Inverse spectral problem for electrical networks.

Clusters and Geometry
Event time: 
Friday, April 2, 2021 - 1:00pm
Terrence George
Speaker affiliation: 
University of Michigan
Event description: 

A biperiodic planar electrical network is a pair (G, c) where G is a graph embedded on the torus and c is a function from the edges of G to non-zero complex numbers. Associated to the discrete Laplacian on a biperiodic planar electrical network is its spectral transform: a triple (C, S, ν), where C is a curve and S is a divisor on it, which we show is a point in the Prym variety of C. We give a complete classification of networks (modulo a natural equivalence) in terms of their spectral transform.