Hearing the shape of a drum
* Presenting author
Abstract:
Since Mark Kac asked his famous question ``Can one hear the shape of a drum?'' in 1965, the spectral determination of domains became a topic of relevance for analysts and geometers.The inverse spectral problem for a bounded planar domain is to determine whether any other domain with the same spectrum is the image of the former one under a rigid motion of the plane.The methods used to provide solutions and counterexamples in this family of problems draw on diverse areas — PDE, group theory, number theory, probability, to name a few.In this talk, we will briefly present the inverse spectral problem and tools that arise in some particular domains.