## 複素解析幾何セミナー

開催情報 月曜日　10:30～12:00　数理科学研究科棟(駒場) 128号室 平地 健吾, 高山 茂晴, 野村 亮介

### 2017年10月23日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
[ 講演概要 ]
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.

### 2017年10月30日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

Odd dimensional complex analytic Kleinian groups
[ 講演概要 ]
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group $G$ of a certain class of discrete subgroups of $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, there is a canonical way to define the region of discontinuity, on which $G$ acts properly discontinuously. General principle in the discussion is to regard $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ as a single point. We can consider the quotient space of the discontinuity region by the action of $G$. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case $n=1$, we explain a new example of compact quotients which is related to a classical Kleinian group.

### 2017年11月13日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室
Georg Schumacher  氏 (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
[ 講演概要 ]
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.

### 2017年11月20日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA

### 2017年12月11日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA

### 2017年12月18日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA

### 2018年01月15日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA

### 2018年01月22日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA