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ABSTRACT / Higher order networks which allow to go beyond the framework of pairwise interactions are attracting increasing attention. In fact, in a large variety of complex systems including the brain, collaborations networks or face-to-face social interactions it is important to capture many-body interactions between two or more nodes. Simplicial complexes are the topological objects that can encode these high-order interactions as they are not only formed by nodes and links as networks but include also higher-order simplices such as triangles, tetrahedra and so on. In this talk I show how the network geometry and topology of simplicilal complexes determines higher-order dynamics. I will present models [1,2] of simplicial complexes and discuss their emergent topology and geometry. These models will be used to reveal the properties of higher-order topological synchronization  and diffusion dynamics. These results will allow us to unveil the surprising effect of network topology and geometry have on dynamics.
 O. T. Courtney, and G. Bianconi Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes. Physical Review E, 93, (2016) 062311
 G. Bianconi and C. Rahmede Emergent hyperbolic network geometry Scientific Reports, 7 (2017) 41974
 Millán, Ana P., Joaquín J. Torres, and Ginestra Bianconi. "Explosive higher-order Kuramoto dynamics on simplicial complexes." Physical Review Letters 124 (2020) 218301.
BIO / Ginestra Bianconi is Professor of Applied Mathematics in the School of Mathematical Sciences of Queen Mary University of London and she is Alan Turing Fellow at the Alan Turing Institute. Currently she is Chief Editor of JPhys Complexity, Editor of PloSOne, and Scientific Reports. She has been nominated Fellow of the Network Science Society in 2020. Her research activity on Statistical Mechanics and Network Science includes Network Theory and its interdisciplinary applications. She has formulated the Bianconi-Barabasi model that displays the Bose-Einstein condensation in complex networks. She has worked in network entropy and network ensembles and on dynamical processes on networks. In the last years, she has been focusing on multilayer networks, simplicial complexes, network geometry and topology, percolation and network control. She is the author of the book Multilayer Networks: Structure and Function by Oxford University Press.