Title: Quantum space-times, quantum symmetries and modified Heisenberg uncertainty principles
Abstract: Quantum effects of gravity are still beyond the reach of contemporary observations. To explore these effects, we can turn into 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 (NCG) 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 framework and the motivation for quantum space-times within NCG and their corresponding quantum relativistic symmetries (as deformations of Hopf algebras). The noncommutative nature of space-time leads to the modifications in quantum mechanical phase space and consequently to the changes in the Heisenberg uncertainty principle. Such modifications (generalizations of) the uncertainty principle and their possible physical (thermodynamical) effects will be also discussed, if time permits.