RTG: Unified Training in Geometry and Topology

RTG：几何和拓扑的统一训练

• 批准号: 1148490
• 负责人: Daniel Freed
• 金额: $ 249.91万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-15 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1148490&HistoricalAwards=false
• 关键词: RTG; Unified; Training; Geometry; Topology

AbstractAward: DMS 1148490 Principal Investigators: Daniel S. Freed, Dan F. Knopf, Alan W. ReidThe University of Texas Geometry/Topology Research Training Grant (RTG) is a vertically integrated program to enhance the training of undergraduates, graduate students, and postdoctoral associates at the University of Texas and, through publication on the web, beyond. The thirteen faculty members will build on the success of our previous RTG grants and also initiate new activities. The latter include a Directed Reading Program pairing undergraduate students and graduate mentors; a new Journal Seminar for all graduate students in geometry and topology; a new series of First Cut Lectures on a variety of core topics, to be disseminated on the web; a new yearly Undergraduate Mathematics Conference; and a new series of Graduate Winter Schools for graduate students and postdocs. All RTG activities are designed around a unified perspective on geometry and topology. They include a healthy mix of ideas from low dimensional topology, algebraic geometry, differential geometry, global linear and nonlinear analysis, geometric group theory, geometric representation theory, and homotopy theory; often concepts and inspiration from theoretical physics play an important role as well. The RTG training activities are designed to promote this unified view of geometry and topology and, more broadly, of mathematics and science to young mathematicians.Mathematics, the study of Number and Space, lies at the foundation of science and technology. Geometry, the study of Space, has long had connections with and applications to the real world. Topology investigates, very roughly, global geometric properties of spaces which do not rely on local structure. There is great interplay between Geometry and Topology-there is not a sharp boundary between them. In the ancient world measurement was introduced to facilitate commerce; more advanced concepts, such as trigonometry, were introduced to understand the stars. In our modern world advanced ideas in Geometry underlie abstract theories in physics and also have more immediate practical implications, for example in navigation, computer graphics, etc. The large scale structures studied in topology appear in biological and physical science; there are new applications to data analysis and signal processing as well. Effective training of the next generation of Geometers and Topologists is vital for the continued development of these ideas, both within mathematics and for external applications. The University of Texas Geometry/Topology Research Training Grant promotes a unified view of the field. An open attitude towards ideas from all directions is essential for success with the challenges facing mathematics and science today. Through local activities in Austin, and via dissemination on the web, the RTG will enhance training at all levels.

摘要：DMS 1148490主要研究人员：Daniel S. Freed，Dan F. Knopf，Alan W. Reidthe Texas University of Texas University of Texas University of Texas University of Decology/Tostology研究培训授予（RTG）是一项垂直整合的计划，旨在增强对本科生，研究生学生，研究生和博士学位协会的培训，并通过德克萨斯大学和德克萨斯大学和网络上的出版物进行出版物。 13名教职员工将以我们以前的RTG赠款的成功为基础，并发起新的活动。 后者包括针对本科生和研究生导师的定向阅读计划；新的日记研讨会，针对几何学和拓扑的所有研究生；在网络上传播的各种核心主题的新系列剪辑讲座；每年的新本科数学会议；以及一系列新的冬季研究生学校，供研究生和博士后。 所有RTG活动均围绕着几何和拓扑的统一视角设计。 它们包括低维拓扑，代数几何形状，差异几何，全球线性和非线性分析，几何群体理论，几何表示理论和同型理论的健康思想的健康混合；理论物理学的概念和灵感通常也起着重要作用。 RTG培训活动旨在促进这种对几何和拓扑的统一观点，更广泛地向年轻的数学家进行数学和科学的观点。学术学，数量和空间的研究，是科学和技术的基础。 几何学是对空间的研究，长期以来一直与现实世界的联系和应用。 拓扑调查了不依赖局部结构的空间的全球几何特性。几何和拓扑之间存在很大的相互作用 - 它们之间没有尖锐的边界。 在古老的世界中，引入了促进商业的测量。引入了更高级的概念，例如三角学，以了解恒星。 在我们的现代世界中，几何学的高级思想是物理学中抽象理论的基础，并且具有更直接的实际含义，例如在导航，计算机图形上等。拓扑中研究的大型结构出现在生物学和物理科学中；数据分析和信号处理也有新的应用。 对下一代几何学家和拓扑师的有效培训对于数学和外部应用中的这些思想的持续发展至关重要。 德克萨斯大学的几何/拓扑研究培训培训补助金促进了该领域的统一观点。 当今数学和科学面临的挑战，对所有方向的思想的开放态度对于成功至关重要。 通过奥斯汀的本地活动以及通过网络传播，RTG将在各个级别上增强培训。