Mathematical Sciences: "L-Adic Representations and Iwasawa Theory"

该奖项支持普林斯顿大学安德鲁·怀尔斯教授在算术代数几何方面的研究。怀尔斯博士计划通过检查与某类赫克特征型相关的表示的对称平方来继续他在岩川理论中的研究。通过这种方式，他希望攻击格林伯格猜想，该猜想涉及新定义的l -进表示相容族的Selmer群。这是算术代数几何领域的研究，是一门结合了代数几何和数论技术的学科。在其最初的公式中，代数几何处理的图形可以用最简单的方程，即多项式在平面上定义。数论始于整数和整数能否被整数整除之类的问题。这两个看似相距甚远的主题，实际上从最早的时代起就相互影响，但在过去的四分之一世纪中，相互影响大大增加。算术代数几何领域现在使用了所有现代数学的技术，并在其本身的边界之外产生了相应的影响。

This award supports the research in arithmetic algebraic geometry of Professor Andrew Wiles of Princeton University. Dr. Wiles plans to continue his researches in Iwasawa Theory by examining the symmetric square of a representation associated to a certain class of Hecke eigenforms. In this way, he hopes to attack the Greenberg conjectures, which concern the newly defined Selmer groups of compatible families of L-adic representations. This is research in the field of arithmetic algebraic geometry, 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.