Tensor, entanglement and dual varieties in Fermionic Fock spaces

par Frédéric Holweck (Université de Technologie de Belfort-Montbéliard)

mercredi 8 mars 2023, 14:00 → 15:00 Europe/Paris

https://greenlight.virtualdata.cloud.math.cnrs.fr/b/fab-49u-gkt

In the past 20 years classical concepts of algebraic geometry such as the notion of dual varieties have been introduced in the quantum information literature to distinguish different classes of entanglement, a quantum property recognized as a resource in quantum information processing. In this talk, after introducing the connection between the basics of quantum information and the geometry of tensors, I will explain how new equations of the duals of homogeneous varieties can be obtained from graded simple Lie algebras. I will in particular focus on the dual of the spinor varieties S_{16}, the projectivization of the highest weight orbit of the 128 dimensional spin module and its connection with what is known in physics as Fermionic Fock spaces. This is joint work with Luke Oeding.