• Gilad Sofer
• Ph.D. student, Technion -- Israel Institute of Technology, Haifa
• Date: Sep. 09, Wednesday, 2026
• Time: 13:00-14:00
• Host: Selim Sukhtaiev
• Room: STEM Ag 2111
• Abstract: A classical result of Bellissard et al. states that the spectrum of a one-dimensional Schrödinger operator with a Sturmian potential is a Cantor set of zero Lebesgue measure. More recently, Damanik, Fang, and Sukhtaiev proved an analogous result for certain aperiodic metric graphs called antitrees.

In this talk, we present an analogous result for a large family of metric graphs inspired by one-dimensional aperiodic tilings. We prove that, for a generic choice of edge lengths, the spectrum of the standard Laplacian on these graphs is a generalized Cantor set of zero Lebesgue measure. The proof combines tools from the theory of ergodic Schrödinger operators with methods from quantum graph theory.

Based on joint work with Ram Band.