Topology and Dynamics of Higher-Order Networks - Information Theory of Network Geometry and Gauge Fields - Lecture 4

Explore the fourth lecture in the CMSP series on "Topology and dynamics of higher-order networks," focusing on the information theory of network geometry and gauge fields. 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. Examine 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. Investigate the applications of these concepts in mathematical physics and dynamical systems, and learn how topology shapes dynamics and how dynamics can learn underlying network topology. Gain insights from speaker Ginestra Bianconi of Queen Mary University of London in this comprehensive 1-hour 17-minute lecture, which is part of a broader course introducing scientists to this cutting-edge field of study.