[geometry-ml:03379] 談話会のご案内 (Viaclovsky 氏, 6/27)

[Nobuhiro Honda]

皆様

Jeff Viaclovsky 氏 (UC Irvine, 東工大) による談話会の情報をおしらせいたします。

日時：6月27日(水) 16:20-17:20
TITLE:  Collapsing Ricci-flat metrics on K3 surfaces

ABSTRACT: In the 1970s, Yau proved that a compact Kahler manifold with vanishing first Chern class admits a Ricci-flat Kahler metric. The proof is an abstract existence theorem via the method of a priori estimates. There are no explicit solutions known, however, near the boundary of the moduli space, one can hope to obtain a more detailed geometric understanding of Yau's metrics.
 In this talk, I will give some general background of moduli problems in geometry, and discuss some known examples of degeneration of Yau's metrics on K3 surfaces. I will then discuss a new construction of families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding singular fibration from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds. This is joint work with Hans-Joachim Hein, Song Sun, and Ruobing Zhang.

談話会（水曜）終了後、大岡山駅周辺にて懇親会を開催いたします。
ご参加下さる方は、

6月25日(月)18時までに

本多までご一報下さい。

また、すでにお知らせしましたように、同氏による集中講義が下記のように開催されます。

本多宣博（東工大理学院数学系）

> 2018/06/05 10:03、Nobuhiro Honda <honda ＠ math.titech.ac.jp>のメール:
> 
> 皆様
> 
> Jeff Viaclovsky 氏 (UC Irvine, 東工大) による集中講義と談話会の情報をおしらせいたします。本多宣博
> 
> 日程　6月25日(月)から6月29日(金)まで
> 各日　15:05-16:05,  16:20-17:20 （水曜2コマ目は談話会を兼ねます）
> 東工大大岡山キャンパス本館201セミナー室
> 講義題目："Kahler manifolds, Ricci curvature, and hyperkahler metrics”.
> 
> In this lecture series, we will begin by reviewing some basic material from Kahler geometry. 
> We will then discuss basic examples of Calabi-Yau manifolds, and Yau's Theorem.  
> In dimension 4, these metrics are hyperkahler, and the Gibbons-Hawking ansatz is an important tool for producing noncompact examples, such as ALE, ALF, ALG, ALH, etc. 
> Noncompact examples also arise from from a construction of Tian-Yau. 
> We will then outline various gluing results, which give a picture of the degenerations of Yau's metrics on K3 surfaces.
> 
> 講義の概要は下記でもご覧になれます。
> 
> http://www.ocw.titech.ac.jp/index.php?module=General&action=T0300&GakubuCD=1&GakkaCD=311111&KeiCD=11&course=11&KougiCD=201820137&Nendo=2018&vid=03
> 
>