Mathematical Sciences: Properties of P-Adic Complex Powers

该奖项支持波士顿大学Diane Meuser教授在p进分析和代数几何方面的研究。默瑟博士的项目包括对p进复幂的性质的研究，也被称为伊古萨局部zeta函数。特别是，她打算探索局部zeta函数的行为与衍生该函数的代数变量的几何之间的联系。这是代数几何领域的研究，是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。

This award supports the research in p-adic analysis and algebraic geometry of Professor Diane Meuser of Boston University. Dr. Meuser's project involves an investigation of the properties of p-adic complex powers, otherwise known as the Igusa local zeta function. In particular, she intends to explore the connections between the behavior of the local zeta function and the geometry of the algebraic variety from which this function is derived. This is research in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.