Mathematical Sciences: Twisted Endoscopy

该奖项支持Robert Kottwitz博士在自构形方面的研究。他的项目包括与D.Shelstad合作，涉及一种扭曲形式的轨迹公式及其与扭曲内窥镜检查组的关系。他还将研究某些模空间上模p的点的空间，并研究该领域中的一个猜想的“基本引理”，根据该引理，某些球函数具有匹配的轨道积分。非欧几里得平面几何起源于十九世纪初的一种数学奇观，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产生了现代数学的几个分支，其中自同构形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 of Dr. Robert Kottwitz in Automorphic Forms. Among his projects are joint work with D. Shelstad involving a twisted form of the Trace Formula and its relation to twisted endoscopic groups. He will also investigate the spaces of points modulo p on certain moduli spaces, and work on a conjectured "Fundamental Lemma" in the field, according to which certain spherical functions have matching orbital integrals. 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 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.