The Taub-NUT vacuum solution to Einstein's field equations is characterized by electric (ordinary) and magnetic mass parameters. A variety of classical fields are known to selfgravitate in such a way that spacetime shares the structure of Taub-NUT. We apply the theory of circular bundles and circular 2-bundles to such classical configurations. We find natural topological charges and unexpected flux quantizations.

We present the first evidence on the fact that topological invariants should renormalize anti-de Sitter gravity with quadratic-curvature corrections. This argument is based on the computation of energy for Einstein black holes in the theory, which appears as an alternative procedure to linearized methods (e.g., Deser-Tekin formula). (Based on arXiv:1806.11075)

All presently known matter has non-negative energy density, and the assumption of non-negative energy densities underlies some of the foundational results in general relativity -- the singularity theorems and the area theorem. Yet quantum field theory predicts the existence of negative energy densities in certain circumstances. The possibility of negative energy densities is curiously linked to several things: the finite temporal and spatial averaging needed to do measurements, the question of whether the observers measuring the densities are following trajectories generated by isometries of space- time, and the question of whether the evolution of the quantum fields is unitarily implementable. I will outline our present understanding of this material, emphasizing the conceptual issues and links with open questions.

Correlation functions constitute the building blocks of a quantum field theory, from which physical quantities like scattering amplitudes and decay rates are computable. In Quantum Chromodynamics the connection between the correlation functions of fundamental fields and physical observables is more indirect, due to the fact that quarks and gluons do not belong to the physical spectrum of asymptotic states. Nevertheless, vertices and propagators are the input ingredients for the 2-body and 3-body equations that describe the hadronic bound states. Moreover, the infrared behavior of these correlation functions is believed to play a fundamental role in understanding the mechanism of confinement and chiral symmetry breaking. The infrared region is usually considered inaccessible by the perturbative expansion, due to the growing of the running coupling constant at large distances, and non perturbative methods, like Lattice Monte Carlo simulations or functional methods like Dyson-Schwinger equations, are required in order to probe this region. Here we present a new kind of approach, started by M. Tissier and N. Wschebor, based on an extension of the usual Yang-Mills action augmented by a massive gauge term, that mimics the effect due to the presence of the Gribov horizon, that breaks the usual BRST symmetry. This framework yields to renormalization schemes where the coupling constant runs towards and infrared trivial fixed point, hence justifying the perturbative approach, whose results for the correlation functions are in good agreement with the Lattice data. We also show a derivation of the Landau-Khalatnikov-Fradkin transformations, that allow to interpolate n-point correlation functions between different values of the gauge parameter, within the class of covariant gauges, a byproduct of a recent formulation of the Gribov-Zwanziger scenario for this class of gauges and which up to now were only known in the Abelian case.

We present an operator algebraic approach to two-dimensional conformal field theory. We start with basics without assuming any knowledge on operator algebras or conformal field theory, and put emphasis on representation theoretic aspects. We touch the Jones theory of subfactors and recent advances on tensor categories, and discuss their connections to three-dimensional topology.

The Moonshine conjecture predicts mysterious relations between the Monster group and the modular elliptic functions. It has been resolved in the context of vertex operator algebras which describe chiral conformal field theory. We present this theory from a viewpoint of operator algebras. No knowledge on operator algebras, vertex operator algebras or conformal field theory is assumed.