Vector-Valued Automorphic Forms and Applications

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This research proposal is in the area of number theory. This is a theory that has attracted the human mind since the time of ancient Greece. Today it is still a theory that fascinates people with its challenging problems and sophisticated abstraction. However, it has also been very useful in the practical world. For example, data encryption and the security of internet communication and  business transactions could not be achieved without the help of number theory.***In this proposal, I study the theory of vector-valued automorphic forms. These are intriguing objects that have immediate applications in other branches of number theory, algebra, geometry  as well as physics.***In the next five years, my goal is develop a complete theory of vector-valued forms in the general case, building on important  discoveries I made recently with my students in the area.**