Mathematical Sciences: Number Theory and Algebraic Geometry

这项研究是在算术代数几何领域进行的，它是数论和代数几何之间的桥梁。Adolphson将继续他对指数和及其相关的L函数的研究。赖特将继续研究全局场的判别式的分布、与表示有关的Zeta函数的基本理论以及在Maskit的嵌入中使用他的组合码来证明Bers关于尖点密度的猜想。Cogdell将研究非齐次型Zeta函数和变分形式之间的联系。Yukie是博士后，将学习几何不变量理论、代数群和Shintani的Zeta函数。

This research is in arithmetic algebraic geometry, the bridge area between number theory and algebraic geometry. Adolphson will continue his research on exponential sums and their associated L-functions. Wright will continue his research on the distribution of discriminants of global fields, on the basic theory of zeta functions associated to representations and on the use of his combinatorial code for the boundary of the Teichmuller space of once punctured tori in Maskit's embedding to prove Bers' conjecture on the density of cusps. Cogdell will investigate connections between zeta functions of prehomogeneous type and metaplectic forms. Yukie, the postdoctoral associate, will study geometric invariant theory, algebraic groups, and Shintani's zeta functions.