[geometry-ml:01955] 勉強会「複素射影構造，ホロノミー表現，モジュライ」のお知らせ（１月２８日）

[Hideki Miyachi]

各位
大阪大学の宮地です．

いつもお世話になっております．
カリフォルニア工科大学の馬場伸平氏をお迎えして，下記の勉強会を企画しておりま
す．基本的なことからの講演をお願いしております．皆様のご参加をお待ちしており
ます．

この勉強会について，いくつかのメーリングリストにてお知らせをしております．重
複をお許し下さい．

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タイトル: 複素射影構造，ホロノミー表現，モジュライ
場所：大阪大学理学研究科B棟 B342/344/346号室（豊中キャンパス）
日時：２０１４年１月２８日（火）
１回目：１０：００−１１：３０：Introduction to complex projective structure
s, overview
２回目：１：００ー２：３０： Background materials for third lecture
３回目：３：００−４：３０： Density of holonomy map fibers in the moduli sp
ace

アブストラクト：
Complex projective structure is a geometric structure on surfaces, and it
is a natural  structure at the boundary at infinity of three-dimensional
hyperbolic manifolds.
In particular each projective structure enjoys a complex structure on the
base surface and a homomorphism of the fundamental group of the surface into
PSL(2,C), called holonomy representation.
We investigate on a relation between  complex structures and holonomy
representations of projective structures via three-dimensional hyperbolic
geometry.

In general, holonomy representations are not necessarily discrete, and
moreover one representation typically corresponds to many different
projective structures.
Our goal of this lecture series is to consider the projection of the set
of complex projective structures with a fixed holonomy representation into
the moduli space of complex structures on the surface.

In the case that  the fixed representation is fuchsian, i.e. discrete
faithful representation into PSL(2,R), Gupta showed the density of the
projection in the moduli space, proving asymptotic of grafting rays to
Teichmuller rays. We generalize his result to arbitrary holonomy.
This is joint work with Gupta.

First two lectures will mainly be on the background on  hyperbolic
geometry and complex projective structure, including Thurston coordinates
and grafting of complex projective structure.


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なお，大阪大学へのアクセスと理学研究科の建物の配置については

http://www.osaka-u.ac.jp/ja/access/
http://www.sci.osaka-u.ac.jp/location/maps-jp-b.html

をご覧ください．

どうかよろしくお願いいたします．

以上です．
失礼します．
===========

Hideki Miyachi
Department of Mathematics,
Graduate School of Science, Osaka University,
Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan
miyachi ＠ math.sci.osaka-u.ac.jp
http://www.math.sci.osaka-u.ac.jp/~miyachi/index.html