AMUSE

Date: April 18, 2024

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Dr. William Rundell, Texas A&M University, Mathematics

Title: Eigenvalues; matrices and into differential equations: Can you hear the density of a vibrating string or the shape of a drum?

Abstract: In an undergraduate curriculum one sees eigenvalues in linear algebra and in the basic o.d.e. class one writes systems of equations, converts to a matrix question, and interprets the eigenvalues as pointers to the system's behaviour. We will go over this briefly enough to see the pattern of: "have problem, find eigenvalues, interpret behaviour." But it is a more interesting question to turn this around: "I have a differential equation or a system of such and its eigenvalues are known; what can you say about the system?" This is a partial explanation for the cryptic title. The purpose of the talk is to fill in some of the reasoning (and of course answer the questions in the title).