Workshop on "Geometry and Representation Theory"
“几何与表示论”工作坊
基本信息
- 批准号:0400785
- 负责人:
- 金额:$ 1.65万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2004
- 资助国家:美国
- 起止时间:2004-08-01 至 2006-01-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
AbstractAward: DMS-0400785Principal Investigator: Philip A. Foth, Paul Bressler, Kirti N. JoshiA powerful influx of methods and ideas from geometry into therepresentation theory led to significant breakthroughs andstimulated the emergence of geometric representation theory as animportant area of research in modern mathematics. Geometricmethods have been utilized to explore many significant problemsin representation theory. The Langlands program provides anexample of the synthesis of representation theory, arithmetic andgeometry. In its arithmetic avatar the Langlands correspondenceenvisages a description of certain kinds of representations ofthe Galois group of a number field or a function field in termsof automorphic representations. The geometric avatar of theLanglands correspondence pioneered by Drinfel'd and Laumon hasalso attracted a lot of attention and has turned out to be aconfluence of several areas of mathematics: representationtheory, D-modules, Kac-Moody and vertex algebras and integrablesystems, Hitchin maps to name a few. Representation theory hasbeen omnipresent in theoretical physics and conversely, problemsand developments in physics motivated much progress inrepresentation theory which, in turn, was a significant inputinto other branches of mathematics. Conformal Field Theory ledto intensive study of the representation theory of the Virasoroalgebra, Kac-Moody algebras and vertex operator algebras. Resultsin representation theory have had a significant impact on theunderstanding of the structure of moduli spaces. In the theoryof integrable systems it has been observed long ago in numerousexamples that physically meaningful completely integrable systemsas well as explicit formulas for the integrals of motion areintimately related with the geometric representation theory. Allthese developments serve as our motivation to organize aconference on geometric representation theory, a forum where themajority of participants will be young researchers and advancedgraduate students, learning from leading specialists and furtheradvancing their research projects.Representation theory is a quintessential branch of modernmathematics which studies symmetries of various algebraicsystems. The results and ideas from representation theory foundmany important applications in pure and applied mathematics aswell as quantum physics, biology, economics, just to name afew. More recently a powerful merge of ideas from geometry made asignificant impact on the discipline and led to importantbreakthroughs. The main goal of our conference is to gatherleading specialists in representation theory as well as beginningresearchers and advanced graduate students, to create a forumwhere participants can exchange new ideas, communicate recentadvances and assist younger participants in developing successfulresearch strategies. A special emphasis is made on attractingwomen and underrepresented minority participants, especiallythose at the dawn of their careers.
摘要奖:DMS-0400785主要研究者:Philip A.放大图片作者:Paul Bressler. Joshi一个强大的方法和思想从几何涌入表示理论导致了重大突破,并刺激了出现的几何表示理论作为一个重要的研究领域,在现代数学.几何方法已被用来探讨许多重要的问题,在表示论。朗兰兹程序提供了一个综合表示论、算术和几何的例子。在它的算术化身朗兰兹对应设想了一个描述的某些种类的表示伽罗瓦群的数域或功能领域的自守表示.由Drinfel'd和Laumon开创的Langlands对应的几何化身也吸引了很多关注,并已被证明是几个数学领域的影响:表示论,D-模,Kac-穆迪和顶点代数和积分系统,Hitchin映射仅举几例。表示论在理论物理学中无处不在,相反,物理学中的问题和发展推动了表示论的发展,而表示论反过来又是数学其他分支的重要投入。 共形场论导致了Virasoro代数、Kac-Moody代数和顶点算子代数的表示论的深入研究。结果表示理论对模空间结构的理解产生了重大影响。 在可积系统的理论中,很久以前就有大量的例子表明,物理意义上的完全可积系统以及运动积分的显式公式与几何表示论密切相关.所有这些发展都是我们组织一个关于几何表示论的会议的动机,这个论坛的主要参与者将是年轻的研究人员和高级研究生,从领先的专家那里学习并进一步推进他们的研究项目。表示论是现代数学的一个典型分支,它研究各种代数系统的对称性。表示论的结果和思想在纯数学和应用数学以及量子物理学、生物学、经济学等领域都有重要的应用。最近,几何学思想的有力融合对这门学科产生了重大影响,并导致了重要的突破。我们会议的主要目标是培养代表性理论的领先专家以及资深研究人员和高级研究生,创造一个论坛,参与者可以交流新思想,沟通最近的进展,并帮助年轻的参与者制定成功的研究策略。特别强调吸引女性和代表性不足的少数族裔参与者,特别是那些处于职业生涯初期的人。
项目成果
期刊论文数量(0)
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Philip Foth其他文献
Geometry of Four-Vector Fields on Quaternionic Flag Manifolds
- DOI:
10.1007/s00220-003-0821-9 - 发表时间:
2003-07-01 - 期刊:
- 影响因子:2.600
- 作者:
Philip Foth;Frederick Leitner - 通讯作者:
Frederick Leitner
Philip Foth的其他文献
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{{ truncateString('Philip Foth', 18)}}的其他基金
Workshop on "Analysis on Homogeneous Spaces"
“均质空间分析”研讨会
- 批准号:
0628812 - 财政年份:2007
- 资助金额:
$ 1.65万 - 项目类别:
Standard Grant
Workshop: Geometry and Topology of Quotients, December 5-8, 2002, Tucson, Arizona
研讨会:商的几何和拓扑,2002 年 12 月 5-8 日,亚利桑那州图森
- 批准号:
0217057 - 财政年份:2002
- 资助金额:
$ 1.65万 - 项目类别:
Standard Grant
Geometry and Topology of Moduli Spaces of Parabolic Bundles, Toric Varieties, and Partial Flag Manifolds
抛物线丛、环面簇和部分旗流形的模空间的几何和拓扑
- 批准号:
0072520 - 财政年份:2000
- 资助金额:
$ 1.65万 - 项目类别:
Standard Grant
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