Representation Theory and Automorphic Forms

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AbstractSavinThis award supports research in several areas of representation theory and modular forms with applications to number theory. In particular, we propose to determine the Howe correspondence for generic square-integrable representations of classical p-adic groups. This work is based on the recent classification of generic square-integrable representations of classical p-adic groups due to Goran Muic. The theory of modular forms was born more then a century ago, as powerful techniques of complex analysis were introduced to attack classical problems in number theory. It has remained a vibrant mathematical subject throughout the 20th century with applications in physics, and more recently in computer science, coding theory in particular.