Staff profile

• Global Analysis
• Graph Theory
• Mathematical and computational aspects of X-ray crystallography
• Riemannian Geometry

Authored book

• Twisted Isospectrality, Homological Wideness, and Isometry
  Cornelissen, G., & Peyerimhoff, N. (2023). Twisted Isospectrality, Homological Wideness, and Isometry. Springer Verlag. https://doi.org/10.1007/978-3-031-27704-7
• Mathematik in Anwendung mit C++
  Huettenhofer, M., Lesch, M., & Peyerimhoff, N. (1994). Mathematik in Anwendung mit C++. Quelle & Meyer

Chapter in book

• Curvature Calculations for Antitrees
  Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Curvature Calculations for Antitrees. In M. Keller, D. Lenz, & R. K. Wojciechowski (Eds.), Analysis and geometry on graphs and manifolds (21-54). Cambridge University Press. https://doi.org/10.1017/9781108615259.003
• Signatures, Lifts, and Eigenvalues of Graphs
  Liu, S., Peyerimhoff, N., & Vdovina, A. (2020). Signatures, Lifts, and Eigenvalues of Graphs. In F. M. Atay, P. B. Kurasov, & D. Mugnolo (Eds.), Discrete and continuous models in the theory of networks : operator theory : advances and applications (255-269). Birkhäuser Verlag. https://doi.org/10.1007/978-3-030-44097-8_13

Conference Paper

• NP-completeness of the combinatorial distance matrix realisation problem
  Fairbairn, D., Mertzios, G., & Peyerimhoff, N. (2025, December). NP-completeness of the combinatorial distance matrix realisation problem. Presented at 14th International Symposium on Algorithms and Complexity (CIAC 2025), Rome, Italy
• Isoperimetric and ergodic properties of horospheres in symmetric spaces
  Peyerimhoff, N. (2001, December). Isoperimetric and ergodic properties of horospheres in symmetric spaces. Presented at Smooth Ergodic Theory and Its Applications, University of Washington, Seattle

Journal Article

• A note on Steinerberger’s curvature for graphs
  Cushing, D., Kamtue, S., Law, E., Liu, S., Münch, F., & Peyerimhoff, N. (in press). A note on Steinerberger’s curvature for graphs. Journal of Combinatorics,
• Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spaces
  Fischer, F., & Peyerimhoff, N. (online). Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spaces. Israel Journal of Mathematics, https://doi.org/10.1007/s11856-024-2713-y
• Bakry–Émery and Ollivier Ricci Curvature of Cayley Graphs
  Cushing, D., Kamtue, S., Kangaslampi, R., Liu, S., Münch, F., & Peyerimhoff, N. (in press). Bakry–Émery and Ollivier Ricci Curvature of Cayley Graphs. Electronic Journal of Combinatorics,
• Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: theory
  Cushing, D., Kamtue, S., Liu, S., Münch, F., Peyerimhoff, N., & Snodgrass, B. (2025). Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: theory. manuscripta mathematica, 176(1), Article 11. https://doi.org/10.1007/s00229-024-01606-7
• Rigidity properties of the hypercube via Bakry–Émery curvature
  Liu, S., Münch, F., & Peyerimhoff, N. (2024). Rigidity properties of the hypercube via Bakry–Émery curvature. Mathematische Annalen, 388(2), 1225-1259. https://doi.org/10.1007/s00208-022-02537-y
• Refinement of X‐ray and electron diffraction crystal structures using analytical Fourier transforms of Slater‐type atomic wavefunctions in Olex2
  Kleemiss, F., Peyerimhoff, N., & Bodensteiner, M. (2024). Refinement of X‐ray and electron diffraction crystal structures using analytical Fourier transforms of Slater‐type atomic wavefunctions in Olex2. Journal of Applied Crystallography, 57, 161-174. https://doi.org/10.1107/s1600576723010981
• Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: A collaborative study between early years teachers and University-based mathematicians
  Oughton, R., Nichols, K., Bolden, D. S., Dixon-Jones, S., Fearn, S., Darwin, S., Mistry, M., Peyerimhoff, N., & Townsend, A. (2024). Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: A collaborative study between early years teachers and University-based mathematicians. Mathematical Thinking and Learning, 26(3), 306-325. https://doi.org/10.1080/10986065.2022.2119497
• Parameterized Counting and Cayley Graph Expanders
  Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A., & Wellnitz, P. (2023). Parameterized Counting and Cayley Graph Expanders. SIAM Journal on Discrete Mathematics, 37(2), 405-486. https://doi.org/10.1137/22m1479804
• Bakry–Émery Curvature Sharpness and Curvature Flow in Finite Weighted Graphs. Implementation
  Cushing, D., Kamtue, S., Liu, S., Münch, F., Peyerimhoff, N., & Snodgrass, B. (2023). Bakry–Émery Curvature Sharpness and Curvature Flow in Finite Weighted Graphs. Implementation. Axioms, 12(6), Article 577. https://doi.org/10.3390/axioms12060577
• Going round in circles: Geometry in the early years
  Oughton, R. H., Wheadon, D. M., Bolden, D. S., Nichols, K., Fearn, S., Darwin, S., Dixon-Jones, S., Mistry, M., Peyerimhoff, N., & Townsend, A. (2023). Going round in circles: Geometry in the early years. Mathematics teaching, 286, 29-34
• Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms
  Egidi, M., Gittins, K., Habib, G., & Peyerimhoff, N. (2023). Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms. Journal of Spectral Theory, 13(4), 1297-1343. https://doi.org/10.4171/JST/480
• Refinement of anomalous dispersion correction parameters in single-crystal structure determinations
  Meurer, F., Dolomanov, O. V., Hennig, C., Peyerimhoff, N., Kleemiss, F., Puschmann, H., & Bodensteiner, M. (2022). Refinement of anomalous dispersion correction parameters in single-crystal structure determinations. IUCrJ, 9(5), https://doi.org/10.1107/s2052252522006844
• Bakry-Émery curvature on graphs as an eigenvalue problem
  Cushing, D., Kamtue, S., Liu, S., & Peyerimhoff, N. (2022). Bakry-Émery curvature on graphs as an eigenvalue problem. Calculus of Variations and Partial Differential Equations, 61, Article 62. https://doi.org/10.1007/s00526-021-02179-z
• Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement
  Midgley, L., Bourhis, L. J., Dolomanov, O. V., Grabowsky, S., Kleemiss, F., Puschmann, H., & Peyerimhoff, N. (2021). Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement. Acta Crystallographica Section A: Foundations and Advances, 77(6), 519-533. https://doi.org/10.1107/s2053273321009086
• A note on eigenvalue bounds for non-compact manifolds
  Keller, M., Liu, S., & Peyerimhoff, N. (2021). A note on eigenvalue bounds for non-compact manifolds. Mathematische Nachrichten, 294(6), 1134-1139. https://doi.org/10.1002/mana.201900209
• Curvatures, Graph Products and Ricci Flatness
  Cushing, D., Kamtue, S., Kangaslampi, R., Liu, S., & Peyerimhoff, N. (2021). Curvatures, Graph Products and Ricci Flatness. Journal of Graph Theory, 96(4), 522-553. https://doi.org/10.1002/jgt.22630
• Accurate Crystal Structures and Chemical Properties from NoSpherA2
  Kleemiss, F., Dolomanov, O. V., Bodensteiner, M., Peyerimhoff, N., Midgley, L., Bourhis, L. J., Genoni, A., Malaspina, L. A., Jayatilaka, D., Spencer, J. L., White, F., Grundkötter-Stock, B., Steinhauer, S., Lentz, D., Puschmann, H., & Grabowsky, S. (2021). Accurate Crystal Structures and Chemical Properties from NoSpherA2. Chemical Science, 12, 1675-1692. https://doi.org/10.1039/d0sc05526c
• Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds
  Egidi, M., Liu, S., Muench, F., & Peyerimhoff, N. (2021). Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds. Communications in Analysis and Geometry, 29(5), 1127-1156. https://doi.org/10.4310/cag.2021.v29.n5.a4
• Eigenfunctions and the Integrated Density of States on Archimedean Tilings
  Peyerimhoff, N., & Taeufer, M. (2021). Eigenfunctions and the Integrated Density of States on Archimedean Tilings. Journal of Spectral Theory, 11(2), 461-488. https://doi.org/10.4171/jst/347
• The Fourier Transform on harmonic manifolds of purely exponential volume growth
  Biswas, K., Knieper, G., & Peyerimhoff, N. (2021). The Fourier Transform on harmonic manifolds of purely exponential volume growth. Journal of Geometric Analysis, 31(1), 126-163. https://doi.org/10.1007/s12220-019-00253-9
• Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
  Cushing, D., Kamtue, S., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature. Advances in Mathematics, 360, Article 107188. https://doi.org/10.1016/j.aim.2020.107188
• A support theorem for the X-ray transform on manifolds with plane covers
  Peyerimhoff, N., & Samiou, E. (2020). A support theorem for the X-ray transform on manifolds with plane covers. Mathematical Proceedings of the Cambridge Philosophical Society, 169(1), 149-158. https://doi.org/10.1017/s0305004119000148
• Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces
  Knieper, G., Parker, J. R., & Peyerimhoff, N. (2020). Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces. Differential Geometry and its Applications, 69, Article 101605. https://doi.org/10.1016/j.difgeo.2020.101605
• Quartic graphs which are Bakry-Émery curvature sharp
  Cushing, D., Kamtue, S., Peyerimhoff, N., & Watson May, L. (2020). Quartic graphs which are Bakry-Émery curvature sharp. Discrete Mathematics, 343(3), Article 111767. https://doi.org/10.1016/j.disc.2019.111767
• Bakry-Émery Curvature Functions on Graphs
  Cushing, D., Liu, S., & Peyerimhoff, N. (2020). Bakry-Émery Curvature Functions on Graphs. Canadian Journal of Mathematics, 72(1), 89-143. https://doi.org/10.4153/cjm-2018-015-4
• Trivalent expanders, $(Delta – Y)$-transformation, and hyperbolic surfaces
  Ivrissimtzis, I., Peyerimhoff, N., & Vdovina, A. (2019). Trivalent expanders, $(Delta – Y)$-transformation, and hyperbolic surfaces. Groups, Geometry, and Dynamics, 13(3), 1103-1131. https://doi.org/10.4171/ggd/518
• Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature
  Liu, S., Münch, F., Peyerimhoff, N., & Rose, C. (2019). Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature. Analysis and Geometry in Metric Spaces, 7(1), 1-14. https://doi.org/10.1515/agms-2019-0001
• Curvature and higher order Buser inequalities for the graph connection Laplacian
  Liu, S., Muench, F., & Peyerimhoff, N. (2019). Curvature and higher order Buser inequalities for the graph connection Laplacian. SIAM Journal on Discrete Mathematics, 33(1), 257-305. https://doi.org/10.1137/16m1056353
• Minimizing length of billiard trajectories in hyperbolic polygons
  Parker, J. R., Peyerimhoff, N., & Siburg, K. F. (2018). Minimizing length of billiard trajectories in hyperbolic polygons. Conformal Geometry and Dynamics, 22, 315-332. https://doi.org/10.1090/ecgd/328
• Eigenvalue ratios of non-negatively curved graphs
  Liu, S., & Peyerimhoff, N. (2018). Eigenvalue ratios of non-negatively curved graphs. Combinatorics, Probability and Computing, 27(5), 829-850. https://doi.org/10.1017/s0963548318000214
• Ollivier-Ricci idleness functions of graphs
  Bourne, D., Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2018). Ollivier-Ricci idleness functions of graphs. SIAM Journal on Discrete Mathematics, 32(2), 1408-1424. https://doi.org/10.1137/17m1134469
• Bakry–Émery curvature and diameter bounds on graphs
  Liu, S., Münch, F., & Peyerimhoff, N. (2018). Bakry–Émery curvature and diameter bounds on graphs. Calculus of Variations and Partial Differential Equations, 57(2), Article 67. https://doi.org/10.1007/s00526-018-1334-x
• Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space
  Peyerimhoff, N., Täufer, M., & Veselić, I. (2017). Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space. Nanosistemy: fizika, himiâ, matematika Наносистемы: физика, химия, математика (Print), 8(2), 216-230. https://doi.org/10.17586/2220-8054-2017-8-2-216-230
• Sectional curvature of polygonal complexes with planar substructures
  Keller, M., Peyerimhoff, N., & Pogorzelski, F. (2017). Sectional curvature of polygonal complexes with planar substructures. Advances in Mathematics, 307, 1070-1107. https://doi.org/10.1016/j.aim.2016.10.027
• Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians
  Lange, C., Liu, S., Peyerimhoff, N., & Post, O. (2015). Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians. Calculus of Variations and Partial Differential Equations, 54(4), 4165-4196. https://doi.org/10.1007/s00526-015-0935-x
• An infinite family of 2-groups with mixed Beauville structures
  Barker, N., Boston, N., Peyerimhoff, N., & Vdovina, A. (2015). An infinite family of 2-groups with mixed Beauville structures. International Mathematics Research Notices, 2015(11), 3598-3618. https://doi.org/10.1093/imrn/rnu045
• Geometric properties of rank one asymptotically harmonic manifolds
  Knieper, G., & Peyerimhoff, N. (2015). Geometric properties of rank one asymptotically harmonic manifolds. Journal of Differential Geometry, 100(3), 507-532. https://doi.org/10.4310/jdg/1432842363
• Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials
  Leonhardt, K., Peyerimhoff, N., Tautenhahn, M., & Veselic, I. (2015). Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials. Reviews in Mathematical Physics, 27(04), https://doi.org/10.1142/s0129055x15500075
• Harmonic Functions on Rank One Asymptotically Harmonic Manifolds
  Knieper, G., & Peyerimhoff, N. (2015). Harmonic Functions on Rank One Asymptotically Harmonic Manifolds. Journal of Geometric Analysis, 26(2), 750-781. https://doi.org/10.1007/s12220-015-9570-1
• Integral Geometric Properties of Non-compact Harmonic Spaces
  Peyerimhoff, N., & Samiou, E. (2015). Integral Geometric Properties of Non-compact Harmonic Spaces. Journal of Geometric Analysis, 25(1), Article 122. https://doi.org/10.1007/s12220-013-9416-7
• Some spectral applications of McMullen's Hausdorff dimension algorithm
  Gittins, K., Peyerimhoff, N., Stoiciu, M., & Wirosoetisno, D. (2012). Some spectral applications of McMullen's Hausdorff dimension algorithm. Conformal Geometry and Dynamics, 16, 184-203. https://doi.org/10.1090/s1088-4173-2012-00244-5
• Billiards in ideal hyperbolic polygons
  Castle, S., Peyerimhoff, N., & Siburg, K. (2011). Billiards in ideal hyperbolic polygons. Discrete and Continuous Dynamical Systems - Series A, 29(3), 893-908. https://doi.org/10.3934/dcds.2011.29.893
• Cheeger constants, growth and spectrum of locally tessellating planar graphs
  Keller, M., & Peyerimhoff, N. (2011). Cheeger constants, growth and spectrum of locally tessellating planar graphs. Mathematische Zeitschrift, 268(3-4), 871-886. https://doi.org/10.1007/s00209-010-0699-0
• Cayley graph expanders and groups of finite width
  Peyerimhoff, N., & Vdovina, A. (2011). Cayley graph expanders and groups of finite width. Journal of Pure and Applied Algebra, 215(11), 2780-2788. https://doi.org/10.1016/j.jpaa.2011.03.018
• Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces
  Peyerimhoff, N., & Samiou, E. (2010). Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces. Arkiv för Matematik, 48(1), 131-147. https://doi.org/10.1007/s11512-009-0105-5
• Continuity of the integrated density of states on random length metric graphs.
  Lenz, D., Peyerimhoff, N., Post, O., & Veselic, I. (2009). Continuity of the integrated density of states on random length metric graphs. Mathematical Physics, Analysis and Geometry, 12(3), 219-254. https://doi.org/10.1007/s11040-009-9059-x
• Ergodic properties of isoperimetric domains in spheres
  Knieper, G., & Peyerimhoff, N. (2008). Ergodic properties of isoperimetric domains in spheres. Journal of Modern Dynamics, 2(2), 339-358. https://doi.org/10.3934/jmd.2008.2.339
• Continuity properties of the integrated density of states on manifolds
  Lenz, D., Peyerimhoff, N., Post, O., & Veselic, I. (2008). Continuity properties of the integrated density of states on manifolds. Japanese Journal of Mathematics, 3(1), 121-161. https://doi.org/10.1007/s11537-008-0729-4
• Geometric heat comparison criteria for Riemannian manifolds
  Karp, L., & Peyerimhoff, N. (2007). Geometric heat comparison criteria for Riemannian manifolds. Annals of Global Analysis and Geometry, 31, 115-145. https://doi.org/10.1007/s10455-006-9038-4
• Groupoids, von Neumann algebras and the integrated density of states
  Lenz, D., Veselic, I., & Peyerimhoff, N. (2007). Groupoids, von Neumann algebras and the integrated density of states. Mathematical Physics, Analysis and Geometry, 10(1), 1-41. https://doi.org/10.1007/s11040-007-9019-2
• Geodesics in non-positively curved plane tessellations
  Baues, O., & Peyerimhoff, N. (2006). Geodesics in non-positively curved plane tessellations. Advances in Geometry, 6(2), 243-263. https://doi.org/10.1515/advgeom.2006.014
• Spherical means on compact locally symmetric spaces of non-positive curvature
  Peyerimhoff, N. (2006). Spherical means on compact locally symmetric spaces of non-positive curvature. Forum Mathematicum, 18(3), 391-417. https://doi.org/10.1515/forum.2006.022
• Elliptic operators on planar graphs: unique continuation for eigenfunctions and nonpositive curvature
  Klassert, S., Lenz, D., Peyerimhoff, N., & Stollmann, P. (2006). Elliptic operators on planar graphs: unique continuation for eigenfunctions and nonpositive curvature. Proceedings of the American Mathematical Society, 134(5), 1549-1559
• Integrated density of states for random metrics on manifolds
  Lenz, D., Peyerimhoff, N., & Veselic, I. (2004). Integrated density of states for random metrics on manifolds. Proceedings of the London Mathematical Society, 88(3), 733-752. https://doi.org/10.1112/s0024611503014576
• The Cheeger constant of simply connected, solvable Lie groups
  Peyerimhoff, N., & Samiou, E. (2004). The Cheeger constant of simply connected, solvable Lie groups. Proceedings of the American Mathematical Society, 132(5), 1525-1529
• The dynamics of magnetic flows for energies above Mane's critical value
  Peyerimhoff, N., & Siburg, K. (2003). The dynamics of magnetic flows for energies above Mane's critical value. Israel Journal of Mathematics, 135, 269-298
• Random Schroedinger operators on manifolds
  Lenz, D., Peyerimhoff, N., & Veselic, I. (2003). Random Schroedinger operators on manifolds. Markov processes and related fields, 9, 717-728
• Simplices of maximal volume or minimal total edge length in hyperbolic space
  Peyerimhoff, N. (2002). Simplices of maximal volume or minimal total edge length in hyperbolic space. Journal of the London Mathematical Society, 66(3), 753-768. https://doi.org/10.1112/s0024610702003629
• Integrated density of states for ergodic random Schrödinger operators on manifolds
  Peyerimhoff, N., & Veselić, I. (2002). Integrated density of states for ergodic random Schrödinger operators on manifolds. Geometriae Dedicata, 91(1), 117-135. https://doi.org/10.1023/a%3A1016222913877
• Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane
  Karp, L., & Peyerimhoff, N. (2002). Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane. Archiv der Mathematik, 79, 223-231. https://doi.org/10.1007/s00013-002-8308-z
• Curvature and Geometry of Tessellating Plane Graphs
  Baues, O., & Peyerimhoff, N. (2001). Curvature and Geometry of Tessellating Plane Graphs. Discrete & Computational Geometry, 25(1), 141-159. https://doi.org/10.1007/s004540010076
• Spectral gaps of Schroedinger operators on hyperbolic space
  Karp, L., & Peyerimhoff, N. (2000). Spectral gaps of Schroedinger operators on hyperbolic space. Mathematische Nachrichten, 217, 105-124
• Horospherical means and uniform distribution of curves of constant geodesic curvature
  Karp, L., & Peyerimhoff, N. (1999). Horospherical means and uniform distribution of curves of constant geodesic curvature. Mathematische Zeitschrift, 231, 655-677. https://doi.org/10.1007/pl00004745
• On index formulas for manifolds with metric horns
  Lesch, M., & Peyerimhoff, N. (1998). On index formulas for manifolds with metric horns. Communications in Partial Differential Equations, 23(3 & 4), 649-684
• On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space
  Karp, L., & Peyerimhoff, N. (1998). On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space. Analysis: International mathematical journal of analysis and its applications, 18, 217-225. https://doi.org/10.1524/anly.1998.18.3.217
• Areas and intersections in convex domains
  Peyerimhoff, N. (1997). Areas and intersections in convex domains. The American Mathematical Monthly, 104(8), 697-704. https://doi.org/10.2307/2975231
• The del-bar-operator on algebraic curves
  Bruening, J., Peyerimhoff, N., & Schroeder, H. (1990). The del-bar-operator on algebraic curves. Communications in Mathematical Physics, 129, 525-534. https://doi.org/10.1007/bf02097104