Robert Ghrist - Laplacians and Network Sheaves

Explore the fascinating world of cellular sheaves and their applications in network analysis through this 48-minute lecture. Begin with a simple introduction to cellular sheaves as a generalized concept of algebraic object networks. Delve into the geometric aspects that allow for the definition of Laplacians for these sheaves. Discover how Hodge theory connects the Laplacian's geometry to the sheaf's algebraic topology. Learn about using the sheaf Laplacian as a diffusion operator for sheaf dynamics, leading to decentralized methods for computing sheaf cohomology. Gain insights into joint works with Jakob Hansen and Hans Riess, covering topics such as linear transformations, coilology, structural features, spectral chief theory, discourse sheaves, and lattices. Conclude with a Q&A session addressing the reasoning behind the term "Laplacians" in this context.

Introduction
What are sheaves
Linear transformations
Sheaves
Coilology
Applications
Structural Features
Laplacians
Hodge Laplacian
Spectral Chief Theory
Current Work
Discourse Sheaves
Lattices
Conclusion
Questions
Why call them Laplacians