Mathematical Research at FSU
Harmonic analysis had its start with the study of Fourier series. Modern harmonic analysts work in many areas where Fourier methods are applicable. Some of these are: (1) the behavior of translation-invariant operators - a "moving average" is a very simple example; (2) the behavior of differential operators (this is related to PDE's); (3) geometric measure theory - problems like the Kakeya problem (you could "Google" it!) concerning Hausdorff dimension. You might consider working in this area if you like epsilons and deltas and the sort of stuff you did in Advanced Calculus.