(UR) PHYSICS, MATHEMATICAL

The group is dedicated to the following research activities:

1) Construction of mathematical models based on partial and ordinary differential equations linked to the description of phenomena arising in different applied fields, in particular ecology and engineering;

2) Extension of nonlocal elasticity theories based on stress-driven spatial convolutions;

The subject of our research is the application of methods of modern functional analysis, the theory of operator algebras and linear algebra to the description of physical phenomena. In particular, we study

• the notion of quantum entanglement,
• entanglement witnesses,
• quantum correlations,
• steering inequalities.

Our goal is also to describe the structure of positive mappings on matrix algebras. In particular we are focused on the problem of NPT bound entanglement.

The research is focused on realizations of noncommutative spaces in the context of deformation theory and their applications to geometry and physics. Specifically, we investigate realizations of the kappa-deformed space, the Lorentz and Poincare algebras as well as general Lie-algebra type noncommutative spaces by formal power series in the Heisenberg-Weyl algebras and their generalizations. We also study realizations of some Lie superalgebras which arise naturally in the geometry of differential forms on noncommutative spaces.