Structure and dynamics of simplicial complexes

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Simplicial complexes are generalized network structures that are essential to investigate complex systems such as the brain, nanoscale aggregates and social systems. Simplicial complexes are not only formed by nodes and links but also by triangles, tetrahedra etc. and they allow to go beyond the paradigm of pairwise interactions. Simplicial complexes are formed by geometric building blocks and as such are key to investigate the relation between network geometry, topology and dynamics. In this project I take a comprehensive approach to study simplicial networks models using equilibrium and non-equilibrium statistical mechanics approach. Moreover I will investigate the rich phenomena that couple the structure, topology and geometry of simplicial complexes to dynamical processes such as synchronization, percolation and spin models.