I will begin by discussing the problem of placing a given number of n-dim. subspaces of m-space so they are as far apart as possible. This has applications to displaying multi-dimensional data. Last year we discovered a miraculous connection between this problem and the problem of constructing quantum codes, which has greatly benefitted both fields. This is based on joint work with A.R. Calderbank, R.H. Hardin, E.M. Rains and P.W. Shor.
References: http://www.research.att.com/~njas/doc/grass.ps # three http://www.research.att.com/~njas/doc/shor.ps # main http://www.research.att.com/~njas/doc/qc2a.ps # references http://www.research.att.com/~njas/grass # web site for grass. packings http://www.research.att.com/~berthiau/seminar.html # seminar web site