**SUMMARY**:

The main scientific objectives of the project are the following:

- To study applications of Hopf algebras and quantum groups in problems of quantum simulation, and to analyse the effects of the quantum nature of reference frames concerning several problems in quantum communication.
- To introduce and solve new exact and effective Hamiltonian models for optical lattices in cavities, stressing their applications in quantum simulation and precision metrology.
- To solve different models in classical and quantum field theory that include topological defects and are amenable to be used in spintronic applications.
- To solve spectral problems of Schrödinger-Dirac type with singular potentials and boundaries that turn out to be relevant for the description of graphene layers with impurities and defects, as well as to analyze those effects in the electronic and confinement properties of two dimensional nanomaterials which are induced by their geometry and curvature.

**RESEARCH GROUP**:

The research will be realized by an **interuniversity research group UIC-011** composed by 15 senior researchers in Mathematical Physics belonging to the Universities of Burgos, Salamanca and Valladolid. Group P.I.: Angel Ballesteros.

**SUPPORTED BY**:

Junta de Castilla y León, Project BU229P18

The Project is running from 11/07/2018 until 31/10/2021