Workshop on LÏ2-methods in Geometry

摘要奖：DMS-9972298首席研究员：帕特里克·T·麦克唐纳成功的L2方法出现，以解决许多上下文(例如，数学物理、几何和拓扑)中的各种问题。在这种情况下，方法本身往往是截然不同的。尽管如此，这些不同的方法往往可以用来提供针对相同或相似问题的洞察力。“几何中的第二语言方法”研讨会的主要目的是聚集几何分析领域的领军人物，他们开发了不同的第二语言方法来研究相关的几何现象。研讨会的主题将包括：伪微分算子的指数定理、迹和行列式及其应用、谱不变量(包括解析挠率和Novikov-Shubin不变量)以及(谱)几何中的Von Neumann代数方法。研讨会将为年轻的研究人员提供一个独特的机会与杰出的资深同事互动，他们开发了各种共同测量问题的方法，并将集体注意力集中在一系列明确定义的问题上。分析方法极大地促进了我们对许多数学学科的集体理解，以及我们对物理学中一些基本主题的理解，其中一些已经进入重要的应用程序(例如，各种成像技术)。这次研讨会将汇聚一批在几何分析领域做出重大贡献的国际知名学者。这些贡献反映了为解释相同或相似的现象而提供的各种观点的集合。将这些观点结合在一起，将促进就广大数学界感兴趣的问题进行思想交流和合作。这样的环境将为许多年轻的研究人员提供一个宝贵的机会，来比较和对比各种想法和方法，确定他们的前进方向。

AbstractAward: DMS-9972298Principal Investigator: Patrick T. McDonaldSuccessful L2-methods arise to address a wide variety of problemsin a number of contexts (for example, mathematical physics,geometry, and topology). As this is the case, the methodsthemselves are often strikingly different. Nonetheless, it isoften the case that these different methods can be used toprovide insight directed towards the same or similar problems.The primary purpose of the workshop ``L2-methods in Geometry'' isto bring together leading figures in geometric analysis who havedeveloped different L2-methods for investigating relatedgeometric phenomena. Topics which will be addressed at theworkshop will include: index theorems, traces and determinants ofpseudodifferential operators and their applications, spectralinvariants including analytic torsion and Novikov-Shubininvariants, and Von Neumann algebra methods in (spectral)geometry. The workshop will provide the young investigators witha unique opportunity to interact with distinguished seniorcolleagues who have developed a variety of approaches togeometric problems and who will focus their collective attentionon a sharply defined collection of problems.Analytic methods have contributed immensely to our collectiveunderstanding of many mathematical disciplines, as well as to ourunderstanding of a number of fundamental topics in physics, someof which have found their way into important applications (forexample, various imaging techniques). This workshop will bringtogether a distinguished international collection of scholars whohave made fundamental contributions to the field of geometricanalysis. These contributions reflect a diverse collection ofperspectives offerred as explanations for the same or similarphenomena. Bringing these perspectives together will foster anexchange of ideas and collaboration on problems of deep interestto the mathematics community at large. Such an environment willprovide many young investigators with a valuable oppportunity tocompare and contrast a variety of ideas and approaches, shapingthe direction in which they will move.