Mathematical Sciences: K-Theory for Operator Algebras, IndexTheory, Riemann-Roch

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Baum is currently working on five projects: (1) K-homology and C*-algebra K-theory (with A. Connes). (2) Intersection theory and bivariant K-theory (with J. Block) (3) Cyclic homology and higher Riemann-Roch (with J. Block). (4) Equivariant index theory for proper actions of discrete groups (with M. Davis and C. Ogle). (5) Index theory on compact C-infinity manifolds with boundary (with R. Douglas and M. Taylor). It is hard to characterize these topics as falling within one area of mathematics. (1) combines algebraic topology and modern analysis. (2) is more algebra and algebraic geometry. (3) combines algebraic topology and algebraic geometry. (4) and (5) combine analysis and algebraic topology. To the extent that there are applications of Baum's work, they are now mostly to other parts of mathematics. It is clear that these applications are very widely distributed within mathematics, however.