Speaker:** Flavio Mercati (La Sapienza, Rome)**

Date and time: November 29, 17:00

Place: Seminario del Departamento de Física, Facultad de Ciencias

# Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions

In this new paper (**arXiv:1711.05050**), curved momentum spaces associated to the κ-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the κ-deformation with non-vanishing cosmological constant. The κ-de Sitter and κ-Anti-de Sitter curved momentum spaces are separately analysed, and they turn out to be, respectively, half of the (6+1)-dimensional de Sitter space and half of a space with SO(4,4) invariance. Such spaces are made of the momenta associated to spacetime translations and the “hyperbolic” momenta associated to boost transformations. The known κ-Poincaré curved momentum space is smoothly recovered as the vanishing cosmological constant limit from both of the constructions.

# Seminar “From Poisson geometry to non-commutative spacetime”

Speaker:** Iván Gutiérrez-Sagredo (University of Burgos)**

Date and time: October 23, 14:15

Place: Mathematics Department, FAU Erlangen-Nürnberg

# Seminar “Some new aspects about symmetries for central forces”

Speaker:** Stephen Anco (Brock University, Canada)**

Date and time: October 11, 17:30

Place: Seminario del Departamento de Física, Facultad de Ciencias

# Poisson-Hopf algebra deformations of Lie-Hamilton systems

In this paper (**arXiv:1708.08185**) Hopf algebra deformations are merged with a class of Lie systems of Hamiltonian type, the so-called Lie-Hamilton systems, to devise a novel formalism: the Poisson-Hopf algebra deformations of Lie-Hamilton systems. This approach applies to any Hopf algebra deformation of any Lie-Hamilton system. Remarkably, a Hopf algebra deformation transforms a Lie-Hamilton system, whose dynamic is governed by a finite-dimensional Lie algebra of functions, into a non-Lie-Hamilton system associated with a Poisson-Hopf algebra of functions that allows for the explicit description of its t-independent constants of the motion from deformed Casimir functions. We illustrate our approach by considering the Poisson-Hopf algebra analogue of the non-standard quantum deformation of sl(2) and its applications to deform well-known Lie-Hamilton systems describing oscillator systems, Milne-Pinney equations, and several types of Riccati equations. In particular, we obtain a new position-dependent mass oscillator system with a time-dependent frequency.

# Curved momentum spaces from quantum groups with cosmological constant

In this paper (**arXiv:1707.09600**) we bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant Λ. In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1+1) and (2+1) dimensions is explicitly constructed as a dual Poisson-Lie group manifold parametrized by Λ. Such momentum space includes both the momenta associated to spacetime translations and the `hyperbolic’ momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit Λ→0, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3+1)-dimensional ones.

# Seminar “Superintegrable Classical and Quantum Lissajous Systems on the Sphere”

Speaker:** Sengul Kuru (University of Ankara)**

Date and time: May 29, 12:30

Place: Aula 14, Facultad de Ciencias