9 may 2022 -- 15:00
Aula Tricerri, DIMaI, Firenze
Abstract.
The Jordan decomposition of linear operators is a powerful conjugation invariant which allows, in particular, for classification of orbits. When a group G acts on a space of tensors M we can construct a graded algebra, on which elements of both G and M act as linear operators (the adjoint action). This generalizes an idea of Vinberg, and allows us to construct adjoint operators, and hence Jordan decompositions, of tensors for many more cases than were previously thought possible. I will explain this construction and how we are using it to separate orbits that are relevant for quantum information. I will also explain how we may use this construction to study tensors relevant for computational complexity. I will start from a basic level and I will show how to implement these ideas in Macaulay2, a popular platform for computations in algebraic geometry. This is joint work in progress with Frederic Holweck