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: University of Illinois at Urbana-Champaign
• 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
• 起止时间: 2013-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1342531&HistoricalAwards=false
• 关键词: Gone; Fishing; series; meetings; Poisson

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

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。它起源于经典力学作为量子力学半经典极限的数学表述。泊松结构可以追溯到19世纪泊松、汉密尔顿、雅可比和李的经典著作。泊松几何作为一个独立领域始于 1980 年左右，以 Lichnerowicz 和 Weinstein 的基础工作为基础。由于与数学和数学物理的许多领域的联系，包括微分几何和李理论、量子化、非交换几何、表示论和量子群、几何力学和可积系统，该领域发展迅速。过去 15 年发生了许多重大发展；其中一些亮点是 Kontsevich 的形式定理、泊松-西格玛模型的研究以及与李代数体可积性问题的关系、与平坦连接的模空间和各种矩图理论、奇异约简、（广义）复几何、簇代数等的关系。钓鱼研讨会旨在促进数学家、物理学家和从事泊松相关领域工作的团体之间的互动 从不同角度观察几何。他们汇集了这些学科的顶尖专家和年轻研究人员，以鼓励不同领域之间更多的互动和交叉融合。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交流想法和促进可能合作的绝佳机会。每个研讨会的一个重要主题是解决该主题的重要问题和未来方向。 Gone Fishing 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）；和加州大学伯克利分校，（2014 年 9 月/10 月）。URL：poissongeometry.org