Spectral Geometry on Graphs and Beyond

CIG grant 618468

This project concerns the extraction of geometric information about graphs from the spectra of the graph’s Schrödinger operator, and from the distribution of zeros of the corresponding eigenfunctions. The spectral geometric point of view shows intrigue links between quantum and combinatorial graphs, which go over towards higher dimensional domains. In this sense our research offers a cross disciplinary perspective – the investigation of spectral geometry covers both quantum and combinatorial graphs. We make connections between quantum graphs which are one dimensional objects and domains which are of higher dimension and further apply graph related methods for real-life composite materials.

This project is funded by Marie Curie Actions (Grant No. PCIG13-GA-2013-618468).

Relevant publications

**Quotients of finite-dimensional operators by symmetry representations**

R. Band, G. Berkolaiko, C. H. Joyner, W. Liu

arXiv:1711.00918**Nodal Statistics on Quantum Graphs**

L. Alon, R. Band, G. Berkolaiko

arXiv:1709.10413**Nonlinear Sturm Oscillation: from the interval to a star**

R. Band, A. J. Krueger

arXiv:1610.07068**Lyndon word decompositions and pseudo orbits on q-nary graphs**

R. Band, J. M. Harrison, M. Sepansky

arXiv:1610.03808**Quantum graphs which optimize the spectral gap**

R. Band, G. Lévy

Annales Henri Poincaré, Volume 18 (2017), p. 3269-3323.**Courant-sharp Eigenvalues of Neumann 2-Rep-tiles**

R. Band, M. Bersudsky, D. Fajman

Letters in Mathematical Physics. , Volume 107 (2017) p. 821-859.**Universality of the frequency spectrum of laminates**

G. Shmuel, R. Band,

Journal of the Mechanics and Physics of Solids 92 (2016) p. 127.**Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs**

R. Band, G. Berkolaiko, T. Weyand,

J. Math. Phys. 56 (2015) p. 122111. Chosen as Featured Article of the issue.