Title: The shape of physical networks

Speaker: Xiangyi Meng

Abstract:

The brain's connectome and the vascular system are examples of physical networks--tangible, web-like objects that exist in real space (not just in our papers). This physical reality means these networks combine a graph structure, describing their topological connectivity, with a physical structure, capturing the shape of all nodes and links. How do we best describe this physical structure? Naturally, we model it as a geometric object, i.e., a manifold embedded in 3D space. To do this, we turn to an unexpected mathematical tool: the framework of covariant closed string field theory, developed in the 1980s. This framework provides an exact correspondence between network-like graphs and smooth surfaces. We show that, as interpreted by this string-theoretical framework, geometric objects acquire network shapes precisely because they tend to minimize their surface areas. We developed both a Riemann surface formulation and a numerical algorithm to simulate this minimization process, finding that it predicts structural features challenging traditional explanations of network formation. Specifically, this minimization predicts the emergence of trifurcations and branching angles that, while defying conventional models such as Steiner graphs, are in excellent agreement with the local tree-like organization of physical networks across diverse domains, from human neurons to corals. We conclude by discussing potential applications of this fundamental discovery, from interpreting structural changes in neurological disorders to designing novel metamaterials.

(A popular summary of the work can be found at: Finally A Use for String Theory! https://www.youtube.com/watch?v=Hj5b0ieVWSo )

Zoom: https://northwestern.zoom.us/j/94402153768

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