. M G ] 1 1 N ov 1 99 8 SPHERE PACKINGS III

N ov 1 99 8 Sphere Packings II

An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of R into polyhedra. The polyhedra are divided into two classes. The first class of polyhedra, called quasi-regular tetrahedra, have density at most that of a regular tetrahedron. The polyhedra in the remaining ...

ar X iv : c on d - m at / 9 51 11 05 v 1 2 1 N ov 1 99 5 A Model for Force Fluctuations in Bead Packs

We study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials. We present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile. We compare our results for force distri...

ar X iv : h ep - t h / 94 10 11 8 v 2 2 2 N ov 1 99 4 WILSON LOOPS , qq̄ and 3 q POTENTIALS , BETHE – SALPETER EQUATION

Packing Planes in Four Dimensions and Other Mysteries

How should you choose a good set of (say) 48 planes in four dimensions? More generally, how do you find packings in Grassmannian spaces? In this article I give a brief introduction to the work that I have been doing on this problem in collaboration with A. R. Calderbank, J. We have found many nice examples of specific packings (70 4-spaces in 8-space, for instance), several general construction...

1 8 N ov 1 99 8 The Density Matrix Renormalization Group , Quantum Groups and Conformal Field Theory

We present an overview of the Density Matrix Renormalization Group and its connections to Quantum Groups, Matrix Products and Conformal Field Theory. We emphasize some common formal structures in all these theories. We also propose two-dimensional extensions of the variational matrix product ansatzs.