Conference: L2-Invariants and their Analogues in Positive Characteristic

这项国家科学基金会奖为美国研究人员参与数学研究和培训项目提供部分资金，该项目将于2018年2月19日至2018年6月15日在西班牙马德里的数学研究所(ICMAT)举行。这是一个及时而雄心勃勃的计划，将专家和初级研究人员聚集在一起，研究被称为L2不变量的对象及其应用。这些不变量借鉴了许多数学领域，如代数、分析、几何和拓扑学，并反过来提供了非常有用的工具来研究这些领域中未解决的问题。该计划的目标有两个：培养新一代领先的研究人员，并促进高级研究。为了实现这些目标，该计划将从为期两周的入门课程开始，以研究生和博士后研究员等早期职业研究人员为目标，然后是几个为期一周的高级课程，最后是结束研讨会。在整个过程中，它将包括薄弱的研究和学习研讨会。资助优先考虑职业生涯早期的研究人员。在历史上，L2不变量理论起源于M.Atiyah的工作，在他的工作中，他提出了紧流形上椭圆微分算子的Atiyah-Singer指标理论的推广到非紧的情形。这些不变量的现代定义更加代数，并且使用CW-复形的语言。正特征的第一个L2-Betti数的类比p-梯度是M.Lackenby在他研究双曲三维流形群时引入的。L2-不变量的研究涉及到拓扑学、几何学、整体分析、算子论、环论、群论和K-理论。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。这是在一个成功解决重要问题的领域培训年轻研究人员的绝佳机会，例如鲍姆-康尼斯猜想和汉娜·诺伊曼猜想，是解决许多数学领域有趣的开放问题的重要工具和想法的重要来源。欲了解更多信息，请访问该计划的网站：https://www.icmat.es/rt/l2invariants2018/

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/