Abstract: A function is said to be quasiperiodic if its constitutive frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window embedding of such function s can be shown to be dense in a torus of dimension equal to the number of independent frenquencies. I will show in this talk that understanding the persistent homology of these sets can be reduced to a Kunneth theorem for persistent homology and a bit of harmonic analysis. Needles to say, we will describe the needed persistent Kunneth formulae, as well as applications to time series analysis and computational chemistry.