During the week January 10-14, 2005, the American Institute of Mathematics,
in Palo Alto, California held a workshop on the emerging mysterious
numerical coincidences that involve the dual Garside structures on the
braid groups (and other Artin groups of finite type), the cluster
algebras of Fomin and Zelevinsky and the corresponding generalized
associahedra, the theory of free probability and its close connection
with the lattice of noncrossing parititions, and the ad-nilpotent
ideals in the Borel subalgebra of a semisimple Lie algebra as encoded
in the poset of nonnesting partitions.|
The workshop, entitled ``Braid groups, clusters and free probability'', was organized by Jon McCammond, Alexandru Nica, and Victor Reiner and the original AIM conference website is still available, as is the website they put together with open problems, etc. This website is designed to be a more permanent compilation of the information gathered and the connections made during the workshop. The following are currently available.
Other information will be added as it is produced. For example, a problem list from the conference is being compiled by Drew Armstrong and will be added as soon as it is avaible.