Time: Tuesday, Oct 31, 2017, 2:00pm @ MTH1311

Speaker: Joey Iverson (UMD)

Title: Optimal coherence from finite group actions

Abstract: In applications such as compressed sensing and quantum information theory, it is critically important to find examples of frames whose vectors are spread apart in the sense of having wide angles between them, as measured by the coherence. This is an old problem, going back at least to the work of van Lint and Seidel in the 1960s, and it remains an active and challenging area of research today. In this talk we will present a new recipe for converting transitive actions of finite groups into tight frames, many of which have optimal coherence. The main idea is to use an association scheme as a kind of converter to pass from the discrete world of permutation groups into the continuous setting of frames. This process is easy to implement in a program like GAP. We will present several examples of optimally coherent frames produced in this way, including the first infinite family of equiangular tight frames with Heisenberg symmetry. (These are not SIC-POVMs, but they appear to be related.) Back to seminar