Computer Methods for L-functions
and Automorphic Forms

March 22 – 26, 2010
Organizers: Craig Citro (Seattle), B. Edixhoven (Leiden),
M. Rubinstein (Waterloo), W. Stein (Seattle)

For years, computers have also played a key role in investigating the most central questions in the analytic theory of automorphic forms such as the existence of Maass wave forms. Recently, a team of researchers, including M. Rubinstein (Waterloo) and W. Stein (Seattle), has embarked on an ambitious collaborative effort to systematically gather vast amounts of data concerning, among other things, automorphic forms on higher rank groups. This effort is part of a three year (2008-2011) NSF funded Focused Research Group (FRG) grant dealing with L-functions and automorphic forms. The FRG effort is sure to generate challenges and new questions for people working both on the theoretical and the experimental side of the subject, as well as gathering valuable data that will be precious in suggesting conjectures or revealing new lines of enquiry.

A parallel theme of the workshop will be the emerging role of specialised software in number theory. While they have been on the scene for many years, symbolic algebra systems  have become a lot more powerful and integrated in recent years. The possibilities offered by the world wide web have caused some  packages (the computer system SAGE, notably) to embrace the “wikipedia model” whereby all  members of the community can contribute code in a decentralised manner. The possibilities of such an approach are tremendously exciting, but also raise a host of challenges.

This workshop will bring together the “experimentalists” who develop the sofware and the “theoreticians” who are primarily interested in using it to test conjectures or discover patterns, so that each group can become better aware of each other's needs, priorities, and capabilites.

The Aisenstadt Chair Akshay Venkatesh will be giving the Aisenstadt Chair lectures during this workshop.