Can one hear the shape of a drum? A glimpse into spectral geometry and flat tori

Abstract: What can the sound of a drum tell us about its shape? This simple-sounding question, famously posed by Mark Kac in 1966, lies at the heart of spectral geometry - a field that explores how the eigenvalues of the Laplacian relate to the geometry of a space. In this talk, we'll look at what information can and cannot be recovered from the spectrum, guided by classical results, clever counterexamples, and a few open problems. We'll then focus on the case of flat tori, where many of these results become particularly elegant (and sometimes surprisingly tricky). In the end, I will present a new result: a 6-dimensional triplet of isospectral, non-isometric flat tori. No prior knowledge is expected - just bring your curiosity!

Mathematics

Audience: general audience

( paper )

Gothenburg PhD seminar

Series comments: Rooms and times may vary, please check the latest update. In-person only.