Mathematical Sciences: Studies in the Analytic Theory of Automorphic Forms

该奖项支持分析理论的研究， 大学教授艾萨克·埃弗拉特的自守形式 马里兰州的学院公园。Efrat博士提议研究一种 图的调和分析问题集， 作为秩为1的模空间的导数出现的曲面， 离散群体这些问题源于对 这类群的离散谱的存在性，以及 离散本征函数的作用。的其他方面 Efrat教授的项目包括研究某些arith- 附于非同余的Eisenstein级数 分组。 非欧平面几何始于19世纪初 世纪作为一个数学的好奇心，但在年底， 世纪，数学家们已经意识到， 基本的重要性是非欧几里德在其基本性质。 对非欧平面几何的详细研究， 上升到现代数学的几个分支，其中 模和自守形式的研究是最活跃的研究之一。 此字段主要涉及有关 整数，但在其使用的几何和分析，它 与其历史根源保持联系。

This award supports the research in the analytic theory of automorphic forms of Professor Isaac Efrat of the University of Maryland at College Park. Dr. Efrat has proposed to investigate a collection of problems in the harmonic analysis of graphs and surfaces that arise as quotients of spaces of rank one, modulo discrete groups. These problems stem from questions about the existence of discrete spectra for such groups, and the construc- tion of discrete eigenfunctions for them. Other aspects of Professor Efrat's project involve the study of certain arith- metically defined Eisenstein series attached to non-congruence subgroups. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of modular and automorphic forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots.