The Topological Dirac Operator and the Dynamics of Topological Signals
Applied Algebraic Topology Network via YouTube
Overview
Syllabus
Intro
Simplicial complex data
The boundary of a boundary is null
Square d-dimensional lattice
Apollonian and pseudo-fractal hyperbolic simplicial complexes
Network Geometry with Flavor GROWTH
Hausdorff and spectral dimension
Spectral dimension of Apollonian networks and effect of randomness
Higher-order spectral dimension
Spectral dimension of the up-higher-order Laplacian
Higher-order Diffusion
Topological Dirac operator on a network
Sketch of the derivation
Topological Dirac equation on simplicial complexes
Directional Dirac operator on lattices
3-dimensional lattice
Directional Dirac operators on
Synchronization is a fundamental dynamical process
Synchronization transition
Order parameters using the n-dimensional phases
Synchronization of uncoupled topological signals • The uncoupled dynamics of nodes and links of a network
Phase diagram of topological synchronisation
Rhythmic phase
Conclusions
References and collaborators
Taught by
Applied Algebraic Topology Network