Topics in representation theory and number theory

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)资助的。本尼迪克特·格罗斯计划对表象理论和数论之间的边界进行研究，探索当地和全球朗兰兹对应的含义。他期望将他与D.Prasad的猜想从SO(N)限制推广到SO(n-1)，以适用于所有经典群的限制问题。这将对厄米特变种和正交下村变种的算术产生影响。格罗斯还计划调查他与M·里德介绍的简单的超尖球面陈述。他希望在所有情况下确定它们的野伽罗瓦参数，并利用它们在迹公式中的简单矩阵系数。本尼迪克特·格罗斯计划研究数论中的问题之间的边界，例如伽罗瓦群的表示，以及群表示论中的问题，例如将酉群U(N)的表示的限制分解到子群U(n-1)。通过猜想的朗兰兹通信，这些问题是相当神秘的关联，格罗斯希望更详细地探索它们之间的联系。

"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)." Benedict Gross plans to do research on the boundary between representation theory and number theory, exploring the implications of the local and global Langlands correspondence. He expects to extend his conjectures with D. Prasad, on restriction from SO(n) to SO(n-1), to restriction problems for all classical groups. This will have implications for the arithmetic of Hermitian and orthogonal Shimura varieties. Gross also plans to investigate the simple supercuspidal representations he introduced with M. Reeder. He hopes to determine their wild Galois parameters in all cases, and to exploit their simple matrix coefficients in the trace formula.Benedict Gross plans to work on the boundary between questions in number theory, such as the representations of Galois groups, and questions in the representation theory of groups, such as the decomposition of the restriction of representations of the unitary group U(n) to the subgroup U(n-1). These problems are quite mysteriously related, via the conjectural Langlands correspondence, and Gross hopes to explore their connections in more detail.