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

2003 年阿肯色州春季系列讲座：关于安德鲁斯-柯蒂斯和庞加莱猜想；

• 批准号: 0245047
• 负责人: Yoav Rieck
• 金额: $ 2.4万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-03-15 至 2004-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0245047&HistoricalAwards=false
• 关键词: Arkansas; Spring; Lecture; Series; 2003

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.

摘要奖项：DMS-0245047 首席研究员：Yoav Rieck 拟议会议的中心将是耶鲁大学安德鲁·卡森教授的一系列讲座。 这些讲座将集中讨论拓扑和群论领域中两个最重要的开放问题。 第一个问题是庞加莱猜想，由亨利·庞加莱在大约 100 年前提出。 它涉及非常简单的 3 维空间的基本结构；而安德鲁斯-柯蒂斯猜想是关于代数结构的，与庞加莱猜想非常相关。 除了对与这些猜想相关的现有方法、部分结果和悬而未决的问题进行调查之外，这些演讲还将尝试描述这两个猜想之间的一些有趣的异同。 此外，来自世界各地的10位顶尖专家将就他们自己的工作发表演讲。本次会议将是第28届年度阿肯色州春季系列讲座。 系列讲座的形式是由一位世界顶尖数学家进行 5 场一小时的演讲，并伴有约 10 场特邀专家的演讲，以及包括研究生在内的各种人士的几场简短演讲。 这种结构很有价值，特别是对于年轻的研究人员来说，他们获得了极好的学习机会。今年的系列讲座是关于 3 维拓扑的。近年来，低维拓扑的重要性与日俱增，其众多应用从机器人和控制开始，一直到理论物理和宇宙学。 例如，一个有趣的问题是宇宙的形状是什么。 地球的球形形状在两千年前就被发现了，但我们对宇宙的形状一无所知。 卡森教授以及其他顶尖数学家的工作，可能有助于回答这个问题，引导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·维克斯将在向公众开放的演讲中讨论此类实验。公众并使用所有人都能理解的语言。这将使公众有机会了解世界领先数学家的工作。 杰夫·威克斯的演讲对于激励年轻学生享受基础研究应该具有巨大的教育价值。