Mathematical Sciences: Exponential Sums and Toric Varieties

该奖项支持阿道夫森教授的研究， 从事数论工作。 这个项目将探索 在有限域上的指数和和环面簇之间。 将探讨两个主要专题。 第一个主题是研究 的p-adic微分方程，产生于 指数和族的上同调变分 的 第二个课题是研究完全的p-adic上同调 路口 这是数论领域的研究。 Number 理论开始于整数和问题，如 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已经成为开发新算法的重要工具， 计算机科学和新的电子纠错码。

This award supports the research of Professor Adolphson to work in number theory. This project will explore the connections between exponential sums over finite fields and toric varieties. Two major topics will be pursued. The first topic is the study of the p-adic differential equations that arise from the variation of cohomology of families of exponential sums. The second topic is the study of the p-adic cohomology of complete intersections. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.