Identities in Automorphic Descent

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This award supports the principal investigator's research on the theory of automorphic forms, a special topic in the general area of number theory. Number theory has its historical roots in the study of natural numbers. It is among the oldest branches of mathematics. Within the last half century it has become an indispensable tool, with diverse applications in areas such as data transmission and processing, communication systems, and internet security. In more detail, the project centers on the theory of automorphic forms. The main goal of the project is to develop the automorphic descent method, which provides construction of automorphic forms on classical groups. The PI will establish identities relating the constructed automorphic forms to the data used in the descent construction. The PI will also investigate the application of these identities to a quantitative refinement of the Gan-Gross-Prasad conjecture, which is a conjecture that can be viewed as a far-reaching local to global principle for period integrals.