Representations, Geometry, and Quantization

“表示、几何和量子化”会议将于2018年5月28日至6月1日在麻省理工学院举行。自从100年前引入量子力学以来，一个基本问题就是如何理解经典物理学和量子物理学之间的关系。经典物理学对大尺度和低能量的世界进行了非常精确和完整的描述，而量子物理学则对小尺度和高能量的世界进行了明显不同的描述。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。这次会议将汇集这一领域的世界领导人，介绍他们的研究成果。本文将要讨论的一些最新发展包括：一种识别实约李群的酉表示的算法；提高了对倾斜模块字符理论的理解；非紧流形的几何量化格拉斯曼人的镜像对称。会议的网址是https://math.mit.edu/conferences/kostant/.This，奖项反映了NSF的法定使命，并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，认为值得支持。

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.