Topology of random 2-dimensional cubical complexes (Erika Roldan, UNIGE)

11.05.2026 16:15 – 18:00

Abstract:
I will discuss a natural model of random 2-dimensional cubical complexes, built as subcomplexes of the n-dimensional cube by including each square face independently at random. The goal is to understand how topological features emerge as the density of square faces increases. I will describe a sharp phase transition for homology to vanish, in the same spirit as classical threshold phenomena for random graphs and as a cubical analogue of well-known results for random simplicial complexes. Along the way, I will highlight several ways in which the cubical setting behaves differently from its simplicial counterpart, and I will explain what this implies for fundamental group behavior and the relationship between homology vanishing and simple connectivity. I will also discuss, via extremal analysis, regimes in which torsion appears (and how/why this happens).

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire Math Physics

entrée libre