An overview of Strassen's spectral theory for tensors

par Fulvio Gesmundo

mardi 4 févr. 2025, 11:00 → 12:00 Europe/Paris

Salle Picard (IMT)

Motivated by the study of matrix multiplication complexity, Strassen developed a framework to systematically study asymptotic degeneration of tensors; informally, this is a measure of the hardness of multiplication maps in finite-dimensional algebras. Recently, work by Christandl-Vrana-Zuiddam, and Bürgisser-Garg-Oliveira-Walter-Wigderson related this theory to classical notions in invariant theory, and in particular the one of moment polytope, which keeps track of the representation theoretic structure of the coordinate ring of orbit-closures. I will give a friendly overview of this subject, emphasizing the connections to geometry and representation theory.