Topology and Dynamics of Higher-Order Networks - Lecture 3: Topological Dirac Equation and Discrete Network Geometry

Explore the third lecture in the CMSP series on "Topology and dynamics of higher-order networks," focusing on the Topological Dirac equation and Discrete Network Geometry-Metric cohomology. Delve into the emerging field of topological signals, which combines higher-order structures with discrete topology and dynamics to reveal new dynamical states and collective phenomena in complex interacting systems. Learn how topological signals, sustained on nodes, edges, triangles, and higher-order cells of networks, are treated using algebraic topology operators like the Hodge Laplacian and discrete Dirac operator. Discover the applications of these concepts in mathematical physics and dynamical systems, and gain insights into how topology shapes dynamics and how dynamics learns underlying network topology. Benefit from speaker Ginestra Bianconi's expertise as she introduces this cutting-edge field, covering recent developments and their wide-ranging applications in physics, mathematics, computer science, and neuroscience.