Rocky Mountain Mathematics Consortium Summer School: The Structure of C*-Algebras

落基山数学联盟暑期学校：C*-代数的结构

• 批准号: 1501137
• 负责人: Zhuang Niu
• 金额: $ 3.52万
• 依托单位: University of Wyoming
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-05-01 至 2016-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1501137&HistoricalAwards=false
• 关键词: Rocky; Mountain; Mathematics; Consortium; Summer

This award provides funding to help defray the expenses of participants in the "Rocky Mountain Mathematics Consortium Summer School: The Structure of C*-Algebras" that will be held from June 1-5, 2015, on the campus of the University of Wyoming. Operator algebras were introduced by John von Neumann and his collaborator Murray during the 1930's, when mathematicians and physicists began the development of a rigorous description of matter on the atomic scale. The physical theory developed for that description was quantum theory. Mathematically, the possible configurations or states of matter (an electron moving around an atom, for example) are described by certain vector spaces. Performing an experiment on the physical system corresponds mathematically to applying an operator to the vector space of possible states. The collection of such operators is described mathematically as an algebra of operators. Nowadays, the study of operator algebras has become an important mathematical pursuit with applications to many other branches of mathematics and theoretical physics. The study of operator algebra itself also has been developed into several closely related subareas, of which one is structural investigation of the important class called C*-algebras. The classification of C*-algebras has developed rapidly in the past few years, with several exciting results. One goal of this summer school is to pull together these recent results to get a clear picture of the current status of the classification of C*-algebras.The Rocky Mountain Mathematics Consortium (RMMC) has run a summer school, in which topics vary widely from year to year, for over thirty years. The theme of the 2015 installment in the series is the structure of C*-algebras. The set of topics includes the following: von Neumann algebra techniques in the classification of C*-algebras; an introduction to the K-theory of operator algebras; and higher-rank graph C*-algebras. The event's lecturers include four of the world's leading authorities on C*-algebras: George Elliott, Guihua Gong, Yasuhiko Sato, and Alex Kumjian. The choice of topic was motivated by the secondary purpose of the activity; namely, to prepare the summer school's participants, especially the junior ones, for the regional conference sponsored by the Conference Board of the Mathematical Sciences (CBMS) that will follow it during the second week of June and that has as its focus the so-called basic homotopy lemmas and the asymptotic uniqueness theorem, one of the key ingredients in the recent breakthroughs in the classification of C*-algebras. Summer school web site: http://www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/

该奖项提供资金，以帮助支付参加者的费用“落基山数学联盟暑期学校：C*-代数的结构”，将于2015年6月1日至5日，在怀俄明州的大学校园。算子代数是由约翰·冯·诺依曼和他的合作者默里在20世纪30年代引入的，当时数学家和物理学家开始在原子尺度上对物质进行严格的描述。为这种描述而发展的物理理论是量子理论。在数学上，物质（例如围绕原子运动的电子）的可能配置或状态由某些向量空间描述。在物理系统上执行实验在数学上对应于将算子应用于可能状态的向量空间。这些算子的集合在数学上被描述为算子代数。如今，算子代数的研究已经成为一个重要的数学追求，并应用于许多其他数学分支和理论物理。算子代数本身的研究也已经发展到几个密切相关的子领域，其中之一是对重要的C*-代数的结构研究。C*-代数的分类在过去的几年里发展迅速，并取得了一些令人兴奋的结果。这个暑期学校的一个目标是把这些最新的结果汇总在一起，以清楚地了解C*-代数分类的现状。落基山数学联盟（RMMC）已经开办了一个暑期学校，其中的主题每年都有很大的不同，超过30年。2015年系列的主题是C*-代数的结构。这套主题包括以下内容：冯诺依曼代数技术在分类的C*-代数;介绍了K-理论的算子代数;和高秩图C*-代数。该活动的讲师包括四个世界领先的C*-代数权威：乔治埃利奥特，龚桂华，佐藤康彦和亚历克斯Kumjian。主题的选择是出于活动的次要目的;即，准备暑期学校的参与者，特别是初级的，为区域会议主办的会议委员会的数学科学（CBMS），将遵循它在6月的第二个星期，其重点是所谓的基本同伦引理和渐近唯一性定理，最近在C*-代数分类上取得突破的关键因素之一。暑期学校网址：http://www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/