CBMS Conference: The Basic Homotopy Lemma, The Asymptotic Uniqueness Theorem, and Classification of C*-Algebras, June 1-5, 2015

这一奖项将资助将于2015年6月在怀俄明大学与首席讲师林华新共同举办的CBMS会议，题为《C*-代数的基本同伦引理、渐近唯一性定理和分类》。算子代数的研究是现代数学的一个重要分支。它是由约翰·冯·诺伊曼在1930年的S发起的，目的是解释量子力学。至少是行为更好的顺从C*-代数的分类被认为是目前算子代数理论的主要问题之一。近年来，这一学科发展非常迅速，并取得了实质性进展。这次会议的主要目的是详细和系统地叙述C*-代数分类方面的这一突破，重点是基本同伦引理和渐近唯一性定理。会议将汇集这些最新的成果，以清楚地了解目前的状况，并绘制未来研究的可能方向。这笔赠款将支持研究生和初级教员参加会议，并促进出版一本供更广泛社区使用的专著。该项目的主题是关于C*-代数的分类、基本同伦引理和渐近唯一性定理。在AH-代数的各种奇异例子被发现之后，关于顺从C*-代数的分类的程序一直集中在更好的C*-代数，或吸收了江苏代数Z的一类C*-代数上。利用温特提出的单参数变形技巧，Z-稳定C*-代数的分类可以归结为有理C*-代数的两个同态之间的某种同伦的构造。这种同伦的存在是由Lin最新的渐近唯一性定理和基本同伦引理保证的，它们已经在分类理论之外产生了影响。

This award will fund a CBMS Conference entitled "The Basic Homotopy Lemma, The Asymptotic Uniqueness Theorem, and Classification of C*-Algebras" with principal lecturer Huaxin Lin to be held at the University of Wyoming during June of 2015. The study of operator algebras is one of the major branches of modern mathematics. It was launched by John von Neumann in 1930's with an aim of explicating quantum mechanics. The classification of at least the more well-behaved amenable C*-algebras is considered as one of the main questions at the moment in operator algebra theory. Recently this subject has been developing very rapidly, and substantial progress has been made. The main goal of this conference is to have a detailed and systematic account of this breakthrough in the classification of C*-algebras, with an emphasis on basic homotopy lemmas and asymptotic uniqueness theorems. The conference will pull together these recent results, to get a clear picture of the current status, and to chart the possible direction of future research. This grant will support the participation of graduate students and junior faculty members in the conference, and also foster the production of a monograph which will be used by the wider community. The topic of the project is on the classification of C*-algebras, the basic homotopy lemmas, and the asymptotic uniqueness theorems. After the discovery of various exotic examples of AH-algebras, the program of the classification of amenable C*-algebras has been focused on the more well-behaved C*-algebras, or the class of C*-algebras which absorb the Jiang-Su algebra Z. With the one-parameter deformation technique introduced by Winter, the classification of Z-stable C*-algebras can be reduced to the construction of a certain homotopy between two homomorphisms of the rationalized C*-algebras. The existence of such a homotopy is ensured by Lin's very recent asymptotic uniqueness theorems and basic homotopy lemmas, which have already had an impact outside classification theory.