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).
- Quotients of finite-dimensional operators by symmetry representations
R. Band, G. Berkolaiko, C. H. Joyner, W. Liu
- Nodal Statistics on Quantum Graphs
L. Alon, R. Band, G. Berkolaiko
- Nonlinear Sturm Oscillation: from the interval to a star
R. Band, A. J. Krueger
- Lyndon word decompositions and pseudo orbits on q-nary graphs
R. Band, J. M. Harrison, M. Sepansky
- 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.