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

该奖项提供资金，帮助支付将于2015年6月1日至5日在怀俄明大学校园举行的“落基山数学联盟暑期学校：C*-代数的结构”的参与者的费用。算符代数是由约翰·冯·诺伊曼和他的合作者默里在1930年的S时期提出的，当时数学家和物理学家开始在原子尺度上发展对物质的严格描述。为这一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)的可能的构型或状态由某些向量空间来描述。在物理系统上进行实验在数学上相当于将操作符应用于可能状态的向量空间。这些运算符的集合在数学上被描述为运算符的代数。如今，算子代数的研究已经成为一个重要的数学追求，并应用于数学和理论物理的许多其他分支。算子代数本身的研究也发展到了几个密切相关的子领域，其中一个是对一类重要的C*-代数的结构研究。在过去的几年里，C*-代数的分类得到了迅速的发展，得到了一些令人振奋的结果。这个暑期班的目标之一是综合这些最新的结果，以清楚地了解C*-代数的分类现状。落基山数学联合会(RMMC)举办暑期班已经有30多年了，其中的主题每年都有很大的变化。本系列2015年的主题是C*-代数的结构。这组主题包括：C*-代数分类中的von Neumann代数技巧；算子代数的K-理论的介绍；以及高秩图C*-代数。这次活动的讲师包括四位世界上C*-代数方面的领先权威：乔治·埃利奥特、龚桂华、佐藤康彦和亚历克斯·库姆健。选择这一专题的动机是这项活动的次要目的，即为暑期班的参与者，特别是低年级学生，准备参加将在6月第二周举行的由数学科学会议委员会(CBMS)主办的区域会议，该会议的重点是所谓的基本同伦引理和渐近唯一性定理，这是C*-代数分类最近取得突破的关键因素之一。暑期学校网站：http://www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/

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/