Spanning Trees, Effective Resistances and Curvature on Graphs

Join this talk by Karel Devriendt from the Applied Algebraic Topology Network as he explores the relationship between spanning trees, effective resistances, and curvature on graphs. Discover Kirchhoff's matrix tree theorem which expresses the number of spanning trees as the maximal minor of a graph's Laplacian matrix, reflecting the fact that spanning trees form a regular matroid. Follow a short historical overview of the tree-counting problem and learn about effective resistance from electrical circuit theory. Examine the characterization of effective resistances through a specific polytope and explore recent applications to discrete notions of curvature on graphs. Additional details can be found in the referenced preprint available on arXiv.