Probing QCD at the Highest $Q^2$ Deep Inelastic Scattering
Recent results from the HERA ep collider are reviewed in these proceedings. The results are from measurements that probe QCD at high-energy scales, as defined by $Q^2$, the four-momentum-transfer squared of the collisions. These cross-section measurements provide information about the parton distribution functions (PDFs) of the proton and can be used to constrain global fits of these PDFs. Recent measurements of the strong coupling $\alpha_S$ and jet substructure from HERA at similar energy scales are also reviewed.

title: Single-top production via flavour changing neutral currents
abstract: Recent results on single-top production via flavour changing neutral currents (FCNC) are summarised. Model independent limits can be set directly for the process at both LEP and HERA and indirectly from the decays of the top quark at the TeVatron. No evidence for FCNC are observed at LEP and the TeVatron. Some events compatible with single top production are observed by the H1 collaboration at HERA, but no such events appear at ZEUS. Limits on FCNC from the different experiments are presented, with the strongest coming from the HERA and LEP experiments. 14.65.Ha Properties of Top Quarks

title: Study of taupair production at HERA
abstract: A study of events containing two tau leptons with high transverse momentum has been performed with the ZEUS detector at HERA, using a data sample corresponding to an integrated luminosity of 0.33 fb−1. The tau candidates were identified from their decays into electrons, muons or hadronic jets. The number of tau-pair candidates has been compared with the prediction from the Standard Model, where the largest contribution is expected from Bethe-Heitler processes. The total visible cross section was extracted. Standard Model expectations agree well with the measured distributions, also at high invariant mass of the tau pair.

title: Exclusive electroproduction of two pions at HERA
abstract: The exclusive electroproduction of two pions in the mass range 0.4<Mππ<2.5 GeV has been studied with the ZEUS detector at HERA using an integrated luminosity of 82 pb−1. The analysis was carried out in the kinematic range of 2<Q2<80 GeV2, 32<W<180 GeV and |t|<0.6 GeV2, where Q2 is the photon virtuality, W is the photon-proton centre-of-mass energy and t is the squared four-momentum transfer at the proton vertex. The two-pion invariant-mass distribution is interpreted in terms of the pion electromagnetic form factor, |F(Mππ)|, assuming that the studied mass range includes the contributions of the ρ, ρ′ and ρ′′ vector-meson states. The masses and widths of the resonances were obtained and the Q2 dependence of the cross-section ratios σ(ρ′→ππ)/σ(ρ) and σ(ρ′′→ππ)/σ(ρ) was extracted. The pion form factor obtained in the present analysis is compared to that obtained in e+e−→π+π−.

title: HERA signature-based searches I: events with isolated leptons and missing transverse momentum at HERA
abstract: Recent results of searches for events containing isolated leptons and missing transverse momentum at HERA are presented. Searches in this final state have yielded notable excesses over Standard Model expectations in the past. Searches for isolated leptons in channels corresponding to all three generations of leptons over the full HERA running period are now available. The combined H1+ZEUS results for searches for electrons and muons are compatible with the Standard Model.

title: Inclusive-jet photoproduction at HERA and determination of alpha(s)
abstract: Inclusive-jet cross sections have been measured in the reaction e p → e + jet + X for photon virtuality Q 2 1 GeV 2 and γp centre-of-mass energies in the region 142 W γ p 293 GeV with the ZEUS detector at HERA using an integrated luminosity of 300 pb − 1 . Jets were identified using the k T , anti- k T or SIScone jet algorithms in the laboratory frame. Single-differential cross sections are presented as functions of the jet transverse energy, E T jet , and pseudorapidity, η jet , for jets with E T jet > 17 GeV and − 1 η jet 2.5 . In addition, measurements of double-differential inclusive-jet cross sections are presented as functions of E T jet in different regions of η jet . Next-to-leading-order QCD calculations give a good description of the measurements, except for jets with low E T jet and high η jet . The influence of non-perturbative effects not related to hadronisation was studied. Measurements of the ratios of cross sections using different jet algorithms are also presented; the measured ratios are well described by calculations including up to O ( α s 2 ) terms. Values of α s ( M Z ) were extracted from the measurements and the energy-scale dependence of the coupling was determined. The value of α s ( M Z ) extracted from the measurements based on the k T jet algorithm is α s ( M Z ) = 0.1206 − 0.0022 + 0.0023 ( exp . ) − 0.0035 + 0.0042 ( th . ) ; the results from the anti- k T and SIScone algorithms are compatible with this value and have a similar precision.

title: Physics of Relativistic Perfect Fluids
abstract: A criterion is presented and discussed to detect when a divergence-free perfect fluid energy tensor in the space-time describes an evolution in local thermal equilibrium. 
This criterion is applied to the class II Szafron-Szekeres perfect fluid space-times solutions, giving a very simple characterization of those that describe such thermal evolutions. For all of them, the significant thermodynamic variables are explicitly obtained. 
Also, the specific condition is given under which the divergence-free perfect fluid energy tensors may be interpreted as an ideal gas.

title: An intrinsic characterization of spherically symmetric spacetimes
abstract: We give the necessary and sufficient (local) conditions for a metric tensor to be a nonconformally flat spherically symmetric solution. These conditions exclusively involve explicit concomitants of the Riemann tensor. As a direct application we obtain the ideal labeling of the Schwarzschild, Reissner–Nordstrom and Lemaitre–Tolman–Bondi solutions.

title: On the Weyl transverse frames in type I spacetimes
abstract: We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars Ψ2T, Ψ0T and Ψ4T associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.

title: An intrinsic characterization of 2 + 2 warped spacetimes
abstract: We give several equivalent conditions that characterize the 2 + 2 warped spacetimes: imposing the existence of a Killing–Yano tensor A subject to complementary algebraic restrictions, in terms of the projector v (or of the canonical 2-form U) associated with the 2-planes of the warped product. These planes are the principal planes of the Weyl and/or Ricci tensors and can be explicitly obtained from them. Therefore, we obtain the necessary and sufficient (local) conditions for a metric tensor to be a 2 + 2 warped product. These conditions exclusively involve explicit concomitants of the Riemann tensor. We present a similar analysis for the conformally 2 + 2 product spacetimes and give an invariant classification of them. The warped products correspond to two of these invariant classes. The more degenerate class is the set of product metrics which are also studied from an invariant point of view. The interest of these results in labeling specific solutions of the Einstein equations is outlined.

title: On the Leibniz bracket, the Schouten bracket and the Laplacian
abstract: The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them is obtained. Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie algebra structure. In particular, those algebras generated by the Leibniz bracket of the divergence and the Laplacian operators on the exterior algebra are considered, and the expression of the Laplacian for the product of two functions is generalized for arbitrary exterior forms.