Robert Ghrist (5/1/21): Laplacians and Network Sheaves
Автор: Applied Algebraic Topology Network
Загружено: 2021-05-12
Просмотров: 2557
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, we will be able to do dynamics on sheaves, which leads to decentralized methods for computing sheaf cohomology. This talk will be grounded in examples arising in applications, with a particular focus on social networks and opinion dynamics, with problems of consensus and polarization as being especially well-suited to sheaf-theoretic analysis. The talk represents joint works with Jakob Hansen and Hans Riess.
This talk was part of the workshop on "Topological Data Analysis - Theory and Applications" supported by the Tutte Institute and Western University: https://math.sci.uwo.ca/~jardine/TDA-...
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