Mathematics faculty and graduate students are invited to attend the PhD Defense of Anthony Caine.

Title:  Normalizing Parseval Frames by Gradient Descent

Advisor:  Dr. Chris Peterson

Co-Advisor:  Dr. Clayton Shonkwiler

Committee:  Dr. Henry Adams, Dr. Jamie Neilson

Abstract:  Equinorm Parseval Frames (ENPFs) are collections of equal-length vectors that form Parseval frames, meaning they are spanning sets that satisfy a version of the Parseval identity. As such, they have many of the desirable features of orthonormal bases for signal processing and data representation, but provide advantages over orthonormal bases in settings where redundancy is important to provide robustness to data loss. We give three methods for normalizing Parseval frames: that is, flowing a generic Parseval frame to an ENPF. This complements prior work showing that equal-norm frames could be “Parsevalized” and potentially provides new avenues for attacking the Paulsen problem, which seeks sharp upper bounds on the distance to the space of ENPFs in terms of norm and spectral data. This work is based on ideas from symplectic geometry and geometric invariant theory.

Join also on Zoom:

Join Zoom Meeting:  https://zoom.us/j/95378648758?pwd=TDRVVU1XTnNCUjEwemxhQ0hJUWJJUT09

Meeting ID: 953 7864 8758

Passcode: 878034