Mathematical Sciences: Higher Algebraic K-theory

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This research is concerned with algebraic K-theory. The principal investigator will study the special lambda-ring identities for the general exterior power operations. In addition he will study the connection between the algebraic K-groups and the motivic cohomology groups and work on higher periods of symmetric powers of elliptic curves. This project is in the general area of algebraic K-theory. K-theory concerns the evolution of the ideas of vector space, basis, linear mapping and general linear group to a context where the scalars are from a commutative or noncommutative ring. In this context, K-theory can be utilized in algebraic geometry and other mathematical models involving coefficients from rings.