Conference: Singularities in Analysis and Geometry

摘要奖：DMS-0506270主要研究员：Robert M.Hardt和Michael Wolf关于潜在奇异对象的奇点对象和正则性理论已经并将继续在几何、拓扑和分析领域发挥重要作用。哈维和波尔金的著作，包括奇点的分析和结构，既有共同的，也有单独的，涵盖了所有这三个领域。这次会议，为了表彰他们的学术和学术贡献，将讨论涉及他们在过去30年作品中提出的奇点的重要问题。它将集中于奇异空间的最新发展，它是校准几何、特殊的拉格朗日子流形、可移除奇点问题以及相对较新的奇异联络领域的产物。会议将以面向研究生、新近获得博士学位的S和非专业研究人员的介绍性会议开始。会议的主体将涉及来自受邀讲师的广泛专业知识的主题，包括：校准几何中的奇点，特殊完整，CR几何，微分特征，奇异空间的几何，复子流形和簇的奇点，分析对象的延拓问题，奇异联络的几何方面，特殊拉格朗日理论，连接空间的紧致，调和映射的正则性理论，特殊拉格朗日极小化，和杨-米尔斯联系。会议的最后一节将专门研究技术在课堂上的具体实施。从宏观经济系统到宇宙的宇宙模型，再到固体的微观力学，通过对各种现象的数学模型，“奇点”的概念在过去的30年里变得突出起来。它被认为是一种光滑介质在空间或时间上的突然破裂。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，或在一些更高维的“表面”，如在多参数经济模型中发生的。纯数学中的分析、几何和拓扑学的基本领域都攻击了理解奇点的形成和结构的问题。在两位学术领袖退休之际，这一定期会议汇集了来自所有这些领域的杰出研究人员和学生，以协同方式交流思想。会议演讲的许多具体主题既起源于数学物理，又应用于数学物理，从经典力学系统的拉格朗日描述(1800年的S)到弦理论的问题(1990年的S)。奇点的数学分析不仅为这些成熟的应用提供了重要的信息，而且也为生物和计算问题产生的新奇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.