#
The property of rapid decay

January 23 to January 27, 2006
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Indira Chatterji and Laurent Saloff-Coste

## Original Announcement

This workshop will be devoted to the
property of Rapid Decay.
The property of Rapid Decay (abbreviated by property RD) is a
property of
convolution operators that captures certain aspects of the asymptotic
geometry of a finitely generated group. Property RD is a very focused area
of research in harmonic analysis and operator algebra. However, it has
ramifications in geometry, topology and algebra.

Valette's conjecture that all cocompact lattices in a semisimple Lie group
have property RD is still open in many cases. Some cases are settled
positively but, for the remaining ones, new ideas are needed. Discussions
between people from operator algebras and non-commutative geometry and
specialists in arithmetic groups, ergodic theory, random walks and
geometric group theory will help gain a better insight on property RD.

Initial lectures will be devoted to the basics of property RD and stress
its importance in various areas of mathematics. They will be accessible to
people unfamiliar with property RD and its applications.

Specific topics to be addressed include:

- Property RD for cocompact lattices in semisimple Lie groups
- Obstructions to property RD
- New caracterisation of property RD

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

An introduction to rapid decay by the organizers.