Mathematical Sciences: Properties of P-Adic Complex Powers

该奖项支持波士顿大学Diane Meuser教授在p-adic分析和代数几何方面的研究。Meuser博士的项目涉及对p-adic复数幂的性质的研究，也被称为Igusa局部zeta函数。特别是，她打算探索当地zeta函数的行为和几何的代数品种，从这个功能是派生之间的联系。这是代数几何领域的研究，它是现代数学中最古老的部分之一，但在过去的四分之一世纪里，它已经有了革命性的发展。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，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.