Low eigenvalues of Laplace and Schrodinger operators
May 22 to May 26, 2006
American Institute of Mathematics,
Palo Alto, California
and Richard Laugesen
This workshop will bring together people
interested in eigenvalue problems for Laplace and Schrodinger operators, for focused discussions and intensive investigation of
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.
- sharp constants in the classical Lieb-Thirring inequalities, and
- 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
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
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.