An Extension of Delsarte's Method: The Kissing Problem in
Three and Four Dimensions
Oleg Musin
Friday, August 11, 2006
3:00 - 4:00 PM
Terman Engineering Center, Room 453
Abstract:
The kissing number k(n) is the maximal number of equal nonoverlapping
spheres in n-dimensional space that can touch another sphere of the
same size. This problem in dimension three was the subject of a
famous discussion between Isaac Newton and David Gregory in 1694. In
three dimensions the problem was finally solved only in 1953 by
Schutte and van der Waerden. It was proved that the bounds given
by Delsarte's method are not good enough to solve the problem in
4-dimensional space. Delsarte's linear programming method is widely
used in coding theory. In this talk we will discuss a solution of
the kissing problem in four dimensions which is based on an
extension of the Delsarte method. This extension also yields a new
proof of k(3) < 13.
Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html