Mathematical Physics and Harmonic Analysis Seminar

Date: February 11, 2021

Time: 11:00AM - 11:50AM

Location: Zoom

Speaker: Marvin Plümer, FernUniversität in Hagen

Title: Eigenvalue bounds for the Laplacian on embedded metric graphs

Abstract: In this talk, we present some new developments in the theory of Laplacians on metric graphs. We discuss the role played by planarity or -- more generally -- the graph's genus and derive bounds for the eigenvalues of the Laplacian. For the derivation of these bounds, we make use of a recently developed transference principle by Amini and Cohen-Steiner that compares eigenvalues of continuous and discrete objects in a very convenient way. As a by-product of our methods we also obtain eigenvalue bounds for Laplacian on discrete weighted graphs.