Research

My interests: algebraic and combinatorial topology, in coarse geometry, Hochschild and cyclic homology theories, stable homology, representations of categories, and K-theory. I am also interested in 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, 2023. Journal of Applied and Computational Topology. Available online here and at the link arXiv:2204.00462 .

  6. Caputi, L., Celoria, D. and Collari, C. From the Mayer-Vietoris spectral sequence to überhomology, 2023. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 1-24. doi:10.1017/prm.2023.104 Available also at the arXiv:2304.10134 .

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

  8. Caputi, L., Celoria, D. and Collari, C. Monotone cohomologies and oriented matchings, 2022. Accepted for publication on Homology, Homotopy and Applications. Available online at the arXiv:2203.03476v1 .

  9. 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 .

  10. Caputi, L. and Riihimäki, H. On reachability categories and commuting algebras of quivers, 2023. Accepted for publication on Theory and Applications of Categories. Available online at the arXiv:2306.15388 .

  11. Bunke, U. and Caputi, L., Localization for coarse homology theories, 2019. Accepted for publication on Annals of K-theory. Available at the arXiv:1902.04947 .

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., and Collari, C., On finite generation in magnitude (co)homology, and its torsion, 2023. Available online at the arXiv:2302.06525 .

  2. 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 .

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