# Past Colloquia

**Yves Couder and co-workers
have recently reported the results of a
startling series of experiments in which droplets bouncing on a
fluid surface exhibit several dynamical features previously thought
to be peculiar to the microscopic realm. In an attempt to **

**develop a connection
between the fluid and quantum systems, we
explore the Madelung transformation, whereby Schrodinger's
equation is recast in a hydrodynamic form. New experiments
are presented, and indicate the potential value of this hydrodynamic
approach to both visualizing and understanding quantum mechanics.**

** **

**Voiculescu
showed how the large N limit of the expected value of the trace of a word on n
independent hermitian NxN matrices gives a well known von Neumann algebra. In
joint work with Guionnet and Shlyakhtenko it was shown that this idea makes
sense in the context of very general planar algebras where one works directly
in the large N limit. This allowed us to define matrix models with a
non-integral number of random matrices. I will present this work and some
of the subsequent work, together with future hopes for the theory.**