# David Pfrang

## "The value range of typically real bounded univalent functions"

 Date: Tue, September 13, 2016 Time: 14:15 Place: Research I Seminar Room

Abstract: A function $$f\in\text{Hol}(\mathbb{D}, \mathbb{D})$$ is called $$\textit{typically real}$$, if $\text{Im } z=0~~~\Leftrightarrow~~~\text{Im } f(z)=0~~~\text{for all}~z\in\mathbb{D}.$ After giving a brief overview about the deterministic Loewner Differential Equation, I will explain how to specialize the general Loewner-Kufarev-ODE in order to obtain the exact value range $\{ f(z_0)~\vert~f\in\text{Hol}(\mathbb{D},\mathbb{D})~\text{is typically real and normalized by }f(0)=0,~f'(0)>0~\}$ for every $$z_0\in\mathbb{D}$$.