Analysis Seminar: Some frame theory questions in the manifold setting

Abstract: The talk will start at the elementary level and introduce some basics of frame theory.  We will make the distinction between a frame and a basis in a Hilbert space and familiarize ourselves with the basic ideas of reconstruction.  We will then expand the theory to the manifold and vector bundle setting.  As we delve deeper, we will present the question and solution of approximating a signal from finitely many samples in a compact manifold.  Hopefully, we will have time to also talk about the phase retrieval side of this problem: how to approximate a signal from finitely many phaseless samples in a compact manifold.  This is joint work with Kieran Favazza, Olivia Frank, Daniel Freeman, Dorsa Ghoreishi, and Bernadette King.

Host: Alan Chang