Inverse Problems, Algebraic Combinatorics, Networks, and Graph Theory, Summer, 2017

The Department of Mathematics at the University of Washington will be offering a summer research opportunity. The program will last for eight weeks, from June 19 until August 11 Participants will be introduced to research problems related to the problem of finding the resistors in a network from boundary measurements. Students in the program will be investigating and formulating discrete problems involving planar and non-planar networks and their relation to continuous inverse problems. Additional problems will come from the areas of algebraic combinatorics and computational number theory. Some papers that have been produced on these problems can be viewed from links on this page. Here are links to the announcement and 2017 application form

Links to relevant papers:

1. The Dirichlet to Neumann Map for a Resistor Network by E. B. Curtis and J. A. Morrow pdf
2. Finding the Conductors in Circular Networks from Boundary Measurements by E. B. Curtis, E. Mooers, and J. A. Morrow pdf
3. Circular Planar Graphs and Resistor Networks by E. B. Curtis, D. Ingerman, and J. A. Morrow pdf
4. Determining the Resistors in a Network by E. B. Curtis and J. A. Morrow pdf
5. On a Characterization of the Kernel of the Dirichlet-to-Neumann Map for a Planar Region by D. Ingerman and J. Morrow
6. Negative Conductors and Network Planarity by Konrad Schroder
7. The Dirichlet to Neumann Map for a Cubic Resistor Network by Todd Hollenbeck and J. Morrow
8. Discrete and Continuous Inverse Boundary Problems on a Disk by David Ingerman
9. Planarity of Networks with Four or Five Boundary Nodes by Amanda Mueller
10. Disjoint Boundary-Boundary Paths in Critical Circular Planar Networks by Ryan Sturgell
11. Using Network Amalgamation and Separation to Solve the Inverse Problem By Ryan Card and Brandon Muranaka
12. The Discrete Inverse Scattering Problem by Michelle Covell and Krzysztof Fidkowski
13. Discrete Inverse Problems for Schrodinger and Resistor Networks by Richard Oberlin
14. Recovering Networks with Signed Conductivities by Michael Goff
15. Applications of the star-K Tool by Tracy Lovejoy
16. Discrete Complex Analysis by Karen Perry
17. Star and K Solve the Inverse Problem by Jeff Russell
18. Global Uniqueness of a two-dimensional inverse boundary value problem by Adrian Nachman
19. Layered Networks, the Discrete Laplacian, and a Continued Fraction Identity

Website for detailed information about the Math REU at the University of Washington. This website includes an archive of papers going back to 1988.