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Harmonic Analysis was created as a tool for understanding the equations of mathematical physics. Quite surprisingly, harmonic analysis finds more and more applications outside of mathematical physics, as an "unreasonably" effective tool of the modern information theory society. This observation is underscored with the advent of Compressive Sensing, a new paradigm for data acquisition, that has received enormous attention from scientists, mathematicians, and engineers alike. I will review the basic principles behind compressive sensing and discuss how we have used these techniques to derive a powerful mathematical framework for radar and remote sensing. Sparse and redundant representations of functions, combined with techniques from convex optimization and random matrix theory are the key ingredients in the proofs. Furthermore, I will describe how ideas from compressive sensing have inspired a new approach to the famous Phase Retrieval problem. Our approach, called PhaseLift, shows that in some instances, the combinatorial phase retrieval problem can be solved exactly by convex programming techniques.

w/reception from 5:10-7:00p