The Kissing Problem in Three and Four Dimensions
Oleg R. Musin, University of Texas at Brownsville
Location: Stevenson 5211
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 Sch\"utte 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. We also going to discuss our recent solution of the strong thirteen spheres problem. It is a joint work with Alexey Tarasov. Tea at 3:30 pm in SC 1425.