# Sabyasachi Mukherjee

## "Discontinuity of the straightening map in antiholomorphic dynamics"

 Date: Wed, June 14, 2017 Time: 11:15 Place: Research I Seminar Room

Abstract: Abstract< In this talk, we will consider the tricorn, the connectedness locus of quadratic antiholomorphic polynomials $${\overline z}^{2}+c$$. Our main goal is to demonstrate that every odd period hyperbolic component of the tricorn is the basis of a baby tricorn (much like the Mandelbrot set), but the straightening map from any baby tricorn to the original one is discontinuous. This is achieved by proving that all non-real umbilical cords of the tricorn wiggle, which generalizes a theorem of Hubbard and Schleicher, and settles a conjecture of Hubbard, Milnor and Schleicher.