American Institute of Mathematics, Palo Alto, California
Indira Chatterji and Laurent Saloff-Coste
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:
An introduction to rapid decay by the organizers.
The workshop schedule.
A report on the workshop activities.
A list of open problems.