Computing arithmetic spectra

March 10 to March 14, 2008

at the

American Institute of Mathematics, Palo Alto, California

organized by

Andew Booker, Sally Koutsoliotas, Stefan Lemurell, and Andreas Strombergsson

Original Announcement

This workshop 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.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:
A non-solvable Galois extension of Q ramified at 2 only