Office: 4115, Math Tower
Stony Brook University
Stony Brook, 11794-3660, NY
Telephone: (631) 632-8277
Fall 2018 Course: MAT 127.03 (Calculus C) - TuTh 10:00am - 11:20am
Fall 2018 Office Hours: W 1:00pm - 3:00pm (in Math Tower Room 4115)
Math Learning Center Hours: Th 12:00pm - 1:00pm (in Math Tower Room S-235)
Parameter spaces of holomorphic and antiholomorphic dynamical systems.
More about my research.
Here is my thesis.
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), to appear in Indiana University Mathematics Journal.
Discontinuity of straightening in antiholomorphic dynamics (joint work with Hiroyuki Inou), submitted.
Invisible tricorns in real slices of rational maps (joint work with Russell Lodge), submitted.
On the support of the bifurcation measure of cubic polynomials (joint work with Hiroyuki Inou), submitted.
Dynamics of Schwarz reflections and the tricorn, Part I: The dynamical plane (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), draft version.
Dynamics of Schwarz reflections and the tricorn, Part I: The parameter plane (joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov), draft version.
Dynamics of Schwarz reflections: mating polynomials with groups, 'Chicago Action Now' Conference, Northwestern University, Evanston, USA, May 2018.
￼Connectedness loci of complex polynomials: beyond the Mandelbrot set, Colloquium, Tata Institute of Fundamental Research, Mumbai, India, June 2016.
Ph.D. defense, Jacobs University, Bremen, Germany, August 2015.
Discontinuity of the straightening map in antiholomorphic dynamics, Conference on 'Perspectives on Parabolic Points in Holomorphic Dynamics', Banff, Canada, March 2015.
Topological differences between the Mandelbrot set and the tricorn, Dynamics seminar, University of Warwick, UK, November 2014.