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A Special SCV Day @ GAIA

posted Aug 31, 2016, 6:31 PM by Hyemin Shin
A Special SCV Day @ GAIA; Special Lecture Series

September 7 2016(Wed), Maths bldg. Room 106

I. 15:30 - 16:20  Thomas Pawlaschyk (Universität Wuppertal)

Title: On the Dirichlet-Bremermann problem for q-plurisubharmonic functions on unbounded domains in C^n

Abstract: Let $D$ be a (possibly unbounded) domain in $\mathbb{C}^n$ and let $f$ be a continuous function prescribed on the boundary of $D$. We are interested in finding a continuous extension $F$ of $f$ into $D$ (or at least some open neighborhood of $bD$ in $\overline{D}$) which is $q$-plurisubharmonic, $(n-q-1)$-plurisuperharmonic (meaning that $(dd^c F)^n=0$) and which is maximal in the following sense: each $q$-plurisubharmonic function $\psi$ on $\overline{D}$ with $\psi\leq f$ on $bD$  satisfies $\psi \leq F$ on $\overline{D}$. We give conditions on $D$ (and $f$) which garantuee the existence of such a function $F$, but these conditions seem to be rather restrictive as we can see in some examples. So further research is required (even in the classical plurisubharmonic case).

Ⅱ.16:30 - 17:20  Toshihiro Nose (Fukuoka Institute of Technology)

Title: Failure of meromorphy for local zeta functions

Abstract: In this talk, we discuss the meromorphy of local zeta functions. It is known that in real analytic setting, local zeta functions can be analytically continued as meromorphic functions to whole complex plane. On the other hand, we obtain a failure of meromorphy for local zeta functions in some non-real analytic settings. In order to show our result, we investigate the asymptotic behavior of local zeta functions at a boundary point of the half plane of convergence. This work is joint with J. Kamimoto.

Ⅲ.20:00 - 20:50   Rafael Andrist (Universität Wuppertal)

Title: The fibred density property and the automorphism group of the spectral ball

Abstract: We generalize the notion of the density property for complex manifolds to holomorphic fibrations, and introduce the notion of the fibred density property. We prove that the natural fibration of the spectral ball over the symmetrized polydisc enjoys the fibred density property and determine the automorphism group of the spectral ball.
Joint work with Frank Kutzschebauch (University of Bern)

Ⅳ.21:00 - 21:50   Shin-ichi Matsumura (Tohoku University)

Title: Version of injectivity and extension theorems

Abstract: In this talk, I would like to give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove an extension theorem for holomorphic sections. As an application, I introduce several results for semi-ampleness related to the abundance conjecture in birational geometry.
This talk is based on a joint work with Yoshinori Gongyo (Tokyo University)
and the paper at arXiv: 1406.6132v2 (to appear in Ann. Sci. Ecole Norm. Sup.).

For further information, please contact: Hyemin Shin

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