Abstract
Abstract In my talk, I will present some works done in the nineties on Laplacians on graphs: from eigenvalue problems to inverse problem for resistor networks. I will focus on the motivations and the main results as well as on the main ideas: • A differential topology point of view on the minor relation: a nice stratification associated to a finite graph Γ whose strata are associated to the minors of Γ • “Discrete” (graphs) versus “continuous” (Riemannian manifolds) • Stability of spectra with respect to singular limits: a finite dimensional theory of operators with domains (Von Neumann theory). The link with topology will appear in some results about my graph parameter μ, in particular the planarity and the linkless embedding properties.
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