Research

Interests: algebraic and combinatorial topology, coarse geometry, Hochschild and cyclic homology theories, homological stability and stable homology, representations of categories, K-theory, applications of these to graph theory and neuroscience.

Accepted papers and Publications:

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

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

  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. Available here.

  4. Caputi, L., Celoria, D. and Collari, C. Categorifying connected domination via graph überhomology. Journal of Pure and Applied Algebra 227(9), 2023. Available online here, or at arXiv:2201.00721 .

  5. Caputi, L. and Riihimäki, H. Hochschild homology, and a persistent approach via connectivity digraphs. Journal of Applied and Computational Topology, 2023. Available online here .

  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 Available also on ArXiv:2304.10134 .

  7. Caputi, L., Collari, C., Di Trani, S., and Smith, J. P. , On the Homotopy Type of Multipath Complexes. Mathematika, 70: e12235, 2024, https://doi.org/10.1112/mtk.12235. Available online at ArXiv:2208.04656 .

  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. Available online here .

  9. Bunke, U. and Caputi, L., Localization for coarse homology theories. Annals of K-theory, Vol. 9, 2024, No. 1, 41–88. Available here and on ArXiv:1902.04947 .

  10. Caputi, L., Celoria, D. and Collari, C. Monotone cohomologies and oriented matchings. Homology, Homotopy and Applications, Vol. 26 (2024) 2. DOI:10.4310/HHA.2024.v26.n2.a7 Available online at the arXiv:2203.03476v1 .

  11. Caputi, L., Collari, C. and Di Trani, S., Multipath cohomology of directed graphs. Accepted for publication on Algebraic & Geometric Topology. Available online at the arXiv:2108.02690 .

  12. Caputi, L., and Collari, C., On finite generation in magnitude (co)homology, and its torsion. Bulletin of the London Mathematical Society, 2024. DOI:10.1112/blms.13143 . Available also at arXiv:2302.06525 .

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. Available here. 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 .

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