Hypergraphs are a generalization of graphs in which vertices are joined by edges of any size. In this talk, we generalize the graph normalized Laplace operators to the case of hypergraphs, and we discuss some properties of their spectra. We discuss the geometrical meaning of the largest and smallest eigenvalues, and we show how the Cheeger inequalities can be generalized to the case of uniform hypergraphs. We also discuss some relations between the eigenvalues and constants such as the coloring number and the independence number of the hypergraph. We talk about hypergraph symmetries, and we discuss spectral measures and spectral classes.
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