# Low Eigenvalues of Laplace and Schrodinger Operators

May 22 to May 26, 2006

at the

American Institute of Mathematics, Palo Alto, California

organized by

Mark Ashbaugh, Rafael Benguria, and Richard Laugesen

This workshop, sponsored by AIM and the NSF, will bring together people interested in eigenvalue problems for Laplace and Schrodinger operators, for focused discussions and intensive investigation of

1. sharp constants in the classical Lieb-Thirring inequalities, and
2. optimal lower bounds for the gap between the two lowest eigenvalues of Laplace and Schr\"odinger operators, specifically the conjectured optimal lower bound $3 \pi^2/d^2$ for a bounded convex domain of diameter $d$ in $n$ dimensions (with the potential being convex on the domain, in the case of a Schr\"odinger operator).
There is particular interest in having a group of participants with a wide range of backgrounds and perspectives and with a variety of technical skills. Participants whose backgrounds and current focus include not only the analytic and geometric aspects of the problems, but also related probabilistic and computational aspects, are particularly sought, because innovative or alternative approaches are likely to be especially valuable.

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 working sessions.

The deadline to apply for support to participate in this workshop has passed.