Codes and Expansions (CodEx) Seminar

Tom Needham (Florida State University):
Symplectic Geometry and Fusion Frames

There has been much recent work on understanding the global structure of collections of finite frames with prescribed properties, such as spaces of unit norm tight frames. We extend some of these results to the more general setting of fusion frames. Namely, we prove analogues of the Frame Homotopy Theorem of Cahill, Mixon and Strawn, and a result of Benedetto and Fickus on the energy landscape of the frame potential. Our results are based on ideas from symplectic geometry and geometric invariant theory. This is joint work with Clayton Shonkwiler.