# Workshop on Discrete Geometry and the Kepler Problem

### Sunday January 17, 1999 to Friday January 22

**Location** Seminar Room

Simonyi Hall

Institute for Advanced Study

Princeton, New Jersey** **

**Scientific Organizer** Gabor Fejes Toth, Mathematical Institute of the Hungarian Academy of Sciences

**Confirmed Participants**

Andras Bezdek--Hungarian Academy of Sciences

Karoly Bezdek--Eotvos University

Robert Connelly--Cornell University

John Conway--Princeton University

Samuel Ferguson--University of Michigan

Tom Hales--University of Michigan

Wu-Yi Hsiang--University of California at Berkeley

Wlodzimierz Kuperberg--Auburn University

Jeffrey Lagarias--AT&T Labs - Research

Guenter Rote--Technische Universitat Graz

Neil Sloane--AT&T Shannon Lab.

Salvatore Torquato--Princeton University

Gabor Fejes Toth--Mathematical Institute of the Hungarian Academy of Sciences

The workshop starts on Sunday, January 17, 1999, at 2 p.m. and will continue until approximately 5 p.m. that day. The following days, Monday through Friday, January 22, it will begin each day at 9:30 a.m. and continue until approximately 5 p.m.

The workshop is co-sponsored by the Institute and the Annals of Mathematics.

The main subject of the workshop will be the new computer-assisted proof of the Kepler Conjecture by Tom Hales. (The Kepler Conjecture asserts that the densest packing of Euclidean three space by non-overlapping spheres of identical size is the one we all expect.) Most of the talks and working sessions will be organized and scheduled during the workshop, and will be on this subject.

Lectures will take place in the Simonyi Hall Seminar Room unless notified to the contrary. Every day at 2 p.m. there will be a more formal lecture on related subjects as follows:

**Sunday
January 17**

- 2 p.m. Tom Hales
**An Introduction to the Kepler Conjecture**

**Monday
January 18**

- 2 p.m. Salvatore Torquato
**Random Packing of Spheres: Statistical-Mechanical Approach**

**Tuesday
January 19**

- 2 p.m. Wu-Yi Hsiang
**On the proof of Kepler's conjecture and the dodecahedron conjecture**

**Wednesday
January 20**

- 2 p.m. Karoly Bezdek
**On the isoperimetric problems for Voronoi polyhedra of unit ball packings in E^3**

- 2:45 Wlodzimierz Kuperberg
**Almost tiling the plane by ellipses**

- 4:30 Tom Hales -- Institute Lecture in WOLFENSOHN HALL
**Cannonballs and Foam**

**Thursday
January 21**

- 2 p.m. Guenter Rote
**Matchings between triangulations of a planar set of points**

- 2:45 p.m. Andras Bezdek
**On efficient packings of E^3 with various convex solids**

**Friday
January 22**

- 2 p.m. John Conway
**What are all the best sphere packings in low dimension?**

*Additional lectures may be scheduled as the conference progresses.*