Mathematical Sciences: Automorphic Representations, L-Packets and Theta Liftings

该奖项支持J.Rogawski教授致力于自同构函数的研究。他打算研究酉群的L-包与theta提升之间的关系。他打算首先研究拟分裂酉群U(3)，然后尝试将这些结果推广到一般酉群。模形式起源于19世纪中叶的非欧几里德几何。因此，数学家和物理学家都早已认识到，许多具有根本重要性的物体本质上都是非欧几里得的。这个领域主要涉及关于整数的问题，但在使用几何和分析时，它保留了与其历史根源的联系，从而与理论物理中的规范理论和信息论中的编码理论等不同领域的问题有关。

This award supports the research of Professor J. Rogawski to work in automorphic functions. He intends to work on the relations between L-packets and theta liftings for unitary groups. He intends to first study the quasi-split unitary group U(3) and then try to extend these results to general unitary groups. Modular forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. 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 and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.