Time: Tuesday, Oct 11, 2016, 2:00pm @ MTH1311

Speaker: Prof. Nate Strawn (Georgetown University)

Title: Connectivity and Irreducibility of Finite Unit-Norm Tight Frame Varieties

Abstract: We demonstrate the connectivity of algebraic varieties of finite unit norm tight frames (FUNTFs). Our central technique involves explicit continuous lifts of paths from the polytope of eigensteps (or, Gelfand-Tsetlin patterns) to spaces of FUNTFs. After demonstrating this connectivity result,, and refine our analysis to show that the set of nonsingular points on these spaces is also connected. Using tools from real algebraic geometry, this refined connectivity result shows that FUNTFs varieties are irreducible in the algebro-geometric sense. This last result allows us to show that generic FUNTFs are full spark, and hence the full spark FUNTFs are dense in the space of FUNTFs. This resolves an important theoretical question regarding the application of FUNTFs in the field of Compressed Sensing. We conclude with open questions and future directions. This is joint work with Dustin Mixon and Jameson Cahill. Back to seminar