Abstract Harmonic Analysis

 The primary goal is to become familiar with the non-commutative Fourier transform which is a very powerful tool. There are beautiful theories developed and we will see some of the special cases, in particular in the abelian case and the compact case. We will start with some review of topological groups and functional analysis (Banach algebras, spectral theory). Depending on the familiarity of the student, we can move quite quickly to unitary representations and functions of positive type before getting to our two main cases of study: analysis on locally compact abelian and compact groups.