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

摘要奖：DMS-0603270主要研究者：Marc E.三维流形拓扑学与数学的其他部分有着深刻而有趣的相互作用。 随着这个课题的发展，这些联系的复杂性随着时间的推移而增加，而且在最近几年里呈爆炸式增长。 这种爆炸与该领域几个主要悬而未决问题的最近解决方案的巧合，使这成为反思其与其他数学关系的好时机。 该补助金将支持参加将在蒙特利尔CRM举行的会议的参与者，该会议旨在汇集各种领先的研究人员，他们的工作展示了3-流形拓扑和其他数学领域之间的深刻联系。 演讲者将包括领先的研究人员在以下领域，如：几何化的3-流形;组合群论和粗糙的几何性质的团体;性质的随机3-流形和渐近性质的双曲曲面;弗洛尔同源性，Khovanov-Rozansky同源性; 3-流形不变量所产生的接触结构;字符品种;和Dehn手术。 这次会议将荣誉彼得沙伦，他的工作一直是一个主要的力量，使许多不同方面的数学承担研究的3-流形，在扩大3-在整个历史上，数学和科学之间的相互作用一直以一种神秘的现象为特征，即在头脑中没有具体应用的数学思想被证明是完全适合的。future未来applications应用to Science科学. 例如，微分几何，这提供了理想的数学基础爱因斯坦的广义相对论，是开发了更早的数学家谁也无法预料的方式，它将被应用在物理学。 在较小的范围内，有一个类似的现象涉及不同的数学领域。 佩雷尔曼对瑟斯顿几何化猜想的证明提供了最近的一个例子，与本次会议的主题直接相关。 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。 发言人已被选定谁的工作涉及重大的新应用这一主题的理念，源于广泛的其他领域ofmathematics。会议的网站http：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.