Francesco Tudisco (Saarland University)
This introductory talk will focus on the eigenvalues and eigenfunctions of the graph p-Laplacian. We shall discuss two definitions of the eigenpairs that come as a natural generalization of the linear case and that allow further generalizations. Then we describe the basis of the index theory for non-linear functionals leading to the variational characterization of a set of eigenvalues of the p-Laplacian. Finally we mention some nodal properties of the eigenfunctions associated to the variational eigenvalues, pointing out few important open questions.