Topology and Dynamics of Higher-Order Networks - Lecture 2: Introduction to Algebraic Topology on Networks and Simplicial Complexes

Explore the second lecture in the CMSP series on "Topology and dynamics of higher-order networks," focusing on the general introduction to algebraic topology on networks and simplicial complexes. Delve into the concepts of Hodge Laplacians and Dirac operators as presented by speaker Ginestra Bianconi from Queen Mary University of London. Gain insights into how higher-order networks capture many-body interactions in complex systems, revolutionizing our understanding of the interplay between topology and dynamics. Discover the emerging field of topological signals and its potential to transform our comprehension of structure-dynamics relationships in complex interacting systems. Learn about the application of algebraic topology operators to treat topological signals, exploring collective phenomena and new paradigms for understanding how topology shapes dynamics and vice versa. Examine the wide-ranging applications of these concepts in mathematical physics and dynamical systems, suitable for a broad audience of scientists, including physicists, mathematicians, computer scientists, and neuroscientists. This two-hour lecture serves as part of an introductory, self-contained course focusing on the mathematical physics aspects of this emerging field.