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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, 2017
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on Youtube: https://youtu.be/b-fUD8Ea0vU