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Electrical networks, hyperplane arrangements and matroids

Algebra & Discrete Mathematics

Speaker: Bob Lutz, MSRI
Location: 1147 MSB
Start time: Mon, Dec 2 2019, 12:10PM

An electrical network is a graph with Dirichlet boundary conditions. In this talk, I will show how to associate a hyperplane arrangement and matroid to any electrical network. These objects allow us to view electrical networks in a new light, by generalizing the elegant ways in which graphic arrangements capture information about graphs. Time permitting, I will present results on harmonic functions with prescribed edge energies; on the relationship between supersolvable arrangements and chordal graphs; and on matroid quotients formed by geometric duals of electrical networks embedded in surfaces.