An Isaac Newton Institute Workshop

Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures

Graphs which sound the same

Author: U. Smilansky (Weizmann Institute of Science)

Abstract

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.