Gekhtman, Michael Evens, Samuel Hall, Brian Liu, Xiaobo

University of Notre Dame, Notre Dame, IN, United States

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.

This proposal helped to fund a program devoted to various mathematical aspects of quantization that took place in May-June, 2011. The program inaugurated a new Center for Mathematics at Notre Dame. In combined 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. Intellectual merit. 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 sys- tems, 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 quan- tization 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 invited speakers at the conference were among the worldâ€™s leading experts in the mathematics of quantization. Broader impact. The summer school and conference promoted research activities in areas of mathematics related to quantization. We have selected lecturers with a broad array of interests and backgrounds, including some physicists. The summer school and conference supported a number of graduate students, and give them access to a wide array of current research activity in quantization, and give the students an opportunity to interact with prominent researchers. Our undergraduated summer school exposed top undergraduates to important ideas in mathematical physics, and encouraged them to learn more about physics. The volume of proceedings of the conference (currently in preparation) will serve as a resource for students and researchers interested in learning about quantization.

- Agency
- National Science Foundation (NSF)
- Institute
- Division of Mathematical Sciences (DMS)
- Type
- Standard Grant (Standard)
- Application #
- 1114152
- Program Officer
- Tie Luo

- Project Start
- Project End
- Budget Start
- 2011-04-15
- Budget End
- 2012-03-31
- Support Year
- Fiscal Year
- 2011
- Total Cost
- $20,000
- Indirect Cost

- Name
- University of Notre Dame
- Department
- Type
- DUNS #

- City
- Notre Dame
- State
- IN
- Country
- United States
- Zip Code
- 46556