Wave packets in harmonic analysis

In harmonic analysis, it is often useful to decompose a given function into sums of wave packets. Such a decomposition is guided by the Heisenberg uncertainty principle, and allows one to access some deep underlying geometric and combinatoric structure of a problem. Many recent breakthroughs in the field hinge upon such a decomposition, and we can seek to understand / investigate some of those in this project. 

Prerequisites: A solid background in linear algebra, multivariable calculus and mathematical analysis. The latter includes measure theory, complex analysis, plus working knowledge about Hilbert spaces, Banach spaces, and Fourier transforms of tempered distributions (say at the level of Stein and Shakarchi's four volumes of undergraduate text).