The twentieth century was witness to the taming of chance.
Today we are harnessing
chance; to approximate impossible high-dimensional integrals, solve intractable counting problems, understand the structure of the genome, and many further tasks from grand to mundane. Mathematical understanding of these new techniques lags way behind applications.

I will illustrate with the physics/chemistry problem of random packing of hard spheres in a box. As usual, I will begin by trying to answer "who cares." This was the first modern application (Metropolis, et.al.). For Sparse systems we can give useful results using micro-local and geometric analysis techniques (work with Gilles Lebeau). The general problem, particularly the most interesting dense case, is wide open.
[Persi Diaconis]

Lecture #12636

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