市大数学教室

大阪市立大学大学院理学研究科数物系専攻 21世紀COEプログラム

結び目を焦点とする広角度の数学拠点の形成
(Constitution of wide-angle mathematical basis focused on knots)
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講義 (2007年度)(2006)


集中講義
授業科目名: COE21特別講義I
講演者: 原田芽ぐみ氏(McMaster University)
タイトル: An introduction to symplectic geometry
日 程: 平成19年7月17日(火)〜20日(金),
平成19年7月23日(月)〜27日(金)
時 間: 9:30〜11:30
場 所: 数学講究室(3040)
講義内容
Abstract:

The intent of this series of lectures is two-fold: in the first week, we will provide a quick overview of equivariant symplectic geometry, starting at the very beginning (i.e. with the definition of a symplectic structure).
In the second week, we will give a series of loosely connected expository overviews of some themes that consistently arise in current research in this field. The purpose is to familiarize the audience with the basic tools and language of the field.

Topics will include (time permitting): In the first week, we will discuss the definition of a symplectic structure, examples of symplectic manifolds, local normal forms, group actions, Hamiltonian actions, moment maps, symplectic quotients, and Delzant's construction of symplectic toric manifolds. In the second week, we will discuss equivariant cohomology and equivariant Morse theory, localization, moment graphs and GKM theory, Duistermaat-Heckman measure, Kirwan surjectivity. I hope to also discuss related quotient theories (e.g. Kahler and hyperKahler quotients), time permitting.
See also Osaka City University Summer School on Symplectic Geometry and Toric Topology


集中講義
講演者: Taras Panov (Moscow State University)
タイトル: Toric topology and complex cobordism
日 程: 平成19年7月17日(火)〜20日(金)
時 間: 13:30〜15:30
(ただし,18日(水)は13:00〜14:00過ぎ)
場 所: 数学講究室(3040)
講義内容
Abstract:

We plan to discuss how the ideas and methodology of Toric Topology can be applied to one of the classical subjects of algebraic topology:

finding nice representatives in complex cobordism classes.

Toric and quasitoric manifolds are the key players in the emerging field of Toric Topology, and they constitute a sufficiently wide class of stably complex manifolds to additively generate the whole complex cobordism ring.
In other words, every stably complex manifold is cobordant to a manifold with a nicely behaving torus action.


An informative setting for applications of toric topology to complex cobordism is provided by the combinatorial and convex-geometrical study of analogous polytopes. By way of application, we give an explicit construction of a quasitoric representative for every complex cobordism class as the quotient of a free torus action on a real quadratic complete intersection.
The latter is a yet another disguise of the moment-angle manifold, another familiar object of toric topology.

We suggest a systematic description for

omnioriented quasitoric manifolds in terms of combinatorial data, and explain the relationship with non-singular projective toric varieties (otherwise known as toric manifolds).
See also Osaka City University Summer School on Symplectic Geometry and Toric Topology


集中講義
講演者: Alexander Premet (Manchester University)
タイトル: Premet's Mini Course on W-Algebras and Modular Representations of Lie Algebras
日 程: 平成19年9月10日(月),9月12日(水),9月14日(金)
時 間: 16:00-17:30、 15:00-17:30(9/14)
場 所: 数学講究室(3040)
講義内容
Abstract:

The course will be on finite W-algebras and their relationship with modular representations and primitive ideals in the characteristic zero case. This area is rapidly becoming very popular; people involved here (apart from physisists) are Arakawa, D'Andrea, DeConcini, DeSole, Kac, Brundan, Kleshchev, Losev, Premet and some others (especially those involved with the Yangians). There has been some important progress lately in this area and there are links with the modular theory as well.


その他の集中講義はこちら

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最終更新日: 2008年2月27日
(C)大阪市大数学教室