Have you heard the question: can one hear the shape of a drum? Do you know the answer? Mathematically, this question is an inverse spectral problem, or equivalently, a question about isospectrality. Although I suspect that many people are familiar with this question and its answer, there are several related questions which remain unsolved. In this talk, we will investigate inverse spectral problems and variations thereof in geometric moduli spaces consisting of certain types of `drums.'
