Conference: Singularities in Analysis and Geometry

摘要奖：DMS-0506270主要研究者：Robert M.奇异对象和潜在奇异对象的正则性理论在几何、拓扑和分析的所有领域中已经并将继续发挥重要作用。F.里斯·哈维和约翰·C. Polking，无论是共同的还是单独的，涉及奇点的分析和结构，在所有三个领域都有广泛的应用。这次会议，在承认他们的学术和学术服务，将处理重要问题，涉及奇点提出的工作在过去的30年。它将集中在最近的发展，奇异空间作为一个副产品的校准几何，特殊的拉格朗日子流形，可移动的奇异性问题，和相对较新的领域奇异连接。会议开始时将有一个针对研究生、博士生的介绍性会议。和非专业研究人员。 会议的主体将涉及来自受邀讲师的广泛专业知识的主题，其中包括：校正几何中的奇异性，例外完整性，CR几何，微分特征，奇异空间的几何，复子流形和簇的奇异性，解析代数的扩张问题，奇异联络的几何方面，特殊拉格朗日理论，联络空间的紧化，调和映射的正则性理论，特殊的拉格朗日极小化和杨-米尔斯联系。最后，会议的一个环节将致力于研究技术在课堂上的具体应用。通过对从宏观经济系统到宇宙的宇宙学模型，再到固体的微观力学的各种现象的数学模型，“奇点”的概念在过去的三十年里变得突出起来。它被认为是平滑介质在空间或时间上的突然中断。它可能发生在一个点上，如两个碰撞的粒子，沿着一条曲线，如闪电，或一个表面，如地震断层，或在一些高维的“表面”，如发生在多参数经济模型。分析、几何和拓扑学等纯数学的基本领域都在研究理解奇点形成和结构的问题。在两位学术领导人退休之际，这次及时的会议汇集了来自所有这些领域的优秀研究人员和学生，进行了协同的思想交流。会议的讲座的许多具体主题都有其起源和应用数学物理，从经典力学系统的拉格朗日描述（1800年）到弦理论问题（1990年）。奇异点的几何分析不仅为这些已建立的应用提供了重要的信息，而且也为生物学和计算问题中产生的新奇异点提供了重要的信息。

AbstractAward: DMS-0506270Principal Investigator: Robert M. Hardt and Michael WolfSingular objects and regularity theory for potentially singularobjects have played and continue to play an essential role in allareas of geometry, topology and analysis. The works of F. ReeseHarvey and John C. Polking, both jointly and separately,involvingthe analysis and structure of singularities, have ranged widelyover all three areas. This conference, in recognition of theirscholarly and academic service, will treat important issuesinvolving singularities raised in their works over the last 30years. It will focus on recent developments in singular spaces asan outgrowth of calibrated geometries, special Lagrangiansubmanifolds, removable singularity problems, and the relativelynew area of singular connections. The conference will begin withan introductory session aimed at graduate students, recentPh.D.'s, and non-specialist researchers. The body of theconference will involve topics from the wide expertise of theinvited lecturers which encompass: singularities in calibratedgeometries, exceptional holonomy, CR geometry, differentialcharacters, geometry of singular spaces, singularities of complexsubmanifolds and varieties, extension problems for analyticobjects, geometric aspects of singular connections, specialLagrangian theory, compactification of spaces of connections, andregularity theory of harmonic maps, special Lagrangianminimizers, and Yang-Mills connections. Finally one session ofthe conference will be devoted to the study of a specificimplementation of technology in the classroom.Through mathematical models of a wide variety of phenomena frommacro-economic systems, to cosmological models of the universe,to microscopic mechanics of solids, the notion of a"singularity" has gained prominence in the last thirtyyears. It is identified with the sudden disruption in space ortime of a smooth media. It may occur at a point, as with twocolliding particles, along a curve, as with lightning, or asurface, as with an earthquake fault, or on some higherdimensional "surface," as occurs in multi-parametereconomic models. The basic fields in pure mathematics ofanalysis, geometry, and topology, have all attacked problems ofunderstanding singularity formation and structure. This timelyconference, on the occasion of the retirement of two academicleaders, brings together outstanding researchers and studentsfrom all these fields for a synergistic exchange of ideas. Manyof the specific topics of the lectures of the conference haveboth their origins in and applications to mathematical physics,from the Lagrangian description of classical mechanical systems(1800's) to problems in string theory (1990's). The mathematicalanalysis of singularities provides important information for notonly these well-established applications but also for newsingularities arising from biological and computational problems.