Conference: L2-Invariants and their Analogues in Positive Characteristic

该国家科学基金会奖为美国研究人员提供部分资金，用于参加将于2018年2月19日至2018年6月15日在西班牙马德里的科学数学研究所（ICMAT）进行的数学研究和培训计划。这是一个很好的时机和雄心勃勃的项目，汇集了专家和初级研究人员来研究被称为L2不变量的对象及其应用。这些不变量涉及数学的许多领域，如代数、分析、几何和拓扑，并反过来为研究这些领域中未解决的问题提供了非常有用的工具。该计划的目标是双重的：培养新一代的领先研究人员，并促进先进的研究。为了实现这些目标，该项目将以为期两周的入门课程开始，针对早期职业研究人员，如研究生和博士后，然后是为期几周的高级课程，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。优先资助早期职业研究人员。历史上，l2不变量理论起源于M. Atiyah的著作，他将紧流形上椭圆微分算子的Atiyah- singer指标理论推广到非紧情况。这些不变量的现代定义更加代数化，并且使用了cw复合体的语言。M. Lackenby在双曲3流形群的研究中，引入了第一个L2-Betti数在正特征p梯度上的类比。l2不变量的研究与拓扑学、几何、全局分析、算子理论、环理论、群论和k理论有关。该计划旨在在ICMAT令人兴奋的研究环境中重聚这些领域的领先专家。这是一个培养年轻研究人员的好机会，该领域已经成功地解决了重要问题，如Baum-Connes猜想和Hanna Neumann猜想，并且是解决许多数学领域有趣的开放问题的工具和思想的重要来源。更多信息请访问该项目网站：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/