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Quantum graphs and Topology

Presented by: 
P Kurasov [Lund Institute of Technology]
Wednesday 4th April 2007 - 16:30 to 17:00
INI Seminar Room 1

Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same characteristics are determined by the scattering data consisting of the scattering matrix and the discrete eigenvalues. This result is generalized for Schr\"odinger operators on metric graphs.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons