## Quantum Gravity

*or General Relativity meets Quantum Mechanics*

Most of our effort are currently concentrated in the investigation of different aspects of linking the theory of General Relativity with quantum field theory and quantum mechanics. A diverse set of approaches to the problem is well represented in CITR.

**Noncommutative space-times:** these are considered as one of the approaches to the description of Planck scale physics. At the Planck scale the idea of size or distance in classical terms is not valid anymore, because one has to take into account quantum uncertainty. Noncommutativity of coordinates is expected to emerge, leaving behind the classical notions of space-time. The relativistic symmetries become deformed and are described in the language of quantum groups. Anna has been developing her work on κ-Minkowski space-time and the κ-Poincaré quantum group, investigating their application in physical theories.

**Lower dimensional models**: with a specific focus on two-dimensional generalized dilaton theories, the simplified settings of these systems is a perfect laboratory to gain a better understanding of genuine quantum gravitational effects. Simone has been working with two-dimensional models of gravity and matter to tackle fundamental issues such as the cosmological constant problem and black hole (thermo)dynamics, with additional results in two-dimensional conformal field theories.

**Affine quantization**: alternative quantization schemes can provide an interesting platform for experimenting with gravity. Affine quantization naturally implements the positive definiteness of classical quantities and comes with very interesting dynamical effects. Simone has applied affine quantization to FLRW cosmology, showing that the big bang/big crunch singularity can be removed via quantum gravitational effects.

**BF Theory and Mathematical gauge theory: **Michal works on topological Field Theory, in particular BF theory in application to 4D gravity and particle physics. He investigates some extension of the Poincare groups, like Maxwell theory, AdS-Maxwell theory, Double-AdS-Maxwell theory, conformal groups and its application to gauge theory.