Journees Peter Shalen - A Conference on 3-Dimensional Topology and Its Role in Mathematics

摘要：项目负责人：Marc E. Culler， Steven boyer三流形拓扑这一学科与数学的其他部分有着深刻而有趣的相互作用。随着这门学科的发展，这些联系的复杂性随着时间的推移而增加，近年来呈爆炸式增长。这一爆炸与该领域最近几个主要突出问题的解决同时发生，这是一个反思其与其他数学领域关系的好时机。该基金将支持会议的参与者，该会议将在蒙特利尔CRM举行，旨在汇集各种领先的研究人员，他们的工作展示了3流形拓扑与数学其他领域之间的深层联系。演讲者将包括以下领域的主要研究人员：3流形的几何化；组合群论与群的粗几何性质随机3流形的性质与双曲曲面的渐近性质花同源性，Khovanov-Rozansky同源性；由接触结构引起的3流形不变量；性格品种;和Dehn手术。会议将向Peter Shalen致敬，他的工作是将数学的许多不同方面用于研究3流形，并将3流形拓扑的影响扩展到其他领域的主要力量。纵观历史，数学与科学之间的相互作用一直以这样一种神秘现象为特征：在没有具体应用的情况下发展起来的数学思想，结果却非常适合未来的科学应用。例如，微分几何为爱因斯坦的广义相对论提供了理想的数学基础，它是由数学家们在更早的时候发展起来的，他们无法预料到它在物理学中的应用方式。在较小的范围内，也存在涉及不同数学领域的类似现象。最近的一个与本次会议的主题直接相关的例子是佩雷尔曼对瑟斯顿几何化猜想的证明。这次会议旨在促进不同数学领域之间意想不到的富有成效的互动。会议的中心议题是三维空间的研究。演讲者被挑选出来，他们的工作涉及到这一主题的重要新应用，或者来自广泛的其他数学领域的思想。会议网址：https://www.crm.umontreal.ca/cal/fr/mois200606.html。

AbstractAward: DMS-0603270Principal Investigator: Marc E. Culler, Steven BoyerThe subject of 3-manifold topology has a long history of deep andinteresting interactions with other parts of mathematics. Thecomplexity of these connections has increased with time, as thesubject developed, and it has exploded in recent years. Thecoincidence of this explosion with the recent solution of severalof the major outstanding problems in the area make this a goodtime for reflection on its relationship to the rest ofmathematics. This grant will support participants in aconference, to be held at CRM in Montreal, which aims to bringtogether a varied group of leading researchers whose workdemonstrates deep connections between 3-manifold topology andother areas of mathematics. The speakers will include leadingresearchers in areas such as: geometrization of 3-manifolds;combinatorial group theory and coarse geometric properties ofgroups; properties of random 3-manifolds and asymptoticproperties of hyperbolic surfaces; Floer homology,Khovanov-Rozansky homology; 3-manifold invariants arising fromcontact structures; character varieties; and Dehn surgery. Theconference will honor Peter Shalen, whose work has been a majorforce in bringing many different aspect of mathematics to bear onthe study of 3-manifolds, and in expanding the influence of3-manifold topology into other areas.Throughout history the interaction between mathematics andscience has been characterized by the mysterious phenomenon thatmathematical ideas which are developed with no specificapplication in mind turn out to be perfectly suited for futureapplications to science. For example, differential geometry,which provided the ideal mathematical foundation for Einstein'sgeneral relativity theory, was developed much earlier bymathematicians who could not have anticipated the way in which itwould be applied in physics. On a smaller scale, there is asimilar phenomenon involving different areas of mathematics. Arecent example of this, which is directly related to the topic ofthis conference, is provided by Perelman's proof of Thurston'sGeometrization Conjecture. This conference aims to facilitatethese sorts of unexpected fruitful interactions between differentareas of mathematics. The central topic of the conference is thestudy of 3-dimensional spaces. Speakers have been selected whosework involves significant new applications to this subject ofideas which originate from a wide range of other areas ofmathematics.The conference web site ishttp://www.crm.umontreal.ca/cal/fr/mois200606.html.