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

摘要：本次会议将以耶鲁大学Andrew Casson教授的系列讲座为中心。这些讲座将集中于拓扑学和群论领域中两个最重要的开放性问题。第一个问题，庞加莱猜想，是由亨利·庞加莱在大约100年前提出的。它关注的是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，并且与庞加莱猜想非常相关。除了对现有方法、部分结果和与这些猜想相关的开放性问题的调查之外，这些会谈将试图描述这两个猜想之间一些有趣的相似点和不同点。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。该系列讲座的形式是由一位世界领先的数学家进行5场一小时的讲座，辅以约10场受邀专家的讲座，以及包括研究生在内的各种人士的几场简短讲座。这种结构很有价值，特别是对年轻的研究人员来说，他们有很好的学习机会。今年的系列讲座是关于三维拓扑的。近年来，低维拓扑的重要性一直在增长，从机器人和控制开始，到理论物理和宇宙学都有许多应用。例如，一个有趣的问题是宇宙的形状是什么。地球的球形在两千年前就被发现了，但我们对宇宙的形状却一无所知。卡森教授和其他顶尖数学家的工作，可能有助于回答这个问题，因为领先的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（Jeff Weeks）将在向公众开放的讲座中讨论这些实验，并使用所有人都能使用的语言。这将给公众一个了解世界顶尖数学家工作的机会。Jeff Weeks的演讲在激励年轻学生享受基础研究方面应该具有很大的教育价值。

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.