# Past Colloquia

There are many recent points of contact of model theory and other

parts of mathematics: o-minimality and Diophantine geometry, geometric group

theory, additive combinatorics, rigid geometry,... I will probably

emphasize long-standing themes around stability, Diophantine geometry, and

analogies between ODE's and bimeromorphic geometry.

Many geophysical flows over topography can be modeled by two-dimensional

depth-averaged fluid dynamics equations. The shallow water equations

are the simplest example of this type, and are often sufficiently

accurate for simulating tsunamis and other large-scale flows such

as storm surge. These hyperbolic partial differential equations

can be modeled using high-resolution finite volume methods. However,

several features of these flows lead to new algorithmic challenges,

e.g. the need for well-balanced methods to capture small perturbations

to the ocean at rest, the desire to model inundation and flooding,

and that vastly differing spatial scales that must often be modeled,

making adaptive mesh refinement essential. I will discuss some of

the algorithms implemented in the open source software GeoClaw that

is aimed at solving real-world geophysical flow problems over

topography. I'll also show results of some recent studies of the

11 March 2011 Tohoku Tsunami and discuss the use of tsunami modeling

in probabilistic hazard assessment.

**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.**