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Frederick Kintanar (Mar 20 2021 at 10:53):I came across this talk: https://www.ias.edu/video/physics-functional-networks by Henrik Ronellenfitsch at the IAS WORKSHOP ON TOPOLOGY: IDENTIFYING ORDER IN COMPLEX SYSTEMS. https://www.ias.edu/event-series/workshop-topology-identifying-order-complex-systems?field_date_value=2
I wonder what would be a categorical take on his 3 or 4 examples? (mechanical meta materials, leaf venation, power grids, loop formation) I am not familiar with the literature on network theory, so pointers to good starting points in relation to these examples would be welcome.
I am also unsure of the best stream to pose questions like this, suggestions are welcome. This is related to network topology, but not necessarily to algebraic topology. But I would be interested in comment on the measures using multi-scale minimum spanning trees and dual trees to a "purely loopy network". This vaguely reminds me of persistent homology in topological data analysis, I would also be interested on a categorical perspective on how that might be relevant to these examples.
Frederick Kintanar (Mar 20 2021 at 10:58):I guess I'm interested in approaches that go beyond a single numerical metric or function, and identifies qualitative models of network invariants, perhaps graphical or algebraic or categorical structures.