Mathematical Physics and Harmonic Analysis Seminar
Date: April 2, 2021
Time: 2:00PM - 3:00PM
Location: Zoom
Speaker: Peter Kuchment, Texas A&M University
Title: The nodal sets mysteries
Abstract: Nodal patterns of oscillating membranes have been known for hundreds of years. Leonardo da Vinci, Galileo Galilei, and Robert Hooke have observed them. By the nineteenth century they acquired the name of Chladni figures. Mathematically, they represent zero sets of eigenfunctions of the Laplace (or a more general) operator. In spite of such long history, many mysteries about these patterns (even in domains of Euclidean spaces, and even more on manifolds) still abound and attract recent attention of leading researchers working in physics, mathematics (including PDEs, math physics, and number theory) and even medical imaging. The talk will survey these issues, with concentration on the most recent results, where A&M mathematicians have been playing a significant role. No prior knowledge is assumed.