Theoretical Insights into Effective Resistance in Simplicial Complexes

The effective resistance originates from electric circuit analysis and becomes an important concept in graph theory due to its connection to random walks and random spanning trees.Notions of effective resistance for simplicial complexes have been introduced in various ways in the literature, as products of matrices acting on the simplices.The relationships among these definitions are not immediately evident. In this talk, we generalize the notion of effective resistance in simplicial complexes by providing a basis-free definition, which encompasses the existing matrix representations above, and we describe its theoretical properties.

This is joint work with Inés Garcia Redondo (Imperial College), Sarah Percival (New Mexico U), Anda Skeja (Uppsala U), Bei Wang (Utah U), and Ling Zhou (Duke U).