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math.SP2026
Zero measure Cantor spectrum for aperiodic metric tiling graphs
Ram Band, Gilad Sofer
We study a family of aperiodic metric graphs generated by one-dimensional tilings. We prove that, generically, the spectrum of the associated Kirchhoff Laplacian has Lebesgue measu…
math.SP2026
Johnson-Schwartzman Gap Labelling for Metric and Discrete Decorated Graphs
Ram Band, Gilad Sofer
We study Schrödinger operators on metric and discrete decorated graphs. The values taken by the integrated density of states (IDS) on spectral gaps are called gap labels. A natural…
math.SP2025
Spectral flow and Robin domains on metric graphs
Ram Band, Marina Prokhorova, Gilad Sofer
This paper is devoted to the Neumann-Kirchhoff Laplacian on a finite metric graph. We prove an index theorem relating the nodal deficiency of an eigenfunction with (1) the Morse in…