This workshop is organized by Bosiljka Tadic, The Jozef Stefan Institute, Ljubljana & CSH External Faculty, and Àlvaro Corral, Centre de Recerca Matematica Barcelona & CSH External Faculty.
The emergence of new features in the evolving complex systems highly correlates with their cooperative response to the driving forces, which also leaves characteristic patterns in the time-varying data. The collective dynamics of this kind can arise from a non-trivial connections that go beyond standard pairwise interactions in the network that underlies the dynamics. This higher order architecture can be described with simplexes of different types (triangles, tetrahedrons, and others) and quantified by using advanced algebraic topology methods. For a given system, the complexes made of these geometric descriptors represent its unique functional topology. Remarkably, the underlying networks, as 1-skeleton of simplicial complexes, have hyperbolic geometry, a feature that can be linked to an improved function.
The goal of this Workshop is to discuss the simplicial complexes representation of various complex systems on the one hand, and their dynamical complexity on the other. By addressing mathematical and theoretical concepts and empirical data analysis, the discussion will aim to provide new answers to the following open problems, specifically, to
- Q1: Reveal the implications of higher-order interactions for the dynamics;
- Q2: Find the relevant information through the topological data analysis;
- Q3: Make these topological approaches to complexity more recognizable.