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

该奖项将资助CBMS会议，该会议题为“基本同伦引理、渐进唯一性定理和C*-代数的分类”，首席讲师林华新将于2015年6月在怀俄明州大学举行。 算子代数的研究是现代数学的主要分支之一。它是由约翰·冯·诺依曼在20世纪30年代发起的，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算子代数理论的主要问题之一。近年来，这一课题发展迅速，并取得了实质性进展。本次会议的主要目标是有一个详细和系统的帐户这一突破的分类C*-代数，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结果，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师参加会议，并促进制作一本专着，供更广泛的社区使用。该项目的主题是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，顺从C*-代数的分类程序一直集中在行为更好的C*-代数，或吸收了Jiang-Su代数Z的C*-代数类上。 利用Winter引入的单参数变形技术，Z-稳定C*-代数的分类问题可以归结为在有理化C*-代数的两个同态之间构造某种同伦.这种同伦的存在性是由林的最近的渐近唯一性定理和基本同伦引理所保证的，这些引理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.