Spectra of Arithmetic Manifolds & L-Functions

9401571 Sarnak该奖项支持Peter Sarnak教授对对称空间的等差商拉普拉斯谱精细结构的研究。这些问题与数的解析理论中的一些核心问题有关。它们也受到了从事量子混沌研究的物理学家的关注。这是数论领域的研究。数论基本上是对整数的研究。在该奖项下进行的研究通过将整数编码为微积分函数来研究它们的性质。数论是最古老的数学领域之一，但它一直在为这门学科的其他部分选择方向方面发挥着重要作用。在过去的半个世纪里，整数的研究变得更加重要，因为这个理论已经被用来为计算机科学开发新的算法，并为电子产品构建新的纠错码。

9401571 Sarnak This award supports Prof. Peter Sarnak's study of the fine structure of the spectrum of the Laplacian for arithmetic quotients of symmetric spaces. These problems turn out to be related to a number of central problems in the analytic theory of numbers. They have also received attention from Physicists working in Quantum Chaos. This is research in the field of number theory. Number theory is basically the study of whole numbers. The research done under this award studies properties of the whole numbers by encoding them into the functions of calculus. Number theory is among the oldest fields of mathematics, yet it has always played an important role in choosing directions for the rest of the subject. Within the last half century, the study of whole numbers has become doubly important as the theory has been used to develop new algorithms for computer science and to construct new error correcting codes for electronics.