Mathematical Sciences: Higher Algebraic K-theory

这项研究涉及到代数K-理论。主要的研究者将研究一般外幂运算的特殊的Lambda-环恒等式。此外，他还将研究代数K-群和上同调群之间的联系，并研究椭圆曲线的对称幂的高周期。本课题属于代数K-理论的一般领域。K-理论研究了向量空间、基、线性映射和一般线性群的思想在标量来自交换或非交换环的背景下的演化。在这种情况下，K-理论可以用于代数几何和其他涉及环系数的数学模型。

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.