Mathematical Sciences: Arithmetic of Automorphic Forms on Certain Shimura Varieties

该奖项支持加州大学洛杉矶分校教授 Don Blasius 的自守形式研究。 Blasius 博士的项目是通过将已为全纯形式建立的某些解释方法扩展到相干上同调，来完成伽罗瓦型 Maass 形式的伽罗瓦表示的构造。从基本引理开始稳定 GSP(4) 的迹公式；并在 Shimura 簇的背景下研究涉及阿贝尔簇的某些提升问题，应用他在 Hodge 类的 p-adic 性质方面的工作。 非欧几里得平面几何始于 19 世纪初，最初是作为一种数学好奇心，但到了该世纪末，数学家们意识到许多具有根本重要性的物体在其基本性质上都是非欧几里得的。 对非欧几里得平面几何的详细研究催生了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之一。 该领域主要关注有关整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系。

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.