Mathematical Sciences: Kloosterman Sums and p-adic Differential Equations

该奖项支持明尼苏达大学Richard Crew博士的代数几何研究。他的研究将集中在研究Kloosterman和几何方法，特别是，他将调查所产生的monodromy组某些p进微分方程，来自这些款项。本研究是在有限特征的代数几何中进行的。虽然该领域起源于连续变化的几何结构，如直线和平面的概念，但在这种情况下，离散接管，并且类似于整数理论的方法是最有用的。反过来，有限特征的代数几何现在对数论产生了巨大的影响，并在计算机科学和编码理论中得到应用。

This award supports the research in Algebraic Geometry of Dr. Richard Crew of the University of Minnesota. His research will center on the study of Kloosterman sums by geometric methods, and in particular, he will investigate the monodromy groups arising from certain p-adic differential equations that come from these sums. This research is work in the Algebraic Geometry of finite characteristic. Although the field originated with notions of continuously varying geometric structures like lines and planes, in this context the Discrete takes over, and methods akin to those from the theory of whole numbers are most useful. Reciprocally, the algebraic geometry of finite characteristic is now having great influence on the Theory of Numbers, and is finding application in Computer Science and Coding Theory.