Speaker
Ion Nechita, Laboratoire de Physique Theorique (Toulouse)
Abstract
We consider linear maps between matrix algebra having diagonal unitary symmetry. We relate the positivity property of these maps to a generalization of the notion of copositive matrices that we call pairwise copositivity. As a primary application of this framework, we define a novel family of linear maps parameterized by a graph and a real parameter. We derive exact thresholds on the parameter that determine when these maps are positive, decomposable, or completely positive, linking these properties to fundamental graph-theoretic parameters. This construction yields vast new families of positive indecomposable maps, for which we provide explicit examples derived from infinite classes of graphs, most notably rank 3 strongly regular graphs such as Paley graphs.
This is joint work with Aabhas Gulati and Sang-Jun Park https://arxiv.org/abs/2509.15201