Edge-modes at interfaces between periodic mediaColloquium CRC 1720

by Ben Schweizer

Tuesday Oct 27, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Starting with the discovery of the integer quantum Hall effect in the 1980ies, questions related to this effect created a huge area of research in physics, multiple Nobel prices were awarded to researchers in the field; google scholar finds more than 7000 publications for "topological insulator" in the year 2025. Nevertheless, as of today, not too many mathematicians have entered this fascinating field which has to do with spectral theory for partial differential equations in periodic media and with micro-local analysis and homogenization theory. Of course, in both my research and in this talk, I can only scratch the surface of this huge and deep topic. I will present an own result that is related to one aspect of the topic. Let us consider two periodic media, both generated as perturbations of a single periodic medium, both being insulators in the sense that no Floquet-Bloch waves can travel the medium. We combine these two media in such a way that, on one side of an hypersurface, there is medium I, on the other side is medium II. We show: In this setting, there necessarily is a surface mode, a wave function that is localized at the separating hypersurface.