Gandalf (Pure Maths Student Seminar): The spectrum of the 1-form Laplacian on a graph-like manifold
13 March 2014 15:00 in CM107A graph-like manifold is a family of neighbourhoods of thickness ε>0 of a metric graph shrinking to the graph itself as ε approaches zero. In spectral geometry, graph-like manifolds were first introduced by Colin de Verdiere to prove that a manifold of dimension n greater or equal than 3 admits a metric with the first non-zero eigenvalue of the Laplacian having multiplicity n and since then, they have been used as a toy model to prove properties of manifolds or disprove conjectures. In physics, they are a model for nano and optical structure and metric graphs are believed to be a good approximation for them since the spectum of their Laplacian is a good approximation of the spectrum of the Laplacian of graph-like manifolds. In my talk I will explore the relation between the spectra of the Laplacian acting on 1-forms on the graph-like manifold and the Laplacian acting on 1-forms on the metric graph with some insights about higher degree forms.
Gandalf is the pure maths student seminar. Gandalf stands for the Geometry AND ALgebra Forum. It is run by and for pure postgraduates, but welcomes anyone who is interested in coming along.
Content from previous talks is available at the gandalf seminar home page.