Conference: L2-Invariants and their Analogues in Positive Characteristic

会议：L2-不变量及其积极特征的类似物

• 批准号: 1748644
• 负责人: Mark Sapir
• 金额: $ 3.5万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1748644&HistoricalAwards=false
• 关键词: Conference; L2; Invariants; their; Analogues

This National Science Foundation award provides partial funding for U.S. based researchers to participate in a mathematical research and training program that will take place at Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain, from February 19, 2018 to June 15, 2018. This is a well-timed and ambitious program to bring together specialists as well as beginning researchers to study objects known as L2 invariants and their applications. These invariants draw on many areas of mathematics, such as Algebra, Analysis, Geometry and Topology, and in turn provide extremely useful tools to study unsolved problems in these areas. The objective of the program is two-fold: to train a new generation of leading researchers, and to facilitate advanced research. In order to achieve these goals, the program will begin with a two-week long introductory school aimed at early career researchers, such as graduate students and postdoctoral fellows, followed by several week-long advanced courses, and end with a closing workshop. Throughout, it will include weakly research and study seminars. Priority for funding is given to early career researchers. Historically, the theory of L2-invariants has its origin in the works of M. Atiyah, in which he proposed an extension of the Atiyah-Singer index theory of elliptic differential operators on compact manifolds to the non-compact case. The modern definition of these invariants is more algebraic and uses the language of CW-complexes. The analogue of the first L2-Betti number in positive characteristic, the p-gradient, was introduced by M. Lackenby in his study of hyperbolic 3-manifold groups. The study of L2-invariants is linked to topology, geometry, global analysis, operator theory, ring theory, group theory and K-theory. This program aims to reunite leading specialists in these areas in an exciting research environment at the ICMAT. It is a great opportunity to train young researchers in an area which has been successful in addressing important problems, such as the Baum-Connes conjecture and the Hanna Neumann conjecture, and is an important source of tools and ideas for attacking intriguing open problems in many areas of mathematics. More information is available at the program website at: https://www.icmat.es/rt/l2invariants2018/

该国家科学基金会奖项为美国研究人员提供部分资助，以参加将于 2018 年 2 月 19 日至 6 月 15 日在西班牙马德里研究所 (ICMAT) 举行的数学研究和培训项目。这是一个适时且雄心勃勃的项目，旨在将专家和新手研究人员聚集在一起，研究 L2 不变量及其应用。这些不变量借鉴了许多数学领域，例如代数、分析、几何和拓扑，反过来又为研究这些领域中未解决的问题提供了极其有用的工具。该计划的目标有两个：培养新一代领先研究人员，并促进高级研究。为了实现这些目标，该计划将以针对早期职业研究人员（例如研究生和博士后研究员）的为期两周的入门学校开始，然后是为期一周的高级课程，最后以闭幕研讨会结束。在整个过程中，它将包括弱研究和学习研讨会。资助优先考虑给早期职业研究人员。从历史上看，L2-不变量理论起源于 M. Atiyah 的著作，其中他提出了将紧流形上的椭圆微分算子 Atiyah-Singer 指数理论扩展到非紧情况。这些不变量的现代定义更加代数化，并使用 CW 复形的语言。 M. Lackenby 在他的双曲 3 流形群研究中引入了正特征中第一个 L2-Betti 数的类似物 p 梯度。 L2不变量的研究与拓扑、几何、全局分析、算子理论、环理论、群论和K理论相关。该计划旨在将这些领域的领先专家重新聚集在 ICMAT 令人兴奋的研究环境中。这是一个培训年轻研究人员的绝佳机会，该领域已成功解决了鲍姆-康尼斯猜想和汉纳·诺依曼猜想等重要问题，并且是解决许多数学领域中有趣的开放问题的工具和思想的重要来源。更多信息请访问该计划网站：https://www.icmat.es/rt/l2invariants2018/