Theta correspondences and related problems in automorphic representations

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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.