Abstract for the talk at 02.05.2012 (15:30 h)

Matthias Keller (Universität Jena)

Negative curvature and spectrum of graph Laplacians

We present spectral estimates for non-positive Gaussian curvature on tessellating planar graphs. Moreover, we can characterize discreteness of spectrum by uniformly unbounded curvature. These estimates work via an isoperimetric inequality and can be extended to general planar graphs of negative curvature.