Preprints
- The Dry Ten Martini Problem for Sturmian Hamiltonians
R. Band, S. Beckus, R. Loewy
arXiv:2402.16703.
A lighter (and much shorter) description of this work appears in
MFO Report: The dry ten Martini problem for Sturmian dynamical systems
arXiv:2309.04351. - Sturm-Hurwitz Theorem for quantum graphs
R. Band, P. Charron
arXiv:2310.03877. - Spectral flow and Robin domains on metric graphs
R. Band, M. Prokhorova, G. Sofer
arXiv:2505.02039.
Published or in press
- Spectral Approximation for substitution systems
R. Band, S. Beckus, F. Pogorzelski, L. Tenenbaum
Journal d’Analyse Mathématique (in press). arXiv:2408.09282. - A review of a work by Raymond: Sturmian Hamiltonians with a large coupling constant – periodic approximations and gap labels
R. Band, S. Beckus, B. Biber, L. Raymond, Y. Thomas.
The Proceedings of the Final Conference of COST Action “CA18232: Mathematical models for interacting dynamics on networks” (in press). arXiv:2409.10920. - Quotients of finite-dimensional operators by symmetry representations
R. Band, G. Berkolaiko, C. H. Joyner, W. Liu
Journal d’Analyse Mathématique (in press). arXiv:1711.00918. - Differences between Robin and Neumann eigenvalues on metric graphs
R. Band, H. Schanz, G. Sofer
Annales Henri Poincaré 25 (2024), p. 3859–3898. arXiv:2310.03877. - Defining the spectral position of a Neumann domain
R. Band, G. Cox, S. K. Egger
Analysis & PDE 16-9 (2023), p. 2147-2171. - Universality of nodal count distribution in large metric graphs
L. Alon, R. Band, G. Berkolaiko
Experimental Mathematics (2022), p. 1-35. - Neumann domains on quantum graphs
L. Alon, R. Band
Annales Henri Poincaré 22 (2021), p. 3391–3454. - The spectral position of Neumann domains on the torus
R. Band, S. K. Egger, A. J. Taylor
The Journal of Geometric Analysis 31 (2021), p. 4561-4585. - Neumann Domains on Graphs and Manifolds
L. Alon, R. Band, M. Bersudsky, S. K. Egger
Analysis and Geometry on Graphs and Manifolds (London Mathematical Society Lecture Note Series). Edited by Keller, M., Lenz, D., & Wojciechowski, R. (2020), p. 203-249. - On the nodal structure of nonlinear stationary waves on star graphs
R. Band, S. Gnutzmann, A. J. Krueger
Symmetry, Volume 11(2) (2019). - Lyndon word decompositions and pseudo orbits on q-nary graphs
R. Band, J. M. Harrison, M. Sepansky
Journal of Mathematical Analysis and Applications 470 (2019) p. 135–144. - Quantum Graphs via Exercises
R. Band, S. Gnutzmann
AMS Contemporary Mathematics, 720: Spectral theory and applications (2018) p. 187–203. - Nonlinear Sturm Oscillation: from the interval to a star
R. Band, A. J. Krueger
AMS Contemporary Mathematics, 717: Mathematical problems in quantum physics (2018) p. 129–154. - Nodal Statistics on Quantum Graphs
L. Alon, R. Band, G. Berkolaiko
Communications in Mathematical Physics 362 (2018) p. 909-948. - 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. 127-136. - Topological Properties of Neumann Domains
R. Band, D. Fajman,
Annales Henri Poincaré, Volume 17, Issue 9 (2016) p. 2379-2407. - 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. - The Nodal Count {0,1,2,3,…} Implies the Graph is a Tree
R. Band,
Phil. Trans. R. Soc. A 28 vol. 372 no. 2007 (2014) p. 20120504. - Universality of the momentum band density of periodic networks
R. Band, G. Berkolaiko,
Phys. Rev. Lett. 111 (2013) p. 130404. Chosen as Editor’s selection. - Finite pseudo orbit expansions for spectral quantities of quantum graphs
R. Band, J. M. Harrison, C. H. Joyner,
J. Phys. A: Math. Theor. 45 (2012) p. 325204. - Isospectral graphs with identical nodal counts
I. Oren, R. Band,
J. Phys. A: Math. Theor. 45 (2012) p. 135203. - Nodal domains of a non-separable problem – the right angled isosceles triangle
A. Aronovitch, R. Band, D. Fajman, S. Gnutzmann,
J. Phys. A: Math. Theor. 45 (2012) p. 085209. Featured article of the issue. - The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions
R. Band, G. Berkolaiko, H. Raz, U. Smilansky,
Communications in Mathematical Physics 311 (2012) p. 815. - Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs
R. Band, G. Berkolaiko, U. Smilansky,
Annales Henri Poincaré 13 (2012) p. 145-184. - Note on the Role of Symmetry in Scattering from Isospectral Graphs and Drums
R. Band, A. Sawicki, U. Smilansky,
Acta Physica Polonica A, Vol. 120 (2011), Proceedings of the 5th Workshop on Quantum Chaos and Localisation Phenomena. - Scattering from isospectral quantum graphs
R. Band, A. Sawicki, U. Smilansky,
J. Phys. A: Math. Theor. 43 (2010) p. 415201. - Linear Representations and Isospectrality with Boundary Conditions
O. Parzanchevski, R. Band,
Journal of Geometric Analysis 20, 2 (2010) p. 439-471. - The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
R. Band, O. Parzanchevski, G. Ben-Shach,
J. Phys. A: Math. Theor. 42 (2009) p. 175202. Best paper prize of the Journal of Physics A’. - Nodal domains on graphs – how to count them and why?
R. Band, I. Oren, U. Smilansky,
Analysis on Graphs and its applications Proc. Symp. Pure Math. (Providence, RI: American Mathematical Society) (2008) p. 5-28. - Resolving the isospectrality of the dihedral graphs by counting nodal domains
R. Band, U. Smilansky,
Eur. Phys. J. Special Topics 145 (2007) p. 171-179. - Nodal domains on isospectral quantum graphs: the resolution of isospectrality
R. Band, T. Shapira, U. Smilansky,
J. Phys. A: Math. Gen. 39 (2006) p. 13999-14014.
Mathematics education papers
- Potential and implementation of tasks in linear algebra workshops
M. Wallach, E. Heyd-Metzuyanim, R. Band,
Preprint under review. - The Discourse Mapping Tree as a tool for analyzing the potential and implementation of linear algebra tasks
M. Wallach, E. Heyd-Metzuyanim, R. Band,
Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (2023) p. 315-322. - Explorative Potential of Linear Algebra Tasks
M. Wallach, E. Heyd-Metzuyanim, R. Band,
Proceedings of the 12th conference of the European Society for Research in Mathematics Education (2022). - Mathematical Activity in Collaborative Linear-Algebra Problem-Solving
M. Wallach, E. Heyd-Metzuyanim, R. Band,
Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education (2021).
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