Oberwolfach Seminar: Sphere Packings: Exceptional Geometric Structures and Connections to other Fields

Date:

November 20th - November 26th, 2005

Organizers:

Henry Cohn, Seattle

Robert Griess, Ann Arbor

Achill Schürmann, Magdeburg

Programme:

Going back to a booklet of Kepler in 1611, the problem of packing identical spheres as densely as possible in Euclidean space has a history of almost 400 years. Nevertheless, the problem in arbitrary dimensions is far from being solved. Attempts to solve it have led to the discovery of a wealth of mathematics, and the theory of sphere packings today is an active field of research providing many challenging open problems. It has connections to various mathematical areas, including number theory, coding theory, group theory, and harmonic analysis. The aim of this seminar is to introduce the participants to some of these mathematical flowers and to leave them with many loose ends for further study.

Topics will include: Exceptional structures, lattices, codes, groups, designs, two-point homogeneous spaces, linear programming bounds, spherical codes, hyperbolic sphere packings, positive definite quadratic forms, reduction theories.

Prerequisites:

The seminar is oriented towards advanced students, graduate students, and postdocs. No specific background is required beyond the level of introductory graduate courses, particularly in algebra and discrete geometry.

Deadline for applications:

October 6th, 2005

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.