Office: 4.115, Math Tower
Stony Brook University
Stony Brook, 11794-3660, NY
Telephone: (631) 632-8277
Spring 2017 Course: MAT 308 (Differential Equations with Linear Algebra) - MW 4:00pm - 5:20pm
Spring 2017 Office Hours: F 10:30am - 12:30pm
Math Learning Center Hours: M 1:00pm - 2:00pm (in Math Tower Room S-235)
Parameter spaces of holomorphic and antiholomorphic dynamical systems; Parabolic germs and horn maps.
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.
On Multicorns and Unicorns II: Bifurcations in Spaces of Antiholomorphic Polynomials (joint work with Shizuo Nakane, and Dierk Schleicher), to appear in 'Ergodic Theory and Dynamical Systems'.
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.
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.
Discontinuity of straightening in antiholomorphic dynamics (joint work with Hiroyuki Inou), submitted.
A rigidity result for some parabolic germs (joint work with Luna Lomonaco), submitted.
Antiholomorphic perturbations of Weierstrass Zeta functions and Green's function on tori (joint work with Konstantin Bogdanov, Khudoyor Mamayusupov, and Dierk Schleicher), submitted.
￼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.
Non-landing parameter rays of the tricorn, Dynamics seminar, Stony Brook University, USA, April 2015.
Discontinuity of the straightening map in antiholomorphic dynamics, Conference `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.