Braid Groups, Clusters and Free Probability

January 10 to January 14, 2005

at the

American Institute of Mathematics, San Jose, California

organized by

Jon McCammond, Alexandru Nica, and Victor Reiner

Original Announcement

This workshop will be devoted to deciphering the mysterious connections between the following objects: In each case, the objects of finite type within these classes obey the same numerology, but without satisfactory explanation (so far). The lattices of non-crossing partitions for Weyl groups of types A and B are also closely connected with Voiculescu's notion of free probability and the "R-transform".

The main topics for the workshop are

  1. Garside monoids and non-crossing partitions
  2. Non-crossing partitions and free probability
  3. Cluster algebras and generalized associahedra
  4. Ad-nilpotent ideals in Borel subalgebras

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Some useful background material.

Problem sets for the talks of Victor Reiner and Andu Nica.

Papers arising from the workshop:

Posets of annular non-crossing partitions of types B and D
by  Alexandru Nica and Ion Oancea