Research
Interests: algebraic and combinatorial topology, coarse geometry, Hochschild and cyclic homology theories, homological stability, representations of categories, K-theory, applications to TDA.
Accepted papers and Publications:
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Caputi, L., Cyclic homology for bornological coarse spaces. Journal of Homotopy and Related Structures (15), 2020.
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Bunke, U. and Caputi, L., Controlled objects as a symmetric monoidal functor. Higher Structures 6(1): 182-211, 2022.
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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.
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Caputi, L., Celoria, D. and Collari, C., Categorifying connected domination via graph überhomology. Journal of Pure and Applied Algebra 227(9), 2023.
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Caputi, L. and Riihimäki, H., Hochschild homology, and a persistent approach via connectivity digraphs. Journal of Applied and Computational Topology, 8, 1121–1170, 2024.
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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
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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.
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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.
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Bunke, U. and Caputi, L., Localization for coarse homology theories. Annals of K-theory, Vol. 9, 2024, No. 1, 41–88.
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Caputi, L., Celoria, D. and Collari, C., Monotone cohomologies and oriented matchings. Homology, Homotopy and Applications, Vol. 26 (2), 2024.
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Caputi, L., and Collari, C., On finite generation in magnitude (co)homology, and its torsion. Bulletin of the London Mathematical Society, 2024.
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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:
- 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:
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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 .
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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 .
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Caputi, L., Celoria, D. and Collari, C. Bridging between überhomology and double homology. Available online at the arXiv:2406.18778 .
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Caputi, L., Collari, C. and Di Trani, S., Multipath matroids, digraph colourings, and the Tutte polynomial. Available online at the arXiv:2409.14528 .
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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