Seminar on low-dimensional mathematics Friday, August 1, 2008 Oleg R. Musin Title: "Spherical two-distance sets" Abstract: A set S of unit vectors in n-dimensional Euclidean space is called a spherical two-distance set, if there are two numbers a and b such that inner products of distinct vectors of S are either a or b. It is known that the largest cardinality g(n) of spherical two-distance sets does not exceed n(n+3)/2. This upper bound is known to be tight for n=2,6,22. The set of mid-points of the edges of a regular simplex gives the lower bound L(n)=n(n+1)/2 for g(n). In this talk using the so-called polynomial method will be proved that for nonnegative a+b the largest cardinality of S is not greater than L(n). For the case a+b<0 we propose upper bounds on |S| which are based on Delsarte's method. Using this it could be shown that g(n)=L(n) for 6