Staff profile
Overview
https://apps.dur.ac.uk/biography/image/1431
Affiliation | Telephone |
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Professor in the Department of Mathematical Sciences |
Research interests
- Global Analysis
- Graph Theory
- Mathematical and computational aspects of X-ray crystallography
- Riemannian Geometry
Publications
Authored book
- Twisted Isospectrality, Homological Wideness, and IsometryCornelissen, 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 AntitreesCushing, 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. (pp. 21-54). Cambridge University Press. https://doi.org/10.1017/9781108615259.003
- Signatures, Lifts, and Eigenvalues of GraphsLiu, 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. (pp. 255-269). Birkhäuser. https://doi.org/10.1007/978-3-030-44097-8_13
Conference Paper
- NP-completeness of the combinatorial distance matrix realisation problemFairbairn, D., Mertzios, G., & Peyerimhoff, N. (in press). 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 spacesPeyerimhoff, N. (2001). Isoperimetric and ergodic properties of horospheres in symmetric spaces. In A. Katok, R. de la Llave, Y. Pesin, & H. Weiss (Eds.), Proceedings of Symposia in Pure Mathematics (pp. 797-808). American Mathematical Society.
Journal Article
- A note on Steinerberger’s curvature for graphsCushing, D., Kamtue, S., Law, E., Liu, S., Münch, F., & Peyerimhoff, N. (in press). A note on Steinerberger’s curvature for graphs. Journal of Combinatorics.
- Bakry–Émery and Ollivier Ricci Curvature of Cayley GraphsCushing, 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: theoryCushing, 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
- Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spacesFischer, F., & Peyerimhoff, N. (2025). Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spaces. Israel Journal of Mathematics. Advance online publication. https://doi.org/10.1007/s11856-024-2713-y
- Rigidity properties of the hypercube via Bakry–Émery curvatureLiu, 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 Olex2Kleemiss, 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 mathematiciansOughton, 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 ExpandersPeyerimhoff, 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. ImplementationCushing, 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 yearsOughton, 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 formsEgidi, 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 determinationsMeurer, 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 problemCushing, 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 refinementMidgley, 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 manifoldsKeller, 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 FlatnessCushing, 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
- Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifoldsEgidi, 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 TilingsPeyerimhoff, 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
- Accurate Crystal Structures and Chemical Properties from NoSpherA2Kleemiss, 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
- The Fourier Transform on harmonic manifolds of purely exponential volume growthBiswas, 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 curvatureCushing, 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 coversPeyerimhoff, 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 spacesKnieper, 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 sharpCushing, 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 GraphsCushing, 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 surfacesIvrissimtzis, 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 CurvatureLiu, 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 LaplacianLiu, 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 polygonsParker, 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 graphsLiu, 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 graphsBourne, 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 graphsLiu, 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 spacePeyerimhoff, N., Täufer, M., & Veselić, I. (2017). Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space. Nanosystems : Physics, Chemistry, Mathematics, 8(2), 216-230. https://doi.org/10.17586/2220-8054-2017-8-2-216-230
- Sectional curvature of polygonal complexes with planar substructuresKeller, 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 LaplaciansLange, 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 structuresBarker, 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 manifoldsKnieper, 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 potentialsLeonhardt, 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 ManifoldsKnieper, 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 SpacesPeyerimhoff, 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 algorithmGittins, 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 polygonsCastle, 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
- Cayley graph expanders and groups of finite widthPeyerimhoff, 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
- Cheeger constants, growth and spectrum of locally tessellating planar graphsKeller, 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
- Spherical spectral synthesis and two-radius theorems on Damek-Ricci spacesPeyerimhoff, 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 spheresKnieper, 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 manifoldsLenz, 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 manifoldsKarp, 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 statesLenz, 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 tessellationsBaues, 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 curvaturePeyerimhoff, 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 curvatureKlassert, 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 manifoldsLenz, 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 groupsPeyerimhoff, 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 valuePeyerimhoff, 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 manifoldsLenz, 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 spacePeyerimhoff, 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 manifoldsPeyerimhoff, 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 planeKarp, 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 GraphsBaues, O., & Peyerimhoff, N. (2001). Curvature and Geometry of Tessellating Plane Graphs. Discrete and Computational Geometry, 25(1), 141-159. https://doi.org/10.1007/s004540010076
- Spectral gaps of Schroedinger operators on hyperbolic spaceKarp, 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 curvatureKarp, 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 hornsLesch, 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 spaceKarp, L., & Peyerimhoff, N. (1998). On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space. Analysis, 18, 217-225. https://doi.org/10.1524/anly.1998.18.3.217
- Areas and intersections in convex domainsPeyerimhoff, N. (1997). Areas and intersections in convex domains. American Mathematical Monthly, 104(8), 697-704. https://doi.org/10.2307/2975231
- The del-bar-operator on algebraic curvesBruening, 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
Supervision students
David Fairbairn
3P
Yue Jiang
1CAM