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。Meuser博士的项目涉及到对p-进复幂的性质的研究，也就是众所周知的伊古萨局部Zeta函数。特别是，她打算探索局部Zeta函数的行为与由此函数派生的代数簇的几何之间的联系。这是对代数几何领域的研究，代数几何是现代数学中最古老的部分之一，但在过去的25年里，它取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。

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.