Research

Interests: algebraic and combinatorial topology, homologies of graphs, coarse geometry, Hochschild and cyclic homology theories, homological stability, representations of categories, K-theory, applications to TDA.

Accepted papers and Publications:

  1. Caputi, L., Cyclic homology for bornological coarse spaces. Journal of Homotopy and Related Structures (15), 2020.

  2. Bunke, U. and Caputi, L., Controlled objects as a symmetric monoidal functor. Higher Structures 6(1): 182-211, 2022.

  3. Caputi, L., Collari, C. and Di Trani, S., Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology. Journal of Algebraic Combinatorics 57: 617–658, 2023.

  4. Caputi, L., Celoria, D. and Collari, C., Categorifying connected domination via graph überhomology. Journal of Pure and Applied Algebra 227(9), 2023.

  5. Caputi, L. and Riihimäki, H., Hochschild homology, and a persistent approach via connectivity digraphs. Journal of Applied and Computational Topology, 8, 1121–1170, 2024.

  6. Caputi, L., Celoria, D. and Collari, C., From the Mayer-Vietoris spectral sequence to überhomology. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 1-24, 2023. doi:10.1017/prm.2023.104

  7. Caputi, L., Collari, C., Di Trani, S., and Smith, J. P., On the Homotopy Type of Multipath Complexes. Mathematika, 70 (1): e12235, 2024, https://doi.org/10.1112/mtk.12235.

  8. Caputi, L. and Riihimäki, H., On reachability categories, persistence, and commuting algebras of quivers. Theory and Applications of Categories, Vol. 41, 2024, No. 12, pp 426-448.

  9. Bunke, U. and Caputi, L., Localization for coarse homology theories. Annals of K-theory, Vol. 9, 2024, No. 1, 41–88.

  10. Caputi, L., Celoria, D. and Collari, C., Monotone cohomologies and oriented matchings. Homology, Homotopy and Applications, Vol. 26 (2), 2024.

  11. Caputi, L., and Collari, C., On finite generation in magnitude (co)homology, and its torsion. Bulletin of the London Mathematical Society, 2024.

  12. Caputi, L., Collari, C. and Di Trani, S., Multipath cohomology of directed graphs. Algebraic & Geometric Topology, 24-8 (2024), 4373–4421. DOI 10.2140/agt.2024.24.4373.

Publications in applied mathematics:

  1. Caputi, L., Pidnebesna, A. and Hlinka, J., Promises and pitfalls of Topological Data Analysis for brain connectivity analysis. Neuroimage 2021, vol. 238. Companion software available here.

Preprints:

  1. Caputi, L., Collari, C., and Ramos, E. The weak categorical quiver minor theorem and its applications: matchings, multipaths, and magnitude cohomology, 2024. Available online at the arXiv:2401.01248 .

  2. Caputi, L., Pidnebesna, A. and Hlinka, J., Integral Betti signature confirms the hyperbolic geometry of brain, climate, and financial networks. Available online at the arXiv:2406.15505 .

  3. Caputi, L., Celoria, D. and Collari, C. Bridging between überhomology and double homology. Available online at the arXiv:2406.18778 .

  4. Caputi, L., Collari, C. and Di Trani, S., Multipath matroids, digraph colourings, and the Tutte polynomial. Available online at the arXiv:2409.14528 .

  5. Caputi, L. and Menara, G., Eulerian magnitude homology: diagonality, injective words, and regular path homology. Available online at the arXiv:2503.06722 .

PhD Thesis:

Hochschild and cyclic homology for bornological coarse spaces, PhD thesis, University of Regensburg, 2019. Available here.

Recent recorded seminars:

01/11/2023, From the Mayer-Vietoris spectral sequence to überhomology available on Youtube, Cohomology in algebra, geometry, physics and statistics seminars, Institute of Mathematics of the Czech Academy of Sciences, Prague

10/04/2024, The weak categorical quiver minor theorem and its applications available here, BIMSA Topology Seminar, online