L-Functions and Automorphic Forms Conference, May 16 - 19, 2002, The Johns Hopkins University

Johns Hopkins University, Baltimore MD

Investigators

Abstract

Zeta and L-functions provide an extremely powerful method for studying difficult and fundamental problems in Number theory. Moreover, analogous functions are propping up in other parts of Mathematics as well as in Physics, for example to provide regularizations of seemingly divergent data. The dynamic field of Automorphic Forms is an excellent source of important zeta functions, and in fact a far-reaching conjecture of Langlands says that all zeta functions admitting an Euler product are modular, i.e., associated to automorphic forms on GL(n). This conference will review and examine the positive results and techniques which have come about in the past few years, with a special eye towards the L-function methods leading to various instances of transfer of automorphic forms from one group to another. This award partially supports a conference in number theory. Number theory is that branch of mathematics that studies properties of numbers, such as the distribution of prime numbers. This particular conference focuses on certain types of continuous functions, called automorphic functions, that encode deep symmetries which occur in nature, analogous to waveforms on a small pond. The discrete tones which occur have interesting number theoretic meanings. Instead of starting with the functions and looking for their discrete tones, mathematicians and physicists can start with discrete collections of numbers and from which they construct continuous functions. Then the central problem is to know if these functions admit hidden symmetries. When they do, then still more special properties must be present as well. Exploiting this kind of information is a pressing endeavor and there are many gold mines yet to be discovered.