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

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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.