Robert Ghrist (8/29/21): Laplacians and Network Sheaves

This talk will begin with a simple introduction to cellular sheaves as a generalized notion of a network of algebraic objects. With a little bit of geometry, one can often define a Laplacian for such sheaves. The resulting Hodge theory relates the geometry of the Laplacian to the algebraic topology of the sheaf. By using this sheaf Laplacian as a diffusion operator, one can do dynamics on sheaves, which leads to decentralized methods for computing sheaf cohomology. The talk represents joint works with Jakob Hansen and Hans Riess.