The interaction of flowing fluids with free bodies -- sometimes
compliant, sometimes active, sometimes multiple -- constitutes a class
of beautiful dynamic boundary problems that are central to biology and
engineering. Examples range from how organisms locomote in fluids
(which depends strongly on scale) to how non-Newtonian stresses
develop in complex liquids (strongly dependent on the nature of
fluidic microstructure). I will discuss several interesting examples,
emphasizing how they are formulated mathematically so as to yield
models tractable for analysis or simulation, and show how this work
has interacted with experimental studies.

Partial differential equations on and for evolving surfaces occur in many applications.
For example, traditionally they arise naturally in fluid dynamics and materials
science and more recently in the mathematics of images.
In this talk we describe computational approaches to the formulation and
approximation of transport and diffusion of a material quantity on an
evolving surface.
We also have in mind a surface which not only evolves in the normal direction
so as to define the surface evolution but also has a tangential velocity
associated with the motion of material points in the surface which advects material
quantities such as heat or mass.This is joint work with G. Dziuk

All physical systems in equilibrium obey the laws of
thermodynamics. In other words, whatever the precise nature of the
interaction between the atoms and molecules at the microscopic level,
at the macroscopic level, physical systems exhibit universal behavior in
the sense that they are all governed by the same laws and formulae of
thermodynamics.

The speaker will recount some recent history of universality ideas in
physics starting with Wigner's model for the scattering of neutrons
off large nuclei and show how these ideas have led mathematicians to
investigate universal behavior for a variety of mathematical systems.
This is true not only for systems which have a physical origin, but also
for systems which arise in a purely mathematical context such as the
Riemann hypothesis, and a version of the card game solitaire called
patience sorting.

It is now believed, but proved only in a few cases, that the distribution
functions
of random matrix theory are universal for a wide class of stochastic
problems in combinatorics,
growth processes, and statistics. These developments will be surveyed.
No prior knowledge
of random matrix theory will be assumed.