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Graphs which sound the same

Smilansky, U (Weizmann Institute of Science)
Wednesday 11 April 2007, 15:00-16:00

Seminar Room 1, Newton Institute


After a short review of the conditions for unique spectral inversion for quantum graphs, I shall describe a method for constructing families of isospectral yet not isometric garphs: "graphs which sound the same". I shall then discuss the conjecture that graphs which sound the same can be resolved by the difference between their sequences of counts of nodal domains, and will present a proof that this is indeed the case for a simple yet non trivial example.




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