Analysis Seminar: Annual Progress Seminar
Thursday, 15 February, 3.30 pm
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Venue: Room 215
Host: Sourav Pal
Speaker: Priyanka Aroda
Affiliation: IIT Bombay
Title: Geometric and function theoretic aspects of the tetrablock
Abstract: We study the tetrablock, a domain in \mathbb{C}^3 given by
\mathbb{E}=\left\{\left(x_1,x_2,x_3\right) \in \mathbb{C}^3 : \ 1-x_1 z-x_2 w+x_3 zw \neq 0 \ \ \text{for} \ \ |z| \leq 1,|w| \leq 1\right\}.\]The tetrablock is related to a certain function-theoretic problem that arises in control engineering. We discuss several characterizations for the elements in$\mathbb{E}$ and in its closure. We present a set of necessary and sufficient conditions that provide a Schwarz lemma for $\mathbb{E}$. We also describe the automorphism group of $\mathbb{E}$.