Séminaire de GéométrieOn sums of eigenvalues, and what they reveal about graphs and manifolds
Evans M. Harrell* (Georgia Tech en visite au LMPT)
jeudi 30 janvier 2014 11:00 - Tours - Salle 1180 (Bât E2)
We consider the spectra of different self-adjoint matrices associated with a combinatorial graph, including the adjacency matrix A and the graph Laplacian H=-∆. Using a) a new variational technique, and b) identities related to Chebyshev's inequality, we relate the structure of the graph to sums of eigenvalues and, more generally, the statistical distribution of eigenvalues. This is joint work with J. Stubbe of EPFL. Recently similar results have been obtained for elliptic differential operators on manifolds with El Soufi and Ilias, Univ. de Tours.