Spring Topology and Dynamics Conference 2002, at the University of Texas at Austin on March 21-23, 2002

2002 年春季拓扑与动力学会议，2002 年 3 月 21-23 日在德克萨斯大学奥斯汀分校举行

• 批准号: 0129227
• 负责人: Cameron Gordon
• 金额: $ 3.15万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-02-01 至 2004-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0129227&HistoricalAwards=false
• 关键词: Spring; Topology; Dynamics; Conference; 2002

DMS-0129227Cameron M. GordonThe Department of Mathematics at the University of Texas at Austin will host the 2002 Spring Topology and Dynamics Conference. Now in its 36th year, this is the largest annual topology conference in the US. It has a broad scope that encompasses set-theoretic and general topology, continuumtheory and dynamical systems, geometric group theory and geometric topology. It thus provides a unique forum for researchers in a wide range of disciplines within topology. There will be eight invited plenary one-hour lectures of a semi-expository nature, given by leading researchers in the areas covered. There will also be twenty invited half-hour lectures, together with 15-minute contributed talks, held infour parallel sessions. The invited speakers have been selected with the help of an advisory committee of experts in the various subfields.Topology is one of the major subdisciplines of mathematics, and, at just over a hundred years old, the youngest. It originated with Henri Poincare around 1900, who introduced it as a means of describing the qualitative behavior of certain physical systems (for example, our solar system),whose complexity renders a precise quantitative analysis too difficult. The wide range covered by the subject today is well represented by the Conference. General topology deals with the abstract properties of topological spaces; set-theoretictopology impinges upon the logical foundations of mathematics. The study of dynamical systems is close to Poincare's original motivation, and deals with the behavior of various iterative processes. These often give rise to complex objects, continua,which are studied in their own right. Geometric topology deals with manifolds, objects which are locally like n-dimensional Euclidean space, but whose global structure might be quite complicated. For instance, there is a lot of current activity in 3-dimensional topology, whose goal isessentially to describe all theoretically possible 3-dimensional universes. Rich connections have recently been discovered between this subject and quantum physics, while on the other hand topological techniques from the theory of knots in 3-dimensional space have recently been applied to the study of DNA. Finally, geometric group theory, a relatively new subject, studies groups, which are algebraic objects, from a topological point of view; this is leading to deep connections between topology and algebra. The interaction at the Conference between workers in all these different branches of topology is expected to be very fruitful.

DMS-0129227 Cameron M.戈登得克萨斯大学奥斯汀分校数学系将主办2002年春季拓扑和动力学会议。现在是第36届，这是美国最大的年度拓扑会议。它有一个广泛的范围，包括集理论和一般拓扑，continuumtheory和动力系统，几何群论和几何拓扑。因此，它提供了一个独特的论坛，研究人员在广泛的学科拓扑结构。将有八个邀请全体一小时的讲座半暂时性的，在所涵盖的领域的主要研究人员给出。此外，还将有20个半小时的讲座邀请，连同15分钟的贡献会谈，在四个平行会议举行。邀请演讲者已选定的帮助下，咨询委员会的专家在各个子领域。拓扑学是一个主要的分支学科的数学，并在刚刚超过一百岁，最年轻的。它起源于1900年左右的亨利·庞加莱，他引入它作为描述某些物理系统（例如我们的太阳系）的定性行为的一种手段，其复杂性使得精确的定量分析变得非常困难。 裁谈会充分体现了今天这一议题所涉的广泛范围。一般拓扑学研究拓扑空间的抽象性质，而集合论拓扑学研究数学的逻辑基础。动力系统的研究接近庞加莱的原始动机，并处理各种迭代过程的行为。这些经常会产生复杂的对象，连续体，这是研究自己的权利。几何拓扑学处理流形，局部类似于n维欧氏空间的对象，但其整体结构可能相当复杂。例如，目前有很多三维拓扑学的活动，其目标基本上是描述所有理论上可能的三维宇宙。丰富的连接最近被发现之间的这个问题和量子物理学，而另一方面，拓扑技术的理论结在三维空间最近被应用到DNA的研究。最后，几何群论，一个相对较新的学科，从拓扑的角度研究群，这是代数对象;这导致拓扑和代数之间的深刻联系。预期所有这些不同拓扑学分支的工作者在会议上的互动将是非常富有成果的。