Bernd Sturmfels: Matrices with eigenvectors in a given subspace

Abstract

The Kalman variety of a linear subspace of a complex vector space consists of all endomorphisms that possess an eigenvector in that subspace. In this lecture we discuss the geometry and defining equations of the Kalman variety, and we explore its combinatorial degenerations. This is an ongoing project with Giorgio Ottaviani and Enrique Zuazua.