Mathematical Sciences: Problems in Arithmetics Geometry and Complexity Theory

该奖项支持算术代数的研究 几何学教授杰里米·泰特尔鲍姆的大学 伊利诺斯州在芝加哥。泰特尔鲍姆博士将继续研究 p-adic上半平面的几何和算术， “零”的概念，即零的概念。 值的某些功能，即p-adic L-功能，以 某些曲线的解析几何。另外他还会 继续研究算法的计算复杂性 从代数几何学。 算术代数几何是一门结合了 代数几何和数论的技巧。在其 原始公式，代数几何处理的图形， 可以用最简单的方程在平面上定义，即 多项式数论是从整数开始的 一个整数被另一个整数整除的问题。这两 看似相距甚远的学科，实际上却相互影响 但在过去的四分之一世纪， 影响力大增。算术代数领域 几何学现在使用了所有现代数学的技术， 在其边界之外具有相应的影响力。

This award supports the research in arithmetic algebraic geometry of Professor Jeremy Teitelbaum of the University of Illinois at Chicago. Dr. Teitelbaum will pursue his studies of the geometry and arithmetic of the p-adic upper half plane, guided by the Exceptional Zero Conjecture, which relates the values of certain functions, namely p-adic L-functions, to the analytic geometry of certain curves. In addition, he will continue his study of the computational complexity of algorithms from algebraic geometry. Arithmetic algebraic geometry is a subject that combines the techniques of algebraic geometry and number theory. In its original formulation, algebraic geometry treated figures that could be defined in the plane by the simplest equations, namely polynomials. Number theory started with the whole numbers and such questions as divisibility of one whole number by another. These two subjects, seemingly so far apart, have in fact influenced each other from the earliest times, but in the past quarter century the mutual influence has increased greatly. The field of arithmetic algebraic geometry now uses techniques from all of modern mathematics, and is having corresponding influence beyond its own borders.