Title: Equiangular lines in Euclidean Space
Abstract: Consider the following extremal (geometric) problem: Suppose we
have a set of lines in R^d such that the angle between any two of these is
the same. How many lines can there be?
As it turns out, one can an upper bound that is quadratic in the dimension
d without too much difficulty. There are also (several) examples of sets
of lines of size $\Omega(d^2)$ in $R^d$ that form an equi-angular set.
However, in all these examples, the angle between a pair of lines goes to
0 as d goes to infinity. If we insist that the angle is fixed then the
bound becomes linear. We shall see a proof of this due to B. Bukh.
Abstract: Consider the following extremal (geometric) problem: Suppose we
have a set of lines in R^d such that the angle between any two of these is
the same. How many lines can there be?
As it turns out, one can an upper bound that is quadratic in the dimension
d without too much difficulty. There are also (several) examples of sets
of lines of size $\Omega(d^2)$ in $R^d$ that form an equi-angular set.
However, in all these examples, the angle between a pair of lines goes to
0 as d goes to infinity. If we insist that the angle is fixed then the
bound becomes linear. We shall see a proof of this due to B. Bukh.