Mathematical Sciences: Algebraic K-theory

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This research is concerned with algebraic K-theory, particularly the structure and computability of the K-theory of varieties with singularities. The principal investigator plans to study the recently discovered chern characters, both primary and secondary, which relate K-theory to cyclic homology, as well as, the conjecture that the K-groups of a singular projective variety are built up from the K-groups of rings. The K-theory of special rings will also be studied with an eye toward structural results such as K-regularity and vanishing of negative K-groups. The research supported is in algebraic K-theory and algebraic geometry. In this project, the principal investigator applies K-theoretic techniques to algebraic surfaces, studying the structural changes that occur in K-groups when singularities are introduced.