- Title: Defining Functions and Cores of Unbounded Domains

- Speaker: **Dr. Tobias Harz **(GAIA)

- Abstract: I will explain that every unbounded strictly pseudoconvex domain $\Omega$ in a complex manifold admits a plurisubharmonic defining function, which is defined on a neighborhood of the closure $\bar{\Omega}$, and which is strictly plurisubharmonic near the boundary $b\Omega$. Investigation of the minimal subset of $\Omega$ where every such function fails to be strictly plurisubharmonic leads to the definition of the core $\mathfrak{c}(\Omega)$ of $\Omega$. I will prove that $\mathfrak{c}(\Omega)$ is always $1$-pseudoconcave in $\Omega$, and, if time permits, state some results on Liouville type properties of the core. This is joint work with N. Shcherbina and G. Tomassini.

- Place: GAIA Seminar Room (#**106**, Math Science bldg.)

- Date: 8 p.m. - 10 p.m on Monday,** 5 October **2015