Mathematical Sciences: A Stable Trace Formula for the Rank-Two Symplectic Group

这个奖项支持托马斯·海尔斯教授在朗兰项目中的工作。朗兰程序是现代数论的核心，它为离散几何信息可以分析研究的思想提供了结构。黑尔斯教授致力于建立微量公式的特殊情况。他也对在现实群体中研究一些未解决的问题感兴趣。这些问题在许多不同的数学领域都引起了人们的兴趣。这项研究属于数论的总标题。数论是对整数性质的研究，是数学中最古老的分支。从一开始，数论中的问题就为这门学科几乎所有部分的新数学的创造提供了动力。朗兰程序是一种将数论与微积分联系起来的一般哲学。现代数论是非常技术性和深奥的，但它在理论计算机科学和编码理论等领域有着惊人的应用。＊＊＊

Hales This award supports the work of Professor Thomas Hales in the Langland's Program. The Langland's Program is central to modern number theory by providing structure to the idea that discrete geometric information can be studied analytically. Prof. Hales works on establishing special cases of the trace formula. He is also interested in studying some unsolved problems in real groups. These problems are of interest in a number of different areas of mathematics. This research falls under the general heading of Number Theory. Number Theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished the driving force to creation of new mathematics in almost all parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus. Modern number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory. ***