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

Original Announcement

This workshop 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.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

An introduction to The Fundamental Gap, with many references, has been written by Mark Ashbaugh.

Tomas Ekholm has provided some pictures taken during the workshop.