Mathematical Sciences: Automorphic Forms of Galois Type, andthe L-functions of Some Simple Moduli Varieties

该奖项支持加州理工学院的Dinakar Ramakrishnan教授对自同构形式的研究。Ramakrishnan博士计划继续他在GL(2)上算术类型的尖点形式的工作，并研究与GSP(4)和U(4)所附的Shimura变种有关的某些后续问题。他还计划研究这些变种的上同调和圈类，以期找到与L函数的极点和零点的预期关系的例子。非欧几里得平面几何始于十九世纪初，最初是一种数学奇闻，但到那个世纪末，数学家们已经意识到许多具有根本重要性的物体本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已经形成了现代数学的几个分支，其中模和自同构形式的研究是最活跃的之一。这个领域主要涉及关于整数的问题，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 on Automorphic Forms of Professor Dinakar Ramakrishnan of the California Institute of Technology. Dr. Ramakrishnan plans to continue his work on cusp forms of arithmetic type on GL(2), and to investigate certain ensuing problems concerning the Shimura varieties attached to GSp(4) and U(4). He also plans to study the cohomology and cycle classes on these varieties with a view to finding examples of the expected relationship to poles and zeros of L-functions. 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.