Office: 4115, Math Tower

Stony Brook University

Stony Brook, 11794-3660, NY

E-mail:
*sabya@math.stonybrook.edu*

Telephone: (631) 632-8277

__Teaching:__

Spring 2018 Course: MAT 211 (Introduction to Linear Algebra) - MWF 10:00am - 10:53am

Spring 2018 Office Hours: M 1:00pm - 3:00pm (in Math Tower Room 4115)

Math Learning Center Hours: Th 12:00pm - 1:00pm (in Math Tower Room S-235)

__Research interest:__

Parameter spaces of holomorphic and antiholomorphic dynamical systems; Parabolic germs and horn maps.

Here is my thesis.

__Publications/Pre-prints:__

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.

__Some slides:__

￼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.