# Electrical networks and Lagrangian Grassmannians

`2023-05-17 10:30:00``2023-05-17 11:30:00``Electrical networks and Lagrangian Grassmannians``An electrical network is a graph in a disk with positive weights on edges. The set of response matrices of a (compactified) set of electrical networks admits an embedding into the totally nonnegative Grassmannian $\mathrm{Gr}_{\geq 0}(n-1,2n)$. I will talk about a new parameterization of the space of electrical networks which defines an embedding into the Grassmannian $\mathrm{Gr}(n-1,V)$, where $V$ is a certain subspace of dimension $2n-2$ and moreover an embedding into the totally nonnegative Lagrangian Grassmannian $\mathrm{LG}_{\geq 0}(n-1)\subset\mathrm{Gr}(n-1,V).$ The latter allows us to connect the combinatorics of the space of electrical networks with the representation theory of the symplectic group. The talk is based on the joint work with V. Gorbounov, A. Kazakov and D. Talalaev.``Third floor seminar room and Zoom``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`An electrical network is a graph in a disk with positive

weights on edges. The set of response matrices of a (compactified) set

of electrical networks admits an embedding into the totally

nonnegative Grassmannian $\mathrm{Gr}_{\geq 0}(n-1,2n)$. I will talk

about a new parameterization of the space of electrical networks which

defines an embedding into the Grassmannian $\mathrm{Gr}(n-1,V)$, where

$V$ is a certain subspace of dimension $2n-2$ and moreover an

embedding into the totally nonnegative Lagrangian Grassmannian

$\mathrm{LG}_{\geq 0}(n-1)\subset\mathrm{Gr}(n-1,V).$ The latter

allows us to connect the combinatorics of the space of electrical

networks with the representation theory of the symplectic group. The

talk is based on the joint work with V. Gorbounov, A. Kazakov and D.

Talalaev.

Last Updated Date : 23/04/2023