, 67:2089-2101, 2018.
On the support of the bifurcation measure of cubic polynomials (joint work with Hiroyuki Inou), Mathematische Annalen, 378:1-12, 2020.
Invisible Tricorns in real slices of rational maps (joint work with Russell Lodge), Discrete and Continuous Dynamical Systems-A, 41:1755-1797, 2021.
Discontinuity of straightening in antiholomorphic dynamics: I (joint work with Hiroyuki Inou), Transactions of the American Mathematical Society, 374:6445-6481, 2021.
Schwarz reflections and anti-holomorphic correspondences (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), Advances in Mathematics, 385:107766, 2021.
Univalent polynomials and Hubbard trees (joint work with Kirill Lazebnik and Nikolai Makarov), Transactions of the American Mathematical Society, 374:4839-4893, 2021.
Bers slices in families of univalent maps (joint work with Kirill Lazebnik and Nikolai Makarov), Mathematische Zeitschrift, 300:2771-2808, 2022.
Circle packings, kissing reflection groups and critically fixed anti-rational maps (joint work with Russell Lodge and Yusheng Luo), Forum of Mathematics, Sigma, vol. 10, e3, 2022.
Discontinuity of straightening in antiholomorphic dynamics: II (joint work with Hiroyuki Inou), International Mathematics Research Notices, 2022(9):6948–6990, 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.
Dynamics of Schwarz reflections: the mating phenomena (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), to appear in Annales Scientifiques de l'École Normale Supérieure.
Schwarz reflections and the Tricorn (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), submitted.
On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections (joint work with Russell Lodge, Mikhail Lyubich, and Sergei Merenkov), submitted.
David extension of circle homeomorphisms, welding, mating, and removability (joint work with Mikhail Lyubich, Sergei Merenkov, and Dimitrios Ntalampekos), submitted.
Combining rational maps and Kleinian groups via orbit equivalence (joint work with Mahan Mj).
The Sullivan dictionary and Bowen-Series maps (joint work with Mahan Mj), to appear in the 80th birthday volume of Dennis Sullivan, edited by Basmajian, Koberda, Papadopoulos, Seade and Zeinalian.
On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps (joint work with Russell Lodge and Yusheng Luo).
Dynamics of correspondences, matings, and dessins d'enfants (joint work with Mikhail Lyubich and Jacob Mazor).