Program on Quantization

该项目旨在支持研究生参加将于2011年5月至6月在圣母大学举办的暑期班和量化会议。暑期班和会议的主题围绕量子化展开，涵盖了几个不同的数学领域，包括数学物理、几何量子化、形变量子化和经典物体的量子类比。这些主题与泛函分析、李群表示理论和谱几何的最新发展密切相关。暑期班是面向本科生和研究生的，然后是一个会议。暑期班包括两周的课程，第一周面向本科生，第二周面向研究生。暑期班和会议将促进与量化相关的数学领域的研究活动。组织者挑选了具有广泛兴趣和背景的讲师，其中包括一些物理学家。暑期班和会议将让研究生有机会接触到目前广泛的量化研究活动，并让学生有机会与知名研究人员互动。一位参与欧洲大型强子对撞机项目的物理学家的公开演讲将有助于提高公众的科学意识，并让数学家有机会与实验高能物理学家互动。本科生暑期班将让顶尖本科生接触到数学物理中的重要思想，并鼓励他们学习更多关于物理的知识。会议论文集将作为对学习量子化感兴趣的学生和研究人员的资源。量子化是数学和物理学中的一个重要课题。从物理学的角度来看，量子化方法是从类似的、更直观的经典力学系统中建立量子力学系统的模型的过程，它提供了惊人的精确的实验预测。理论物理学在20世纪的大部分发展可以被认为是改进量子化以提供更好的实验预测的过程，而寻求统一场论是试图以与现有量子理论兼容的方式量子化广义相对论。在数学方面，与量子化和量子力学有关的问题为泛函分析、李群表示理论和谱几何的发展提供了强大的动力。最新的进展包括几何量子化、形变量子化和各种经典物体的量子类似物。量化计划将在巴黎圣母院开设一个新的数学中心。它将结合两个为期一周的暑期学校，一个针对高级本科生，另一个针对研究生，以及一个致力于该领域最新进展的会议。会议的受邀演讲者是世界领先的量化数学专家。

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.