Mathematical Sciences: Regularized Products, Heat Kernal Analysis and Analytic Number Theory

这个项目要解决的问题在于 谱理论和数论的一般领域， 特别感兴趣的轨迹公式，明确的公式和 素数定理，以及各种分析和算术 Arakelov理论的一部分。 拟议的研究非常广泛， 涉及分析、数论和代数几何。 这项研究使用代数几何的技术， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。如今，该领域 不仅使用代数方法，而且使用分析方法， 拓扑学，反过来说， 以及物理学、理论计算机科学， 机器人

The problems that are to be addressed in this project lie in the general area of spectral theory and number theory, with particular interest in trace formulae, explicit formulae and prime number theorems, and various analytic and arithmetic aspects of Arakelov theory. The proposed research is very broad, involving analysis, number theory, and algebraic geometry. This research uses the techniques of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.