Graduate Programs      Graduate Home Ph D Programs Masters Degree Ph D Program Requirements Course Descriptions Current Courses Admissions Current Graduate Students Graduate Student Seminar SIAM Chapter Seminar Recent Graduates Incoming Students Graduate Seminar Giovanni Gravina Carnegie Mellon University Title: Eigenvalues and eigenfunctions of the Laplacian Abstract: The Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. In this talk we will study the associated eigenvalue problem by means of constrained optimization. The main result we'll discuss is the spectral theorem for the Dirichlet Laplacian. This can be stated as follows: the eigenfunctions of the Dirichlet Laplacian form an orthonormal basis for the space of square-integrable functions on a bounded domain. Date: Tuesday, April 18, 2017Time: 5:30 pmLocation: Wean Hall 8220Submitted by:  Yangxi OuNote: Video on Youtube: https://youtu.be/b-fUD8Ea0vU