Arkansas Spring Lecture Series 2003: On the Andrews-Curtis and Poincare Conjectures; April 10-12, 2003; Fayetteville, AR

摘要奖：DMS-0245047首席研究员：Yoav Rieck拟议中的会议的中心将是耶鲁大学安德鲁·卡森教授的一系列演讲。这堂课将集中在拓扑学和群论领域中最重要的两个开放问题上。第一个问题，庞卡雷猜想，是亨利·庞加莱在近100年前提出的。它涉及非常简单的三维空间的基本结构；而Andrews-Curtis猜想是关于代数结构的，并且与Poincare猜想非常相关。除了对与这些猜想相关的现有方法、部分结果和公开问题的综述外，这些讲座还将试图描述这两个猜想之间一些有趣的相似和不同之处。此外，来自世界各地的10位顶尖专家将发表关于他们自己工作的演讲。这次会议将是第28届阿肯色州春季系列讲座。系列讲座的形式是由一位世界领先的数学家进行5场一小时的演讲，并伴随着约10场由特邀专家主持的讲座，以及由包括研究生在内的各种人进行的几次较短的演讲。这种结构很有价值，特别是对于年轻的研究人员来说，他们获得了很好的学习机会。今年的系列讲座是关于三维拓扑的。最近，低维拓扑学的重要性与日俱增，从机器人学和控制学开始，到理论物理学和宇宙学结束，有许多应用。例如，一个耐人寻味的问题是宇宙的形状是什么。地球的球状形状是在两千年前发现的，但我们对宇宙的形状一无所知。卡森教授和其他著名数学家的工作可能会帮助回答这个问题，带领天文学家是正确的方向，并帮助设计正确的实验来回答这些问题。麦克阿瑟研究员杰夫·威克斯将在演讲中讨论这些实验，并使用所有人都能理解的语言。这将让公众有机会了解世界领先数学家的工作。杰夫·威克斯的演讲在激励年轻学生享受基础研究方面应该有很大的教育价值。

AbstractAward: DMS-0245047Principal Investigator: Yoav RieckAt the center of the proposed conference will be a series of lectureby Professor Andrew Casson of Yale University. These lecture willfocus on two of the most important open questions in the fields oftopology and group theory. The first question, the PoincareConjecture, was posed by Henri Poincare almost 100 years ago. It isconcerned with the basic structure of very simple 3-dimensionalspaces; while the Andrews-Curtis Conjecture is about algebraicstructures, and is very relevant to the Poincare Conjecture. Inaddition to a survey of existing approaches, partial results and openquestions related to these conjectures, these talks will attempt todescribe some intriguing similarities and differences between the twoconjectures. In addition, 10 leading experts from around the worldwill deliver talks about their own work.This conference will be the 28th annual Arkansas Spring LectureSeries. The format of the lecture series is 5 one hour talks by aworld leading mathematician, accompanied by about 10 lectures ofinvited experts, and several shorter talks by a variety of people,including graduate students. This structure is valuable, particularlyfor younger researchers, that get an excellent learning opportunity.This year's Lecture Series is about 3-dimensional topology. Theimportance of low dimensional topology has been growing in recenttears, with numerous applications starting at robotics and control,and ending with theoretical physics and cosmology. For example, oneintriguing question is what the shape of the Universe is. Thespherical shape of the earth was discovered two millennia ago, and yetwe have no clue as to the shape of the Universe. The work ofProfessor Casson as well as other leading mathematician, may helpanswer this question by leading astronomers is the right direction,and helping design the right experiments to answer these questions.Jeff Weeks, a McArthur Fellow, will discuss such experiments in alecture open to the public and using a language accessible to all.This will give the public an opportunity to understand the work ofworld leading mathematicians. Jeff Weeks talk should have greateducational value in motivating younger students to enjoy basicresearch.