REU 2011: Inverse Problems for Electrical Networks

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The REU Program on Inverse Problems for Electrical Networks will bring eight undergraduates to the University of Washington in each of the summers 2011-13 to work on discrete inverse problems. The inverse problem for an electrical network is the problem of finding the conductivity of resistors in an electrical network when the boundary current response to boundary voltages (response matrix) is known. Resistances may be specified by directed or undirected edge functions or vertex functions. Students will investigate the relation between the response matrix and the geometry of the network. The best way to imagine the problem is to think of a box that has leads sticking out with an electrical ciruit inside: the problem is to determine the circuit without opening the box. Students will study the relation to other discrete equations such as the Helmholtz equation and will also study permutations, graphs, and knots--problems with similar features to electrical network problems.The program will run for eight weeks. During the first week there will be lectures on foundational material, known results, and open problems. Students will then begin work on projects of their own choosing, using the available human, library, and computer resources. Students will work on their own or in teams of two. They will meet with an advisor daily for the remaining weeks. Students will present intermediate and final oral and written reports.