Representations, Geometry, and Quantization

表示、几何和量化

• 批准号: 1802311
• 负责人: David Vogan
• 金额: $ 5万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-04-01 至 2019-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1802311&HistoricalAwards=false
• 关键词: Representations; Geometry; Quantization

The conference "Representations, Geometry, and Quantization" will take place May 28 - June 1, 2018, at the Massachusetts Institute of Technology. Since the introduction of quantum mechanics a hundred years ago, a fundamental problem has been to understand the relationship between classical physics, which is extraordinarily accurate and complete as a description of the world at large scales and low energies, and quantum physics, which offers an apparently different description of the world, including small scales and high energies. This relationship has many parallels in mathematics, and understanding those parallels is a source of inspiration in both mathematics and physics. The conference will bring together world leaders in this subject to present their research. Some particular recent developments to be discussed include: an algorithm to identify unitary representations of real reductive Lie groups; improved understanding of character theory for tilting modules; geometric quantization for noncompact manifolds; and mirror symmetry for Grassmannians. The conference web site is https://math.mit.edu/conferences/kostant/.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

会议“表示，几何和量化”将于2018年5月28日至6月1日在马萨诸塞州理工学院举行。自从100年前引入量子力学以来，一个基本问题就是理解经典物理学和量子物理学之间的关系，经典物理学在大尺度和低能量下对世界的描述是非常准确和完整的，而量子物理学对世界的描述显然不同，包括小尺度和高能量。这种关系在数学中有许多相似之处，理解这些相似之处是数学和物理学的灵感来源。会议将汇集世界各国领导人在这个问题上提出他们的研究。 要讨论的一些特别的最新发展包括：一个算法，以确定酉表示的真实的还原李群;提高理解的字符理论倾斜模块;几何量化的非紧流形;和镜像对称的格拉斯曼。会议网站是https://math.mit.edu/conferences/kostant/.This奖反映了NSF的法定使命，并已被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。