Program on Quantization

量化计划

• 批准号: 1114152
• 负责人: Michael Gekhtman
• 金额: $ 2万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-04-15 至 2012-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1114152&HistoricalAwards=false
• 关键词: Program; Quantization

This project is to support graduate students to participate in a summer school and a conference on quantization, which will be held at the University of Notre Dame during May and June in 2011. Topics of the summer school and the conference are centered around quantizations, covering several different fields of mathematics, including mathematical physics, geometric quantization, deformation quantization, and quantum analogues of classical objects. These topics are closely related to recent developments in functional analysis, representation theory of Lie groups, and spectral geometry. The summer school is geared toward undergraduate students and graduate students followed by a conference. The summer school consists of two weeks of program with the first week aimed at undergraduate students and the second week geared to graduate students. The summer school and the conference will promote research activities in areas of mathematics related to quantization. The organizers have selected lecturers with a broad array of interests and backgrounds, including some physicists. The summer school and conference will give graduate students access to a wide array of current research activity in quantization, and give the students an opportunity to interact with prominent researchers. A public lecture by a physicist engaged in the Large Hadron Collider project in Europe will help enhance public awareness of science, and also give mathematicians the opportunity to interact with an experimental high energy physicist. The undergraduate summer school will expose top undergraduates to important ideas in mathematical physics, and encourage them to learn more about physics. The volume of proceedings of the conference will serve as a resource for students and researchers interested in learning about quantization. Quantization is an important topic in mathematics and physics. From the physics point of view, methods of quantization are procedures for building models for quantum mechanical systems from analogous and more intuitive classical mechanical systems, which provide strikingly precise experimental predictions. Much of the development of theoretical physics in the 20th century may be regarded as the process of refining quantization to give improved experimental predictions, and the search for a unified field theory is an attempt to quantize general relativity in a manner compatible with existing quantum theory. On the mathematics side, problems related to quantization and quantum mechanics provided a strong motivation for the development of functional analysis, the representation theory of Lie groups, and spectral geometry. More recent developments with much current activity include geometric quantization, deformation quantization, and quantum analogues of various classical objects. The Program on Quantization will inaugurate a new Center for Mathematics at Notre Dame. It will combine two week-long summer schools, one aimed at advanced undergraduates and one aimed at graduate students with a conference devoted to the most recent advances in the area. The invited speakers at the conference are among the world's leading experts in the mathematics of quantization.

该项目旨在支持研究生参加暑期学校和量化会议，该会议将于2011年5月和6月在巴黎圣母院举行。暑期学校和会议的主题围绕量化，涵盖数学的几个不同领域，包括数学物理学，几何量化，变形量化和经典对象的量子类似物。这些主题与功能分析，谎言组的表示理论和光谱几何形状的最新发展密切相关。暑期学校针对本科生和研究生，然后是一次会议。 暑期学校由两个星期的课程组成，第一周针对本科生，第二周旨在研究生。暑期学校和会议将促进与量化有关的数学领域的研究活动。组织者选择了具有广泛兴趣和背景的讲师，包括一些物理学家。暑期和会议将使研究生获得各种当前量化研究活动，并使学生有机会与著名研究人员进行互动。从事欧洲大型强子撞机项目的物理学家的公开演讲将有助于提高公众对科学的认识，并使数学家有机会与实验性的高能量物理学家进行互动。本科暑期学校将使顶级本科生在数学物理学领域接触重要的思想，并鼓励他们更多地了解物理学。会议的会议记录的数量将成为有兴趣学习量化的学生和研究人员的资源。量化是数学和物理学中的重要主题。从物理的角度来看，量化方法是从类似和更直观的经典机械系统中构建量子机械系统模型的程序，这些系统提供了惊人的精确实验预测。在20世纪，理论物理学的大部分发展可能被认为是提高量化以进行改进的实验预测的过程，而搜索统一的田间理论是试图以与现有量子理论相容的方式量化一般相对性的尝试。在数学方面，与量化和量子力学有关的问题为开发功能分析，谎言基团的表示理论和光谱几何形状提供了强大的动力。具有许多当前活动的最新发展包括几何量化，变形量化和各种经典对象的量子类似物。量化计划将在巴黎圣母院开设一个新的数学中心。它将结合两个星期的暑期学校，一所针对高级本科生，另一个针对研究生，其会议致力于该地区的最新进展。会议上受邀的演讲者是世界上量化数学领域的领先专家之一。