abstract: We reformulate dimensional regularization as a regularization of the Feynman propagator in position space. In terms of several examples we will see, how one obtains in this way a solution of the Epstein/Glaser axioms for renormalized time-ordered products. To treat subdivergences, we use an $x$-space version of Zimmermann’s forest formula. For scalar fields the method is always applicable.

abstract:I review the current status of Baryogenesis and why it cannot be quantitatively explained within the Standard Model, even though it in principle encompasses the necessary ingredients: C & CP violation, deviation from thermal equilibrium and baryon number violation. On the example of Leptogenesis, the standard techniques for predictions of the freeze-out asymmetry and their possible shortcomings are explained. The real-time description of Non-Equilibrium Field Theory can address these problems and moreover help identify new ways of creating asymmetries in the Early Universe.

abstract:Recently, a class of so-called “S-J states” has been proposed by several authors as a new class of “local vacuum states” for scalar quantum fields on curved spacetime. In joint work with C.J. Fewster, it has been shown that this class of states has a number of pathological properties which make them unsuitable as physical states for quantum fields in curved spacetime. Among these undesirable properties are failure of the Hadamard condition and inifite variances for Wick-products. It has also been shown that the Hadamard condition is necessary to render fluctuations of Wick-products finite. The main points of these results will be presented in the talk.

abstract: In four dimensions the stationary, asymptotically flat electrovac black holes are given by the family of Kerr-Newman solutions. The Kerr-Newman black holes are uniquely characterized by their global charges, the mass, the angular momentum and the electromagnetic charge(s). A spatial section of their event horizon has the topology of a two-sphere, $S^2$ , other horizon topologies are not allowed. Myers and Perry obtained the generalizations of the four-dimensional Kerr solutions. The rotating Einstein-Maxwell black holes, however, are not known in closed form in higher dimensions. In contrast, the five-dimensional Einstein-Maxwell-Chern-Simons black holes are known explicitly for a particular value of the Chern-Simons coefficient. Beyond this value, so far perturbative or numerical methods need to be used to obtain the black hole solutions. For extremal black holes the near-horizon geometry can be obtained semi-analytically. As discussed in the first part of the talk these charged black holes exhibit surprising properties, among them counter-rotation and non-uniqueness. Moreover, sequences of radially excited extremal black holes arise. Higher dimensions also allow for different horizon topologies. Black rings, black saturns and further composite black objects are known in closed form in five dimensions. In the second part of the talk the properties of black rings in six dimensions are discussed. These can be obtained perturbatively for thin black rings. For the phase diagram, however, also fat black rings are needed, that have only been obtained numerically so far. Further generalizations are briefly addressed.

abstract:Fluctuation operators are introduced in mean field theory to measure fluctuations of a mean field observable around its expectation value. In statistical mechanics they can be used to prove a quantum analog of the central limit theorem: if the particle number goes to infinity and if correlations decay exponentially fast, the fluctuations of a quantum spin system behave like a bosonic system (e.g. a harmonic oscillator) in a Gaussian state. We will use this as a starting point to discuss a number of applications of fluctuation operators, which connect different aspects of quantum mechanics, quantum statistics, functional analysis and group theory. This includes in particular the theoretical description of experiments with quantum memory by E. Polzik and others and the asymptotics (large dimensions) of irreducible representations of unitary groups.

abstract:I will survey the formalism and main results of loop quantum gravity. Then I take a closer look at the way black hole horizons are treated. A Chern-Simons theory on the horizon is coupled to the bulk degrees of freedom by a self-duality equation. I will present some recent results on a new way to solve this equation directly in the quantum theory. I show that these results can also be used to calculate the Jones polynomial and its generalizations for certain links in a novel way.

abstract: In this talk I will first provide an overview of the various kinds of instabilities that afflict higher dimensional black holes, and black rings (i.e., doughnut shaped black holes) in particular, and why the understanding of their endpoints can provide clues about fundamental questions on General Relativity, such as (strong) cosmic censorship. In the second part of my talk I will explain how one can use numerical general relativity to determine these endpoints and I will present some results on the non-linear evolution of black ring instabilities.

abstract: We construct wedge-local fields for two-dimensional QFT models which have factorizing S-matrix with poles. We do this by modifying the fields of Lechner-Schuetzenhofer in order to preserve (weak) wedge-locality. The problem of domains of these fields and spectral commutativity is discussed.

abstract: We propose a theoretical scenario for realisations of supersymmetry, in which the currently known particle spectrum is not embellished by superpartners. Technically, we establish a general `no go’ theorem, regarding the structure of certain types of degenerate supermultiplets, in a class of quadratic deformations of the conformal superalgebra. Possible origins of such non-standard supersymmetry schemes at unification scales are discussed.

abstract: Field theories with rigid conformal supersymmetry on Lorentzian manifolds can be obtained by conformally coupling a supersymmetric multiplet in flat space to a non-dynamical curved background. In this talk, we review the construction of conformal symmetry superalgebra describing the classical symmetry of such theories, as well as a classification of possible Lorentzian manifolds admitting such field theories. At the end, we briefly discuss the question of whether conformal supersymmetries are preserved at the quantum level.

abstract: The conjectured relation between higher spin theories on AdS spaces and weakly coupled conformal field theories is reviewed. I shall then explain the evidence in favour of a concrete duality of this kind, relating a specific higher spin theory on AdS3 to a family of 2d minimal model CFTs.