Nearly orthogonal vectors

Combinatorics Seminar
Friday, October 19, 2018 - 3:00pm
1 hour (actually 50 minutes)
Skiles 005
Carnegie Mellon University
How can d+k vectors in R^d be arranged so that they are as close to orthogonal as possible? We show intimate connection of this problem to the problem of equiangular lines, and to the problem of bounding the first moment of isotropic measures. Using these connections, we pin down the answer precisely for several values of k and establish asymptotics for all k. Joint work with Chris Cox.