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

该奖项支持托马斯·黑尔斯教授在朗格兰项目中的工作。朗兰德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踪迹公式的特殊情况。他还对研究真实群体中一些尚未解决的问题感兴趣。这些问题在许多不同的数学领域都很有趣。这项研究属于数论的总称。数论是研究整体数的性质的学科，是数学中最古老的分支。从一开始，数论中的问题就提供了创造新数学的动力，几乎在该学科的所有部分。朗兰德的计划是一种将数论和微积分联系起来的一般哲学。现代数论是非常技术性和深刻性的，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. ***