Mathematical Sciences: Arithmetic of Automorphic Forms on Certain Shimura Varieties

该奖项支持在自守形式的研究 位于洛杉矶的加州大学的唐·布拉修斯教授 洛杉矶。Blasius博士的项目是完成 伽罗瓦型的马斯形式的伽罗瓦表示 扩展到相干上同调的某些解释方法， 已建立的全纯形式;以 稳定GSp（4）的跟踪公式，从 基本引理;并研究某些提升问题 涉及阿贝尔品种，在志村品种的设置， 应用他的工作对p-adic性质的霍奇类。 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 automorphic forms of Professor Don Blasius of the University of California at Los Angeles. Dr. Blasius's project is to complete the construction of Galois representations for Maass forms of Galois type by extending to coherent cohomology certain methods of interpre- tation that have been established for holomorphic forms; to stabilize the Trace Formula for GSp(4), beginning with the Fundamental Lemma; and to study certain lifting problems involving Abelian varieties, in the setting of Shimura varieties, applying his work on p-adic properties of Hodge classes. 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.