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Gone Fishing: A series of meetings in Poisson Geometry

Gone Fishing: A series of meetings in Poisson Geometry
钓鱼:泊松几何的一系列会议
批准号:
1342531
负责人:
Rui Loja Fernandes
金额:
$2.78万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
2013
资助国家:
美国
项目状态:
已结题
起止时间:
2013-09-01 至 2015-08-31

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中文摘要
翻译
去钓鱼研讨会的统一主题是泊松几何,这是一个位于数学物理和几何交叉的领域。它起源于经典力学的数学表述,作为量子力学的半经典极限。泊松结构可以追溯到19世纪由泊松、汉密尔顿、雅可比和李等人创作的经典作品。泊松几何作为一个独立的领域开始于1980年左右,由Lichnerowicz和Weinstein的基础工作。由于与数学和数学物理中许多领域的联系,包括微分几何和李论、量子化、非交换几何、表示理论和量子群、几何力学和可积系统,该领域发展迅速。在过去的15年里发生了一些重大的发展;一些重点是Kontsevich的形式定理,泊松-西格玛模型的研究及其与李代数可积性问题的关系,平面连接与模空间的关系以及各种矩映射理论,奇异约简,(广义)复几何,聚类代数等。从不同的角度研究泊松几何相关领域的物理学家和团体。他们将这些学科的顶尖专家和年轻研究人员聚集在一起,鼓励不同领域之间更多的互动和交叉施肥。随着这些领域的深入发展,这一点变得越来越紧迫。这些研讨会还为美国科学家提供了一个交流思想和促进可能的合作的绝佳机会。每次研讨会的一个重要主题是讨论该主题的重要问题和未来方向。“消失的钓鱼”研讨会的下一次会议是:费城天普大学(2013年9月28日至29日);以及加州大学伯克利分校(2014年9月/ 10月)。URL: poissongeometry.org
英文摘要
The unifying theme of the Gone Fishing workshops is Poisson Geometry, a field which lies at the intersection of Mathematical Physics and Geometry. It originates in the mathematical formulation of classical mechanics as the semiclassical limit of quantum mechanics. Poisson structures can be traced back to the 19th century classics by Poisson, Hamilton, Jacobi and Lie. Poisson Geometry as an independent field started around 1980 with the foundational works of Lichnerowicz and Weinstein. The field developed rapidly, stimulated by the connections with a large number of areas in mathematics and mathematical physics, including differential geometry and Lie theory, quantization, noncommutative geometry, representation theory and quantum groups, geometric mechanics and integrable systems. A number of major developments took place in the last 15 years; some of the highlights are Kontsevich's formality theorem, the study of Poisson-sigma models and the relationship to the integrability problem for Lie algebroids, the relation with the moduli space of flat connections and various moment map theories, singular reduction, (generalized) complex geometry, cluster algebras, etc.The Gone Fishing workshops aim to promote interaction between mathematicians, physicists and groups working on areas related to Poisson geometry from different points of view. They bring together leading experts and young researchers in these subjects to encourage more interaction and cross fertilization between different fields. This is becoming more and more urgent as these fields progress deeper. The workshops also provide an excellent opportunity for US based scientists to exchange ideas and promote possible collaborations. One important theme of each workshop is to address important questions and future directions of the subject. The next meetings of the Gone Fishing workshops are: Temple University, Philadelphia, (Sept. 28-29, 2013); and the University of California at Berkeley, (Sept./Oct 2014).URL: poissongeometry.org
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