Colloquium - 4/01, 3:00PM, Duncan Hall 1064

Vern Paulsen

Department of Mathematics
University of Houston

"Frames, Redundancy, and the Feichtinger Conjectures"

Frames have become a substitution for orthonormal bases in many areas that use Hilbert space techniques. Like orthonormal bases, frames can be used to sample and reconstruct vectors, but unlike orthonormal bases, frames need not be linearly independent. Thus, frames are often described as "redundant systems". The Feichtinger conjectures are one attempt to make sense of in exactly what sense frames are redundant. In 2005, Casazza and Tremain proved that the Feichtinger conjectures are equivalent to the Kadison-Singer problem, which is a problem that arose from quantum mechanics and has been open since the 1950's. In this talk I will give a short introduction to frame theory and survey some of the recent results and open questions in this area.