Mathematical Sciences: Algebraic K-Theory

该奖项支持代数K-理论和循环同调的研究。主要研究人员将研究K-理论的结构是如何通过映射到更高的Chow群、e-不变量、割圆迹和循环同调来度量的。他还将看到K理论的已知结构中有多少存在于循环同调中。最后，他将通过对有限维代数上的微分的约化来攻击Berger关于曲线的猜想。这项研究涉及到代数K-理论。在广义上，代数K-理论涉及基和向量空间等线性代数概念的演化。这项工作对数论和代数几何具有重大意义，并有望在许多不同的数学领域之间建立令人兴奋的联系。

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.