Mathematical Sciences: Manifolds, Transformation Groups, andSingular Spaces

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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.