Mathematical Sciences: Manifolds, Transformation Groups, andSingular Spaces

Steinberger将研究等变分类空间的同伦群及其稳定性。他和Shaneson将继续研究线性表示的分类，直到拓扑相似性。Shaneson计划研究奇异空间的局部和全局分析以及拓扑结构，特别是代数变异。他还计划继续研究一些关于4-流形的开放性问题。这些都是几何拓扑学的核心问题，如果历史可以作为我们的指导，其中一些问题可以在适当的时间延迟后迁移到理论物理中。

Steinberger will study homotopy groups of equivariant classifying spaces and their stability properties. He and Shaneson will continue to attack the classification of linear representations up to topological similarity. Shaneson plans to study the local and global analysis and topology of singular spaces in general and of algebraic varieties in particular. He also plans to continue to work on some open questions concerning 4-manifolds. These are all central problems in geometric topology, and some of them can be expected to migrate into theoretical physics with an appropriate time lag, if history can be our guide.