Title: Spectra of maximal abelian covers of graphs

Speaker: Joe Thomas, Durham University, UK

Time: 2025. 10. 15 15:45-16:45

Lecture room: 5104

Abstract: The study of periodic graphs, or infinite-fold abelian covers of finite graphs, is central to the mathematical theory of crystal structures arising in chemistry and mathematical physics. In this talk, I will discuss the spectrum of periodic Schrödinger operators on these graphs with a focus on maximal abelian covers. Maximal abelian covers are crucial in the study of periodic graphs as many of their spectral properties are inherited by all abelian coverings of the same finite graph. I will in particular give a complete geometric characterisation of eigenvalues in the spectrum and use this to prove the non-existence of eigenvalues of every periodic Schrödinger operator on maximal abelian covers of any finite regular multi-graph. This is joint work with Wenbo Li (USTC), Michael Magee (Durham), and Mostafa Sabri (NYU Abu Dhabi).