Mathematical Sciences: Connections Between Topology and Representation Theory - Emphasis Year Proposal

数学科学：拓扑与表示论之间的联系 - 重点年份提案

• 批准号: 9104031
• 负责人: Mark Mahowald
• 金额: $ 2.4万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-15 至 1992-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104031&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Connections; Between; Topology

The subject of the special year funded by this award will be interdisciplinary in nature, emphasizing developing connections between topology and modular representation theory with applications to algebraic K-theory, algebraic geometry, algebraic number theory, and the cohomology of groups. Algebraic topology has freely employed numerous techniques from algebra and algebraic geometry. Analysis of splittings in the stable homotopy category now employs modular representation of finite groups and global studies of the stable homotopy category have introduced familiar concepts from algebraic number theory. On the other hand, the application of topological techniques to study algebraic cycles and the topological analysis of rings of integers in number theory provide two very recent examples that the interaction goes both ways. The solutions of the Sullivan and Segal Conjectures have lead to numerous connections with the representation theory of compact Lie groups and these connections have provided powerful new techniques in homotopy theory. This grant will fund an Emphasis Year on the above subject at Northwestern University during 1991-92. An integral part of this special year is an international conference to be held in March, 1992. This special year and conference are timely and will provide a needed forum for new developments and a foundation for further results.

由该奖项资助的特别年的主题将是 跨学科性质，强调发展联系 拓扑和模表示理论之间的联系， 代数K理论、代数几何、代数 数论和群的上同调。 代数拓扑 自由地使用了许多技术，从代数和代数 几何 稳定同伦范畴的分裂分析 现在采用有限群的模表示和全局 稳定同伦范畴的研究已经介绍了熟悉的 来自代数数论的概念。 另一方面 应用拓扑技术研究代数圈和 数论中整数环的拓扑分析 提供了两个最近的例子， 的方式 Sullivan猜想和Segal猜想的解 导致了许多与表征理论的联系 紧李群和这些连接提供了强大的新的 同伦理论中的技巧 这笔赠款将资助上述主题的重点年， 1991- 1992年就读于西北大学。 的组成部分 特别年是将于3月举行一次国际会议， 1992. 这一特殊的年份和会议是及时的， 新发展所需的论坛和进一步发展的基础 结果