#### Research Fields

- Interpretational issues in the applications of noncommutative geometry to physics
- Mathematical formulations of gravitational physics
- The theory of structure formation in the Universe
- Computer algebra systems with application to general relativity

#### Field of interest

Geometry is the core of our understanding of the universe both at the large as well as the small scales. General Relativity, based on Riemannian geometry describes gravity: the motion of planets, formation of galaxies, black holes and the expansion of the universe. Gauge Theories, which are based on the geometry of fibre bundles and connections give a consistent description of fields, which are behind the fundamental interactions of elementary particles. Although this description is a great success of modern physics we are still struggling to get a good mathematically consistent description of Quantum Field Theory and the theory of quantum gravity.

The main aim of the research group is to study modern mathematical structures which aim to fill in the gap in our understanding of fundamental physics. This includes but is not restricted to, models based on noncommutative geometry, cosmological models of the universe as well as the study of relevant experimental evidence.

#### Current Research

- Dirac's operator in the formalism of noncommutative geometry
- Induced representations of groupoids
- Systems of imprimitivity and the concept of the particle
- Noncommutative closed Friedman world model
- Causal structure in noncommutative regime
- Spectral properties of algebras and methods of reconstructing space-time
- Sikorski's differetial spaces in application to the gravity theory
- Exact solutions of the perturbation equations
- Integrability of the dynamic systems of inhomogeneous cosmological models
- Lie symmetry analysis and its application to astrophysics