The Casimir operator of a metric connection with skew-symmetric torsion

For any triple $(M^n, g, \nabla)$ consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator $\Omega$ acting on spinor fields. In case of a reductive space and its canonical connection our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly K\"ahler, cocalibrated $\mathrm{G}_2$-structures) admit unique connections with skew-symmetric torsion. We study the corresponding Casimir operator and compare its kernel with the space of $\nabla$-parallel spinors.Comment: Latex2e, 15 page

Spin(9)-structures and connections with totally skew-symmetric torsion

We study Spin(9)-structures on 16-dimensional Riemannian manifolds and characterize the geometric types admitting a connection with totally skew-symmetric torsion.Comment: Latex2e, 8 page

Does asymptotic simplicity allow for radiation near spatial infinity?

A representation of spatial infinity based in the properties of conformal geodesics is used to obtain asymptotic expansions of the gravitational field near the region where null infinity touches spatial infinity. These expansions show that generic time symmetric initial data with an analytic conformal metric at spatial infinity will give rise to developments with a certain type of logarithmic singularities at the points where null infinity and spatial infinity meet. These logarithmic singularities produce a non-smooth null infinity. The sources of the logarithmic singularities are traced back down to the initial data. It is shown that is the parts of the initial data responsible for the non-regular behaviour of the solutions are not present, then the initial data is static to a certain order. On the basis of these results it is conjectured that the only time symmetric data sets with developments having a smooth null infinity are those which are static in a neighbourhood of infinity. This conjecture generalises a previous conjecture regarding time symmetric, conformally flat data. The relation of these conjectures to Penrose's proposal for the description of the asymptotic gravitational field of isolated bodies is discussed.Comment: 22 pages, 4 figures. Typos and grammatical mistakes corrected. Version to appear in Comm. Math. Phy

Automorphisms of multiplicity free Hamiltonian manifolds

We compute the sheaf of automorphisms of a multiplicity free Hamiltonian manifold over its momentum polytope and show that its higher cohomology groups vanish. Together with a theorem of Losev, arXiv:math/0612561, this implies a conjecture of Delzant: a compact multiplicity free Hamiltonian manifold is uniquely determined by its momentum polytope and its principal isotropy group.Comment: v1: 42 pages; v2: 42 pages, abstract added, minor changes; v3: 43 pages, Corollary 11.4 added, minor change

A uniform refinement property for congruence lattices

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt's construction or from the approach of P. Pudlak, M. Tischendorf, and J. Tuma. In a previous paper, we constructed a distributive algebraic lattice $A$ with $\aleph\_2$ compact elements that cannot be obtained by Schmidt's construction. In this paper, we show that the same lattice $A$ cannot be obtained using the Pudlak, Tischendorf, Tuma approach. The basic idea is that every congruence lattice arising from either method satisfies the Uniform Refinement Property, which is not satisfied by our example. This yields, in turn, corresponding negative results about congruence lattices of sectionally complemented lattices and two-sided ideals of von Neumann regular rings

Tau Lepton Reconstruction and Identification at ATLAS

Tau leptons play an important role in the physics program at the LHC. They are used in searches for new phenomena like the Higgs boson or Supersymmetry and in electroweak measurements. Identifying hadronically decaying tau leptons with good performance is an essential part of these analyses. We present the current status of the tau reconstruction and identification at the LHC with the ATLAS detector. The tau identification efficiencies and their systematic uncertainties are measured using W to tau nu and Z to tau tau events, and compared with the predictions from Monte Carlo simulations.Comment: Presented at the 2011 Hadron Collider Physics symposium (HCP-2011), Paris, France, November 14-18 2011, 3 pages, 10 figure

On the AdS stability problem

We discuss the notion of stability and the choice of boundary conditions for AdS-type space-times and point out difficulties in the construction of Cauchy data which arise if reflective boundary conditions are imposed.Comment: 12 page

On the non-linearity of the subsidiary systems

In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.Comment: 7 page