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

由该奖项资助的特殊年度的主题将是跨学科的，强调发展拓扑和模表示理论之间的联系，并将其应用于代数k理论、代数几何、代数数论和群的上同调。代数拓扑学自由地使用了代数和代数几何中的许多技术。稳定同伦范畴的分裂分析现在采用有限群的模表示，稳定同伦范畴的整体研究引入了代数数论中熟悉的概念。另一方面，将拓扑技术应用于代数循环的研究和数论中整数环的拓扑分析提供了两个非常新的例子，说明这种相互作用是双向的。Sullivan猜想和Segal猜想的解与紧李群的表示理论产生了许多联系，这些联系为同伦理论提供了强有力的新技术。这笔赠款将资助西北大学在1991- 1992年期间开展上述主题的重点年。这个特别年份的一个组成部分是将于1992年3月举行的一次国际会议。这个特别的年份和会议是及时的，将为新的发展提供一个必要的论坛，并为进一步取得成果奠定基础。

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.