South African - Japanese Discrete Homotopy Meeting 2025 (Cape Town, South Africa, 10-11 September 2025)

11th of September 2025  - 09.00/09.40  

Venue: MAM111 - Department of Mathematics and Applied Mathematics - University of Cape Town

Speaker:   Luigi Caputi (University of Bologna, Bologna, Italy)

Title:          Eulerian magnitude homology: diagonality, injective words, and regular path homology

Abstract:  After recalling definition and first properties of Eulerian magnitude homology, we shall focus on some algebraic and topological properties. From one side, we shall show that Eulerian magnitude homology of graphs detects the complete graph. Then, we describe the regular magnitude-path spectral sequence, that is the spectral sequence of the (filtered) injective nerve of the reachability category, and explore some applications; e.g., to regular path homology. This is joint work with Giuliamaria Menara.