Mathematical Sciences: Algebraic K-theory

该奖项支持代数K理论的研究， 特别是在结构和可计算性方面， 奇异簇的K理论 校长 研究人员将研究K理论， Etale上同调和循环同调，通过Etale Chern 特征标、分圆迹和次级陈特征标。 他还将研究K理论上的亚当斯运算， 向动机上同调和负向的消失图发展 K组 本研究涉及代数K理论。 中 广义的代数K理论关注的是 线性代数中的概念，如基和向量空间。 这项工作对数论和 代数几何，并承诺作出令人兴奋的连接 数学中的许多不同领域。

This award supports research in algebraic K-theory, particularly with regard to the structure and computability of the K-theory of varieties with singularities. The principal investigator will investigate the relationship between K-theory, etale cohomology and cyclic homology, via the etale chern character, the cyclotomic trace and secondary chern character. He also will study the Adams operations on K-theory, with an eye toward vanishing conjectures for motivic cohomology and negative K-groups. 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 in mathematics.