Jingyan Li , Pravin Kumar , Jie Wu

Yichen Tong

Thursday, October 15, 2026 3:00 PM - 4:00 PM

A3-4-301

Zoom 242 742 6089 (BIMSA)

Directed graphs admit a variety of homological and homotopical invariants, which capture different features of their directed structure. Understanding how these invariants are related is a natural and useful problem. In previous work, we proved a one-dimensional Hurewicz theorem connecting the r-fundamental groups of a directed graph, in the sense of Di–Ivanov–Mukoseev–Zhang, with the (1,0)-entry of Asao's magnitude–path spectral sequence. In this talk, I will explain another Hurewicz-type theorem for directed graphs. This theorem relates the higher homotopy groups introduced by Li–Wu–Yau–Zhang to the singular cubical homology groups studied by Grigor'yan–Jimenez–Muranov. The proof comes from a more general Hurewicz theorem for discrete homotopy groups of cubical sets. I will also compare our result with the Hurewicz theorem for cubical Kan complexes due to Carranza–Kapulkin–Tonks.
This is based on joint work with Daisuke Kishimoto.