Mathematical Sciences: Analytic Methods for Automorphic Forms

Professor Iwaniec and his postdoctoral associate Dr. Duke will use the methods of Analytic Number Theory to investigate modular and automorphic forms; in particular, Dr. Iwaniec will continue his longterm project of refining the theory of modular forms by means of exponential and character sums. The field of Analytic Number Theory applies to the discrete realm of the whole numbers the techniques of Analysis, dependent on the notions of Continuity and Limit, originating in Calculus. The idea of using continuous methods to investigate the Discrete is two centuries old, but with the work of the modern analytic number theorists such as Professor Iwaniec, the field has had a new rebirth.