IPM Calendar 
Sunday 20 January 2019   Today  
Events for day: Wednesday 09 January 2019    
           15:30 - 17:00     Geometry and Topology Weekly Seminar
Faber Polynomials, Grunsky Matrix and Period Matrices


We extend the idea of Grunsky operator and Faber operator to higher genus compact Riemann surfaces with one boundary curve. In this talk, I will first review the classical concept of Faber Polynomials corresponding to the map $f$, a conformal map on a simply connected domain $ extbf{D}$ of the Riemann sphere with $Gamma=partial f ( extbf{D})$. We define the Grunsky coefficients associated to $f$, and review the necessary and sufficient conditions for $f$ to be univalent on $ extbf{D}$. We will define Grunsky and Faber operators and show that the Faber operator is an isomorphism for quasi-circles. I will present some recent work of m ...