### Dynamics Seminar

# Sabyasachi Mukherjee

### (Stony Brook University)

## "Dynamics of Schwarz reflections"

** Date: ** |
Wed, June 14, 2017 |

** Time: ** |
14:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** Schwarz reflections with respect to the boundaries of quadrature domains have intimate connections with potential theory and mathematical physics. In this talk, we consider the simplest class of quadrature domains, namely disks and cardioids, and study the dynamical properties of the corresponding Schwarz reflections. It turns out that the dynamics of these maps can be regarded as the "mating" of a quadratic antiholomorphic polynomial and a reflection map arising from the ideal triangle group. Using this description, we will explain why the "connectedness locus" of these maps resemble the basilica limb of the tricorn (which is the connectedness locus of quadratic antiholomorphic polynomials).

Joint work with Mikhail Lyubich.