Date: Monday, February 05, 2018
Location: 3866 East Hall (4:00 PM to 5:00 PM)
Title: Electrical networks and hyperplane arrangements
Abstract: What extra information is bestowed on a graph when we assign real values to some vertices? This is the question posed by a linear resistor network with fixed boundary voltages. We model such a network by an "affine slice" of the real graphic hyperplane arrangement. This slice inherits the combinatorics of the underlying network, which we describe in detail. We also show how the bounded chambers of the slice parameterize the harmonic functions on the network. Time permitting, we (briefly!) discuss a connection to mathematical physics. No previous knowledge of electrical networks is assumed.
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Speaker: Bob Lutz
Institution: University of Michigan
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