Julie Rowlett: The mathematics of "hearing the shape of a drum"

Abstract

Have you heard the question, "Can one hear the shape of a drum?" Do you know the answer? In 1966, M. Kac's article of the same title popularized the inverse isospectral problem for planar domains. Twenty six years later, Gordon, Webb, and Wolpert demonstrated the answer, but many naturally related problems remain open today. We will discuss old and new results inspired by "hearing the shape of a drum.''