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.
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.
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.
Invisible tricorns in real slices of rational maps (draft version) (joint work with Russell Lodge).
￼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.