Publications and Pre-prints:

  1. Orbit portraits of unicritical antiholomorphic polynomials, Conform. Geom. Dyn., 19:35-50, 2015.

  2. Non-landing parameter rays of the Multicorns (joint work with Hiroyuki Inou), Invent. Math., 204:869-893, 2016.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. A rigidity result for some parabolic germs (joint work with Luna Lomonaco), Indiana Univ. Math. J., 67:2089-2101, 2018.

  8. On the support of the bifurcation measure of cubic polynomials (joint work with Hiroyuki Inou), Math. Ann., 378:1-12, 2020.

  9. Invisible Tricorns in real slices of rational maps (joint work with Russell Lodge), Discrete Contin. Dynam. Systems, 41:1755-1797, 2021.

  10. Discontinuity of straightening in antiholomorphic dynamics: I (joint work with Hiroyuki Inou), Trans. Amer. Math. Soc., 374:6445-6481, 2021.

  11. Schwarz reflections and anti-holomorphic correspondences (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), Adv. Math., 385:107766, 2021.

  12. Univalent polynomials and Hubbard trees (joint work with Kirill Lazebnik and Nikolai Makarov), Trans. Amer. Math. Soc., 374:4839-4893, 2021.

  13. Bers slices in families of univalent maps (joint work with Kirill Lazebnik and Nikolai Makarov), Math. Z., 300:2771-2808, 2022.

  14. 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.

  15. Discontinuity of straightening in antiholomorphic dynamics: II (joint work with Hiroyuki Inou), Int. Math. Res. Not. IMRN, 2022(9):6948–6990, 2022.

  16. 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.

  17. 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.

  18. 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.

  19. Combining rational maps and Kleinian groups via orbit equivalence (joint work with Mahan Mj), Proc. London Math. Soc. (3), 126:1740-1809, 2023.

  20. The Sullivan dictionary and Bowen-Series maps (joint work with Mahan Mj), EMS Surv. Math. Sci., 10:179-221, 2023.

  21. 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.

  22. Schwarz reflections and the Tricorn (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), to appear in Ann. Inst. Fourier (Grenoble).

  23. David extension of circle homeomorphisms, welding, mating, and removability (joint work with Mikhail Lyubich, Sergei Merenkov, and Dimitrios Ntalampekos), to appear in Mem. Amer. Math. Soc.

  24. Antiholomorphic correspondences and mating I: realization theorems (joint work with Mikhail Lyubich and Jacob Mazor).

  25. Matings, holomorphic correspondences, and a Bers slice (joint work with Mahan Mj).

  26. Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz reflections, and correspondences (joint work with Mikhail Lyubich).

      In preparation:

  1. A general dynamical theory of Schwarz reflections, B-involutions, and algebraic correspondences (joint work with Yusheng Luo and Mikhail Lyubich).

  2. Mating parabolic rational maps with Hecke groups (joint work with Shaun Bullett, Luna Lomonaco, and Mikhail Lyubich).

  3. Antiholomorphic correspondences and mating II: slices of Shabat polynomials (joint work with Mikhail Lyubich and Jacob Mazor).

      PhD thesis:

    Antiholomorphic dynamics: topology of parameter spaces and discontinuity of straightening, 2015.