Mathematical Sciences: Theta Lifting and Cohomology of Discrete Subgroups

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This research, in the area of automorphic forms, makes use of theta-liftings for the construction of automorphic forms related to the representation theory of groups over local fields. Although scholars in local representation theory have obtained deep results about lifting general classes of unitary representations, the applications to automorphic forms have often been restricted to lifting one-dimensional characters. This research involves a specific and important case of the global lifting problem and success should provide guidance for more general work in the future. This research bridges both Modern Analysis and Algebra and Number Theory and concerns the representation theory of classical groups together with automorphic forms on classical groups.