Zusammenfassung für den Vortrag am 05.04.2022 (14:00 Uhr)Seminar on Nonlinear Algebra
Fulvio Gesmundo (University of Saarland)
Subrank of tensors and homomorphism duality
The subrank of a tensor is a value encoding to what extent a tensor is "stronger" than any tensor of a given rank. For this reason, tensors having large subrank play the role of universal objects for tensor rank, and find applications in numerous areas such as quantum physics and computational complexity. In this seminar, I will show that mild genericity properties on a tensor give strong lower bounds on its (asymptotic) subrank. I will emphasize connections with the notion of homomorphism duality, originated in graph theory, as well as the role of classical algebraic geometry and invariant theory. This is based on joint work with Matthias Christandl and Jeroen Zuiddam.