Cornell Topology Festival Support; 2003-2005

康奈尔拓扑节支持；

• 批准号: 0244361
• 负责人: Peter Kahn
• 金额: $ 6.7万
• 依托单位: Cornell University
• 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: 2003-04-15 至 2007-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0244361&HistoricalAwards=false
• 关键词: Cornell; Topology; Festival; Support; 2003

AbstractAward: DMS-0244361Principal Investigator: Peter J. KahnThe topology/geometry group in the Department of Mathematics atCornell University requests funding to continue support for threeyears for the Cornell Topology Festival, which this group hashosted each year since 1963. The Festival provides a significantarena for the dissemination and development of important, newresults from a wide array of areas within the realms ofalgebraic, differential, and geometric topology, and alliedsubjects. While it is planned to continue the broad,interdisciplinary flavor and collaboration-friendly format thathave characterized the Festival over the years, it is alsoproposed to extend the Festival by a day to accommodate specificannual areas of emphasis. In this way the Festival can beresponsive to the dominant trends of this era: namely, thesimultaneous flourishing of both subspecializations andcross-disciplinary activity. An active outreach program, whichincludes some travel support, will be initiated to broadenparticipation in the Festival. For our initial conference underthis grant (May 1-4, 2003), we will have as area of emphasis thevery active field of geometric group theory.The Topology Festival was conceived and initiated in the 1960'sboth as an annual celebration of the burgeoning field of topologyand as an annual conference/workshop for topologists in thenortheastern United States. While topology has deep roots inearly European mathematical investigations of space and geometry,it is in the mid-twentieth century that topology came of age,with American mathematicians providing a large array of seminaldiscoveries. American topology has been a key element inAmerica's world leadership in mathematics. Topology is a broadsubject, which overlaps with areas of `discrete' mathematics(e.g., algebra, combinatorics), as well as with `continuous' or`smooth' mathematics (e.g., differential geometry, dynamicalsystems, mathematical physics). Indeed, a large part ofcontemporary mathematics has been profoundly affected bytopological results and methods. As a foundational subject, theapplications of topology are very widespread. A few examples are:genetics (the study of knotting of DNA molecules), neuroscienceand robotics (dynamical systems modeling), computer science ( ingeometric modeling and simulation), mathematical economics (insmooth equilibrium theory), physics (the theory of gauge fields),and neighboring fields in mathematics (e.g., geometric grouptheory). Although many of the basic questions that powered earlyefforts in topology have been answered, new problems areconstantly being generated as science moves forward, andimportant classical problems remain. An example of the latter isthe Poincare Conjecture, which has been the subject of severalnotable talks at past Topology Festivals and remains one of thepremier unsolved problems of mathematics today---one of the ClayInstitute's seven `millenium problems'--- and the focus ofintense research. The topologists and geometers at Cornell areproud of the useful role that the Topology Festival has playedand will continue to play in the contemporary development of thisdynamic area of mathematics.

摘要奖项：DMS-0244361 首席研究员：Peter J. Kahn 康奈尔大学数学系拓扑/几何小组请求资金继续支持康奈尔拓扑节三年，该小组自 1963 年以来每年主办该节。代数、微分和几何领域内广泛领域的重要新成果的传播和发展拓扑学和相关学科。 虽然计划延续多年来节日的广泛、跨学科风格和协作友好的形式，但也建议将节日延长一天，以适应特定的年度重点领域。通过这种方式，艺术节可以响应这个时代的主导趋势：即子专业化和跨学科活动的同时繁荣。将启动一项积极的外展计划，其中包括一些旅行支持，以扩大节日的参与范围。对于我们在这笔资助下举行的首次会议（2003 年 5 月 1-4 日），我们将把非常活跃的几何群理论领域作为重点领域。拓扑节是在 1960 年代构思和发起的，作为这一新兴领域的年度庆祝活动拓扑学，并作为美国东北部拓扑学家的年度会议/研讨会。 虽然拓扑学深深植根于欧洲早期对空间和几何的数学研究，但拓扑学在二十世纪中叶才成熟，美国数学家提供了大量开创性的发现。美国的拓扑学一直是美国在数学领域处于世界领先地位的关键因素。 拓扑学是一门广泛的学科，它与“离散”数学领域（例如代数、组合学）以及“连续”或“平滑”数学领域（例如微分几何、动力系统、数学物理）重叠。 事实上，当代数学的很大一部分已经受到拓扑结果和方法的深刻影响。拓扑学作为一门基础学科，其应用十分广泛。一些例子是：遗传学（DNA分子打结的研究），神经科学和机器人学（动力系统建模），计算机科学（几何建模和模拟），数理经济学（光滑平衡理论），物理学（规范场理论），以及数学的邻近领域（例如几何群论）。 尽管推动拓扑学早期研究的许多基本问题已经得到解答，但随着科学的进步，新的问题不断产生，重要的经典问题仍然存在。 后者的一个例子是庞加莱猜想，它一直是过去拓扑节上几次著名演讲的主题，并且仍然是当今数学中最重要的未解决问题之一——克莱研究所的七个“千年问题”之一——以及激烈的争论的焦点。研究。康奈尔大学的拓扑学家和几何学家对拓扑节在这一充满活力的数学领域的当代发展中已经并将继续发挥的有益作用感到自豪。