Matthias Keller - Negative curvature and spectrum of graphs, 30th May 2013

 We discuss combinatorial curvature on planar graphs and the consequences of negative curvature on the spectrum of the graph Laplacian. A particular focus lies on  uniformly decreasing curvature. This case is characterized by purely discrete spectrum and one can show eigenvalue asymptotics, exponential decay of eigenfunctions and absence of compactly supported eigenfunctions. (The results include joint work with Michel Bonnefont, Sylvain Golenia, Norbert Peyerimhoff and Daniel Lenz).