Theta correspondences and related problems in automorphic representations

该奖项将用于支持自守形式理论的几个研究项目，特别是在朗兰兹计划的背景下。这些项目主要涉及局部和全局θ对应的理论。其中，PI试图通过建立Siegel-Weil公式的第二项恒等式来解决所谓的theta对应的非零问题，并获得局部zeta积分的某些预期分析性质。自守形式理论是现代数学的核心主题之一。这不仅是因为它被认为是最深刻和最美丽的学科之一，而且还因为它与纯数学和应用数学的各个领域密切相关，特别是数论和表示论以及调和分析。除了这些知识方面，应该提到的是，该奖项将通过出版物和在国家和国际专业会议上的演讲，通过与相关领域和其他领域的研究人员的交流，以及通过正式和非正式的教育活动，如指导研究生和本科生，使各级知识界受益。

This award will be used to support several research projects in the theory of automorphic forms especially in the context of the Langlands program. The projects chiefly concern the theory of both local and global theta correspondences. Among other things, the PI intends to solve the so-called non-vanishing problem of the theta correspondences by establishing the second term identity of the Siegel-Weil formula in full generality and obtaining certain expected analytic properties of local zeta integrals.The theory of automorphic forms is one of the core themes of modern mathematics. This is not only because it has been found one of the deepest and most beautiful subjects, but also because it is closely connected to various areas of both pure and applied mathematics, in particular number theory and representation theory as well as harmonic analysis. Aside from those intellectual aspects, it should be mentioned that this award will be used to benefit a wide range of intellectual communities at various levels through publications and presentations in national and international professional meetings, through communications with researchers in related areas and other fields, and through formal and informal educational activities such as supervising students at both graduate and undergraduate levels.