Workshop on LÏ2-methods in Geometry

摘要：获奖：dms -9972298首席研究员：Patrick T. mcdonald成功的l2方法出现在许多背景下（例如，数学物理，几何和拓扑）解决各种各样的问题。在这种情况下，方法本身往往是截然不同的。尽管如此，通常情况下，这些不同的方法可以用来提供针对相同或类似问题的见解。研讨会“几何中的l2 -方法”的主要目的是汇集几何分析领域的领军人物，他们开发了不同的l2 -方法来研究相关的几何现象。研讨会将讨论的主题包括：指数定理、伪微分算子的迹线和行列式及其应用、谱不变量（包括解析扭和诺维科夫-舒宾不变量）以及谱几何中的冯·诺伊曼代数方法。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，他们已经开发了各种几何问题的方法，并将他们的集体注意力集中在一个明确定义的问题集合上。分析方法极大地促进了我们对许多数学学科的理解，也极大地促进了我们对物理学中许多基本主题的理解，其中一些已经得到了重要的应用（例如，各种成像技术）。本次研讨会将汇集对几何分析领域做出重要贡献的国际知名学者。这些贡献反映了为解释相同或类似现象而提供的不同观点。将这些观点结合在一起，将促进对整个数学界感兴趣的问题的思想交流和合作。这样的环境将为许多年轻的研究者提供一个宝贵的机会来比较和对比各种各样的想法和方法，从而决定他们前进的方向。

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.