ICM 1998, Berlin, Aug. 18–27

Abstracts of Plenary and Invited Lectures

Section:

13. Combinatorics

1991 MS Classification: 52C17 Sloane, N. J. A., AT&T Labs-Research, Florham Park, USA Recent developments on the sphere-packing problem.

A report on recent work (mostly by J. H. Conway, E. M. Rains and myself, but also mentioning C. Bachoc, J. Bierbrauer, A. Bonnecaze, A. R. Calderbank, Y. Edel, Y. Kitaoka, G. Nebe, H. -G. Quebbemann, P. Solé, A. Vardy and others) on the sphere-packing problem, proceeding from dimension 3 to 128. For example: a little-known 3-D analogue of the planar lattice A_{2}; a putative list of all the best packings in dimensions 3 to 8; an astonishing property of the densest packings known in 9 dimensions; codes over ℤ/4ℤ and the E_{8} and Leech lattices; new nonlattice packings in dimensions below 32; shadow lattices and new bounds for unimodular and N-modular lattices; tensor products; new record kissing numbers.

ICM 1998 Berlin · Plenary and Invited Lectures