Mathematical Sciences: Algebraic K-Theory

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This award supports research in algebraic K-theory and cyclic homology. The principal investigator will investigate the manner in which the structure of K-theory is measured by maps to higher Chow groups, e-invariants, cyclotomic traces and cyclic homology. He will also see how much of the known structure for K-theory is present in cyclic homology. Finally, he will attack Berger's conjecture for curves by means of a reduction to differentials on finite-dimensional algebras. This research is concerned with algebraic K-theory. In a broad sense, algebraic K-theory concerns the evolution of concepts from linear algebra such as basis and vector space. This work has significant implications for number theory and algebraic geometry, and promises to make exciting connections between a number of different areas of mathematics.