Mathematical Sciences: Group Proposal in Topology

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9423300 May This project encompasses research in a wide variety of topics in topology and related areas of algebra, algebraic K-theory and algebraic geometry. One focus is global algebraic structures in stable homotopy theory, with applications to such topics as cobordism, topological Hochschild homology, and algebraic K-theory. Another is the study of algebraic and topological vector bundles and of Hochschild homology for algebraic varieties. Another is the study of analytic and combinatorial torsion invariants of manifolds. Research in algebraic and geometric topology at the University of Chicago has for many years explored areas both internal to topology and areas on the borders between topology and algebraic geometry and differential geometry. Ideas developed here, for example the notion of an operad, have been used in diverse fields, from mathematical physics to combinatorial group theory. Graduate students and postdocs involved in the project leave Chicago with especially broad interdisciplinary training and background. ***