Speaker: A. Kazakov (HSE, YarSU, MIAN)

Date and time: 21.10.2026, 17:00 (Moscow time, GMT +03:00)

Title: Positivity in linear systems: combinatorial approach

Abstract: The main problem of electrical network theory is synthesis (finding the topology and values) of an electrical network from a given response matrix, such as a conductance or resistance matrix. However, not every matrix is realizable, which gives rise to the problem of fully characterizing the matrices that admit realization in a given class of networks. For planar resistive networks, such a characterization is given by the condition of complete circular nonnegativity of all minors of the response matrix. Remarkably, this result can be generalized to networks with controlled current sources (which are a linear approximation of networks with transistors) and Schrodinger networks. We will talk about these generalizations and how they are obtained using the general combinatorial theory of linear systems; we will also discuss the connection of these results with positive Grassmannians.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com