Topology shapes dynamics of higher-order networks and more
Ginestra Bianconi (QMUL - UK)
Abstract: Complex systems like the brain, climate, and next-generation artificial intelligence rely on higher-order interactions that extend beyond simple pairwise relationships. These many-body interactions are captured by higher-order networks [1].
By integrating algebraic topology with non-linear dynamics, theoretical physics and machine learning, this talk reveals the critical role of topology in shaping the dynamics of such systems [2].
The research highlights how topological signals, dynamical variables defined on nodes, edges, triangles, and other higher-order structures, drive phenomena such as topological synchronization, pattern formation, and triadic percolation. The surprising result that emerges from this research is that topological operators including the Topological Dirac operator, offer a common language for treating complexity, AI algorithms, and quantum physics.
These findings not only advance the understanding of the underlying mechanisms in neuroscience and climate science but also pave the way for transformative machine learning algorithms inspired by theoretical physics.
We conclude the seminar discussing the role of geometry in shaping dynamics. In particular we will provide an overview of the emergent field of Statistical Mechanics of Geometry, a promising new information theory framework for unifying quantum gravity captured by the Gravity from Entropy [3] approach, complex systems and the theory of computation.
[1] Bianconi, G., 2021. Higher-order networks: An introduction to Simplicial Complexes. Cambridge University Press.
[2] Millán, A.P., Sun, H., Giambagli, L., Muolo, R., Carletti, T., Torres, J.J., Radicchi, F., Kurths, J. and Bianconi, G., 2025. Topology shapes dynamics of higher-order networks. Nature Physics, pp.1-9.
[3] Bianconi, G., 2025. Gravity from entropy. Physical Review D, 111(6), p.066001.
geometric topology
Audience: researchers in the topic
Series comments: Web-seminar series on Applications of Geometry and Topology
| Organizers: | Alicia Dickenstein, José-Carlos Gómez-Larrañaga, Kathryn Hess, Neza Mramor-Kosta, Renzo Ricca*, De Witt L. Sumners |
| *contact for this listing |