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NP-completeness of the combinatorial distance matrix realisation problem (2025)
Presentation / Conference Contribution
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

The k-CombDMR problem is that of determining whether an n×n distance matrix can be realised by n vertices in some undirected graph with n+k vertices. This problem has a simple solution in the case k=0. In this paper we show that this problem is polyn... Read More about NP-completeness of the combinatorial distance matrix realisation problem.

Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: theory (2025)
Journal Article
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

In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-Émery calculus. The flow is described via a time-continuous evolution through the weighting schemes. By adapting this flow to preserv... Read More about Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: theory.

Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spaces (2025)
Journal Article
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

We show various sharp Hardy-type inequalities for the linear and quasi-linear Laplacian on non-compact harmonic manifolds with a particular focus on the case of Damek–Ricci spaces. Our methods make use of the optimality theory developed by Devyver, F... Read More about Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spaces.

Refinement of X‐ray and electron diffraction crystal structures using analytical Fourier transforms of Slater‐type atomic wavefunctions in Olex2 (2024)
Journal Article
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

An implementation of Slater‐type spherical scattering factors for X‐ray and electron diffraction for elements in the range Z = 1–103 is presented within the software Olex2. Both high‐ and low‐angle Fourier behaviour of atomic electron density and ele... Read More about Refinement of X‐ray and electron diffraction crystal structures using analytical Fourier transforms of Slater‐type atomic wavefunctions in Olex2.

Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms (2023)
Journal Article
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

In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions or for the... Read More about Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms.

Bakry–Émery Curvature Sharpness and Curvature Flow in Finite Weighted Graphs. Implementation (2023)
Journal Article
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

In this paper, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry–Émery calculus. This flow can be adapted to preserve the Markovian property and its limits as time goes to infinity turn out to be curvature sharp... Read More about Bakry–Émery Curvature Sharpness and Curvature Flow in Finite Weighted Graphs. Implementation.

Going round in circles: Geometry in the early years (2023)
Journal Article
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

The research described here came from a collaboration between university-based mathematicians and early years (EY) educators. The project emerged naturally, driven by the felt need of the EY educators to develop a broader understanding and appreciati... Read More about Going round in circles: Geometry in the early years.