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.
Ginestra Bianconi is Professor of Applied Mathematics in the School of Mathematical Sciences of Queen Mary University of London. She is member or the European Academy of Sciences. Currently she is Chief Editor of JPhys Complexity, Editor of PloSOne, and Scientific Reports. Awards: Euler Prize, APS Fellow, Network Science Fellow and chair Franqui 2023.
Her research activity focus on Statistical Mechanics, Network Theory and more recently Gravity. She has formulated the Bianconi-Barabasi model that displays the Bose-Einstein condensation in complex networks. She has formulated the statistical mechanics of network ensembles and she has proven their non-equivalence. She has made important contributions on the study of critical phenomena on networks. In 2025 she has proposed a statistical mechanics action for gravity given by the quantum relative entropy between the true metric of spacetime and the metric induced by the matter fields and the curvature (G. Bianconi, Gravity from entropy. Physical Review D. 2025 Mar 15;111(6):066001).
Her recent work focuses on revealing the interplay between geometry, topology and dynamics on complex networks and on generalized network structures such as multilayer networks and simplicial complexes. She is author of two books 'Multilayer networks: structure and function' (Oxford University Press,2018) 'Higher-order networks-An introduction to simplicial complexes' (Cambridge University Press, 2021).
