Singularities in Geometry and Topology

摘要奖：DMS-0706968首席研究员：杰夫·切格，Shmuel Weinberger本次会议将探索现代几何和拓扑学中出现的非光滑空间的不同方法，并在不同的研究人员之间进行交叉培养。其中两个中心推力是基于分层思想的拓扑法和度量度量空间，以及它们的分析，特别是它们的微积分。此外，这些研究的应用是多种多样的，从Novikov猜想、纽结理论、变换群到黎曼几何和几何群论中的Gromov-Hasudorff收敛技术，再到理论计算机科学家感兴趣的问题(在各种Banach空间中嵌入有限元空间)。预计这次会议的结果是，在产生奇异空间上的解析几何结构、群的准等距理论和特征类方面有望取得进展。分析和几何的许多基本思想都是基于线性逼近的思想。第一个例子是微积分本身，其中线性近似定义了导数的基本概念。一个更现代的例子是拓扑学中的流形概念，它是一个在小区域内由欧几里德空间很好地逼近的空间。无数的进一步发展表明，需要更通用的工具来处理这种近似不可行或可能不存在的情况。通过将在不同背景下处理这些问题的工作人员聚集在一起，这次会议将促进新合成的发展，并将在完全不同的环境中出现的共同问题放在突出位置。会议网址为：http://www.math.uchicago.edu/~shmuel/Cappelliday.

AbstractAward: DMS-0706968Principal Investigator: Jeff Cheeger, Shmuel WeinbergerThis conference will explore differing approaches to non-smoothspaces that arise in modern geometry and topology with an eyetowards cross-fertilization among the various groups ofresearchers. Two of the central thrusts are topological methodsbased on the ideas of a stratification, and metric measurespaces, and their analysis, especially their differentialcalculus. Others are based on cohomology with growth conditions,or resolution of singularities, intersection homology, sheaftheory etc. Moreover the applications of these studies arediverse, from the Novikov conjecture, knot theory, andtransformation groups to Gromov-Hasudorff convergence techniquesin Riemannian geometry and geometric group theory to problems ofinterest to theoretical computer scientists (embedding finitemetric spaces in various Banach spaces). It is anticipated thatas a result of this meeting, progress can be expected in thedirections of producing analytic geometric structures on singularspaces, the quasi-isometric theory of groups, and characteristicclasses.Many of the basic ideas of analysis and geometry are based on theidea of linear approximation. The first example of this iscalculus itself where linear approximation defines the basicnotion of the derivative. A more modern example is the idea of amanifold in topology, which is a space that is, in small regions,well approximated by Euclidean space. Countless furtherdevelopments have shown the need for more general tools to dealwith situations where such approximations are not feasible or maynot exist. By bringing together workers who have dealt withthese issues in varied contexts, this conference will spur thedevelopment of new syntheses and bring to the fore common issuesthat arise in completely different settings. The conference website is http://www.math.uchicago.edu/~shmuel/Cappelliday.