Abstract.
Quantum effects of gravity are still beyond the reach of contemporary observations. To explore these effects, we can turn to building phenomenological models which rely on modifying the known (classical) solutions to account for the potential quantum gravity effects. One of the approaches is to use Noncommutative Geometry as a possible framework, where the corrections to classical solutions appear naturally. This mathematical language relies on inherently embedded quantum structures (such as noncommuting quantum observables as in quantum mechanics) in describing general relativity (which is fundamentally geometrical, as evidenced by its description through pseudo-Riemannian geometry).
In my talk I will introduce the main ideas of noncommutative geometry as the framework of quantum space-times and their corresponding quantum relativistic symmetries (quantum groups).
(The slides will be available here)