American Institute of Mathematics, Palo Alto, California
Andew Booker, Sally Koutsoliotas, Stefan Lemurell, and Andreas Strombergsson
This workshop, sponsored by AIM and the NSF, concerns methods for computing eigenvalues of the Laplacian on congruence subgroups of SL(2,Z) and generalizations to higher rank groups.
Recently, three new methods for studying eigenvalues of the Laplacian for Hecke congruence groups have been introduced. These methods involve the trace formula, the L-function associated to a Maass form, and creative use of the Hecke operators. All three methods are specific to Hecke congruence groups, and one goal of the workshop is to explore whether there is some underlying similarity to the methods, or whether a hybrid approach can be developed that combines features of the existing methods.
In addition, the workshop will explore possible improvements to the existing methods through a detailed examination of their strengths and limitations. Finally, alternate approaches to computing Maass forms and generalizations to GL(3) and other higher-rank groups will be explored.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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