Electrical networks and Lagrangian Grassmannians

Seminar
Speaker
Boris Bychkov (Haifa University)
Date
17/05/2023 - 11:30 - 10:30Add to Calendar 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 - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room and Zoom
Abstract

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.
 

תאריך עדכון אחרון : 23/04/2023