The UC Berkeley Combinatorics Seminar
Mondays 2:10pm - 3:00pm
939 Evans Hall
Organizers: Florian Block, Max Glick, and Lauren Williams
Inverse problem in cylindrical electrical networks
Speaker: Pavlo Pylyavskyy
The inverse Dirichlet-to-Neumann problem in electrical networks asks one to recover the combinatorial structure of a network and its edge conductances from its response matrix. For planar networks embedded in a disk, the problem was studied and effectively solved by Curtis-Ingerman-Morrow, de Verdière-Gitler-Vertigan and Kenyon-Wilson. I will describe how the problem can be solved for a large class of networks embedded in a cylinder. Our approach uses an analog of the R-matrix for certain affine geometric crystals. It also makes use of Kenyon-Wilson\\'s groves. This is joint work with Thomas Lam.