The importance of counting eigenvalues: From solar radiation to the stability of matter

Zoom: https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09 Meeting ID: 682 8556 4037 Passcode: 636252

The problem of counting the number of eigenvalues of a differential operator is exactly as old as quantum theory and was inspired by various physical questions. In the century since Weyl’s first asymptotic result on the topic, the question has inspired numerous mathematical analyses. In this talk, I will explain some of the physical motivations and present mathematical results, all related in some way to the uncertainty principle. I will also describe a recently developed technique that gives a simple, non-asymptotic answer, which is furthermore convenient for numerical analysis. This is joint work with R. Froese and S. Schraven.