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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., …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.

Parameterized Counting and Cayley Graph Expanders (2023)
Journal Article
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

Given a graph property \Phi , we consider the problem \# EdgeSub(\Phi ), where the input is a pair of a graph G and a positive integer k, and the task is to compute the number of k-edge subgraphs in G that satisfy \Phi . Specifically, we study the pa... Read More about Parameterized Counting and Cayley Graph Expanders.