Malte Schulz (Marburg, Germany)
Día y hora: Jueves 5 de febrero - 14:30 hs.
Modalidad: Presencial (Aula 32 FAMAF).
Título: Representation Theory of Curvature Tensors and Applications to General Relativity
Resumen: The algebraic classification of the Weyl tensor via Petrov types is a cornerstone of four-dimensional General Relativity, yet it loses its efficacy in higher dimensions due to the irreducibility of the Weyl representation. To bridge this gap, we develop a dimension-independent classification framework based on the representation theory of the complex orthogonal group $\mathrm{SO}(n, \mathbb{C})$. By identifying the space of Weyl tensors with the highest weight module $[2,2,0,\dots]$, we derive rigorous branching rules for the restriction $\mathrm{SO}(n) \to \mathrm{SO}(n-(k+1))$, physically corresponding to spacetimes with $k$ commuting Killing vector fields. We prove that symmetries impose strict selection rules: for static and stationary-axisymmetric spacetimes, entire representation submodules, identified as magnetic or electric curvature components, must vanish. This framework not only reproduces the 4D Petrov classification but also provides a novel algebraic fingerprint that distinguishes topologically distinct solutions, such as the Myers-Perry black hole and the Black Ring, solely through their curvature spectrum. Finally, we demonstrate that the decoupling of gravitational degrees of freedom in the Large-$D$ limit can be derived purely from these algebraic weight properties.Dra. Ilka Agricola (Marburg, Germany)
Día y hora: Jueves 26 de febrero - 14:30 hs.
Modalidad: Presencial (Aula 32 FAMAF).
Título: On the Classification of Almost Contact Metric Manifolds
Resumen: In 1990, D. Chinea and C. Gonzalez gave a classification of almost contact metric manifolds into 2^{12} classes, based on the behaviour of the covariant derivative of the fundamental 2-form. This large number makes it difficult to deal with this class of manifolds. We propose a new approach to almost contact metric manifolds by introducing two intrinsic endomorphisms S and h, which bear their name from the fact that they are, basically, the entities appearing in the intrinsic torsion. We present a new classification scheme for them by providing a simple flowchart based on algebraic conditions involving S and h, which then naturally leads to a regrouping of the Chinea-Gonzalez classes, and, in each step, to a further refinement, eventually ending in the single classes. This method allows a more natural exposition and derivation of both known and new results, like a new characterization of almost contact metric manifolds admitting a characteristic connection in terms of intrinsic endomorphisms. We also describe in detail the remarkable (and still very large) subclass of H-parallel almost contact manifolds. This is joint work with Dario Di Pinto, Giulia Dileo, and Marius Kuhrt.