### Abstracts

January 10, 2003

Joel Smoller, University of Michigan

*Cosmology, Black Holes, and Shock Waves Beyond the Hubble Distance*

We construct a class of global exact solutions of the Einstein equations
that extend the Oppenheimer-Snyder (OS) model to the case of non-zero
pressure, "inside a black-hole", by incorporating a shock
wave at the leading edge of the expansion of the galaxies, arbitrarily
far beyond the Hubble length in the Friedman-Robertson-Walker (FRW)
spacetime. Here the expanding FRW universe emerges behind a subluminous
blast wave that explodes outward from the FRW center at the instant
of the Big Bang. The equation of state p=(1/3)(rho) plays a special
role, and only in this case, the shock wave emerges from the Big Bang
at the speed of light, decelerating from that time onward. The entropy
condition implies that the shock wave must weaken to the point where
it settles down to an OS interface, that eventually emerges from the
White Hole event horizon of an ambient Schwarzschild spacetime. The
entropy condition also breaks the time symmetry of the Einstein equations,
selecting the explosion over the implosion. These shock wave solutions
indicate a new cosmological model in which the Big Bang arises from
a localized exlosion occurring inside the Black hole of an asymptotically
flat Schwarzschild spacetime. (This is joint work with Blake Temple.)
I will strive to make this talk understandable to non-experts.

February 17, 2003

**Rafe Mazzeo, Stanford University**

*Poincare-Einstein metrics on the large and small scale*

Poincar\'e-Einstein (also known as asymptotically hyperbolic Einstein)
metrics have received substantial recent attention from both Riemannian
geometers and string theorists. In this talk I will begin by reviewing
the general theory and significant results about these spaces, as set
up by Fefferman, Graham, Witten, Yau, Anderson and others, and go on
to discuss recent work concerning existence, regularity and uniqueness
questions, behaviour of renormalized volume as a function on the moduli
space and properties of the Anderson degree.

March 14, 2003

**Russel Caflisch, U.C.L.A.**

*Dynamics of a Step Edge in Thin Film Growth *

Epitaxial thin films grow by attachment of adatoms to step edges
(or island boundaries). In contrast to the assumptions of classical
models, the state of a step edge is typically in a kinetic steady state
that is far from equilibrium. This talk presents a detailed model for
the dynamics of a step edge, along with analysis of the model in several
limits, and a discussion of equilibrium for this system. The model is
partially validated by comparison to results from kinetic Monte Carlo
simulations. For large adatom diffusion, the asymptotics of this model
includes edge diffusion and line tension, which provides an atomistic,
kinetic derivation of the Gibbs-Thomson formula.

April 11, 2003

**Peter Constantin, University of Chicago**

*Remarks on Rotating Fluids*

I will give a nonlinear version of the Taylor-Proudman theorem
concerning rotating incompressible Euler equations. I will discuss also
the energy spectrum in the inverse cascade regime, for quasi-geostrophic
equations.

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