  We give an overview of the intimate connections between natural direct and
inverse spectral problems for fractal strings, on the one hand, and the Riemann
zeta function and the Riemann hypothesis, on the other hand (in joint works of
the author with Carl Pomerance and Helmut Maier, respectively). We also briefly
discuss closely related developments, including the theory of (fractal) complex
dimensions (by the author and many of his collaborators, including especially
Machiel van Frankenhuijsen), quantized number theory and the spectral operator
(jointly with Hafedh Herichi), and some other works of the author (and several
of his collaborators).
