


Invited Talks 

Explorations of the Singularities of Light
Sir Michael Berry, Professor at the Physics Department of Bristol University
Abstract: Singularities of fields of light rays and waves of light are increasingly recognized as fundamental in optics. In exploring these singularities, Mathematica has played a central role, in computation and in visualizations that have led to the discovery of new phenomena. At the geometrical level, the singularities are caustics  surfaces on which focusing occurs. Waves decorate these with rich interference patterns, whose finest structures are new singularities, namely singularities of phase (a.k.a. nodal lines, or optical vortices, or wave dislocations). The vector nature of light introduces further singularities, associated with polarization. Many phenomena are best understood and illustrated in terms of singularities: rainbows, tsunamis, polarization fingerprints in the blue sky, the complexities of crystal optics..

The Large Hadron Collider at CERN
Dr John Jowett, Accelerator and Beams Department, CERN
Abstract: The LHC, due to be turned on next year, is one of the largest scientific enterprises ever undertaken. Results from its four huge experimental collaborations are expected to dominate elementary particle physics for many years to come. This talk will describe the superconducting particle accelerator itself and how it is being constructed as a worldwide collaboration led by CERN, explain something of how it works, and illustrate some of the ways in which Mathematica fits into a multidisciplinary and heterogeneous computing environment.

Visualisation of Optimal Geometry
John Sullivan, Professor at the Department of Mathematics of the University of Illinois at UrbanaChampaign
Abstract: For any topological object, we can ask for its optimal geometric shape,
minimizing some geometric energy. A classical example is a soap bubble
which is round because it minimizes surface area while enclosing a fixed
volume. Other examples, at the frontier of current mathematical research,
include knots tied tight in thick rope, which minimize their length, and
surfaces which minimize elastic bending energy. The resulting shapes are
not only mathematically elegant, but often exhibit striking visual beauty.
We will watch two short computergraphics videos, illustrating optimal
shapes for knots and a mathematical way to turn a sphere inside out
(controlled by surface bending energy), and see other examples of
mathematical visualizations arising from optimal geometry, including
computergenerated sculpture.

Reinventing Mathematica: the Impact of 6
Conrad Wolfram, Director of Strategic & International Development,Wolfram Research Inc.

