Publications

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.
• Johnson-Schwartzman Gap Labelling for Metric and Discrete Decorated Graphs
  R. Band, G. Sofer
  arXiv:2604.08496.

Published or in press

• From Quasiperiodicity to a Complete Coloring of the Kohmoto Butterfly
  R. Band, S. Beckus
  Europhysics Letters (in press).  arXiv:2509.24025.
• Spectral flow and Robin domains on metric graphs
  R. Band, M. Prokhorova, G. Sofer
  Israel Journal of Mathematics (in press).  arXiv:2505.02039.
• Spectral statistics of preferred orientation quantum graphs
  R. Band, P. Exner, D. Goel, A. Strauss
  Journal of Mathematical Physics 67 (2026), 013502.
• Sturm-Hurwitz Theorem for quantum graphs
  R. Band, P. Charron
  Proceedings of the American Mathematical Society (in press).  arXiv:2310.03877.
• 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” (2026).
• 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.
• 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,
  Journal of Mathematical Physics 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

• The Discourse Mapping Tree as a Tool for Mapping Classroom Discussions in Linear Algebra
  M. Wallach, E. Heyd-Metzuyanim, R. Band,
  The Journal of Mathematical Behavior  83 (2026), p. 101328.
• 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 12^th 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).

The papers listed above are made available as a scientific resource for the private use of individual scholars. None of the material may be used commercially, or for financial gain. Some of it is protected by copyright. Requests for permission to make public use of any of the papers, or material therein, should be sought from the original publisher. It is the responsibility of anyone making use of this material to ensure that they are not breaking copyright.