A survey of existing techniques and open questions for frequency-domain audio processing. Some mathematics and signal processing background will be needed.
Here are the screen movies, patches, and blackboards.

Possible topics (not in chronological order):

the real-time framework
the Portnoff framework
windowing effects
inverse-FFT synthesis
phase coherence across analysis windows and channels
relationships between cosine transform and FFT
multiple-time-scale approaches
sparse decomposition of spectra
convolution, deconvolution, and room impulse response measurement
vocoding and frequency-domain companding
peak finding and characterization

possibly useful references:
https://ccrma.stanford.edu/~jos/st/ - Julius Smith, the mathematics of the Fourier transform
http://msp.ucsd.edu/techniques/latest/book-html/node163.html - chapter 9 of my online book