Hearing the Shape of a Drum (Spring 2023)

In this project, we will explore some well-studied problems of geometric analysis related to a particular Laplace operator. One central question in studying the Laplacian is whether it is possible to "hear the shape of a drum". In other words, if one plays a drum and hears all the tones and overtones created, whether it is possible to uniquely determine the shape of the drum. In mathematical language, this comes down to studying the spectral properties of the operator. We will mostly focus on various numerical/computational techniques to determine certain properties of the Laplace eigenvalues and their associated eigenfunctions.

For a detailed project description, click here.

For more information contact Soumyajit Saha (ssaha1@iastate.edu)

People:

Pre-requisites: