Rational approximations of sectional category and Poincaré duality

Félix, Halperin, and Lemaire have shown that the rational module category Mcat and the rational Toomer invariant coincide for simply connected Poincaré duality complexes. We establish an analogue of this result for the sectional category of a fibration.

Determination of the top-quark pole mass using t(t)over-bar+1-jet events collected with the ATLAS experiment in 7 TeV pp collisions

The normalized differential cross section for top-quark pair production in association with at least one jet is studied as a function of the inverse of the invariant mass of the tt¯+1-jet system. This distribution can be used for a precise determination of the top-quark mass since gluon radiation depends on the mass of the quarks. The experimental analysis is based on proton--proton collision data collected by the ATLAS detector at the LHC with a centre-of-mass energy of 7 TeV corresponding to an integrated luminosity of 4.6 fb−1. The selected events were identified using the lepton+jets top-quark-pair decay channel, where lepton refers to either an electron or a muon. The observed distribution is compared to a theoretical prediction at next-to-leading-order accuracy in quantum chromodynamics using the pole-mass scheme. With this method, the measured value of the top-quark pole mass, mpolet, is: mpolet =173.7 ± 1.5 (stat.) ± 1.4 (syst.) +1.0−0.5 (theory) GeV. This result represents the most precise measurement of the top-quark pole mass to date.

Homogenization of scalar field cosmologies

We summarise recent results about the evolution of linear density perturbations in scalar field cosmologies with an exponential potential. We use covariant and gauge invariant perturbation variables and a dynamical systems' approach. We establish under what conditions do the perturbations decay to the future in agreement with the cosmic no-hair conjecture.

Search for high-mass diboson resonances with boson-tagged jets in proton-proton collisions at √s = 8TeV with the ATLAS detector

A search is performed for narrow resonances decaying into WW, WZ, or ZZ boson pairs using 20.3 fb−1 of proton--proton collision data at a centre-of-mass energy of s√ = 8 TeV recorded with the ATLAS detector at the Large Hadron Collider. Diboson resonances with masses in the range from 1.3 to 3.0 TeV are sought after using the invariant mass distribution of dijets where both jets are tagged as a boson jet, compatible with a highly boosted W or Z boson decaying to quarks, using jet mass and substructure properties. The largest deviation from a smoothly falling background in the observed dijet invariant mass distribution occurs around 2 TeV in the WZ channel, with a global significance of 2.5 standard deviations. Exclusion limits at the 95% confidence level are set on the production cross section times branching ratio for the WZ final state of a new heavy gauge boson, W′, and for the WW and ZZ final states of Kaluza--Klein excitations of the graviton in a bulk Randall--Sundrum model, as a function of the resonance mass. W′ bosons with couplings predicted by the extended gauge model in the mass range from 1.3 to 1.5 TeV are excluded at 95% confidence level.

A search for t(t)over-bar resonances using lepton-plus-jets events in proton-proton collisions at root s=8 TeV with the ATLAS detector

A search for new particles that decay into top quark pairs is reported. The search is performed with the ATLAS experiment at the LHC using an integrated luminosity of 20.3 fb−1 of proton-proton collision data collected at a centre-of-mass energy of s√=8 TeV. The lepton-plus-jets final state is used, where the top pair decays to W+bW−b¯¯, with one W boson decaying leptonically and the other hadronically. The invariant mass spectrum of top quark pairs is examined for local excesses or deficits that are inconsistent with the Standard Model predictions. No evidence for a top quark pair resonance is found, and 95% confidence-level limits on the production rate are determined for massive states in benchmark models. The upper limits on the cross-section times branching ratio of a narrow Z′ boson decaying to top pairs range from 4.2 pb to 0.03 pb for resonance masses from 0.4 TeV to 3.0 TeV. A narrow leptophobic topcolour Z′ boson with mass below 1.8 TeV is excluded. Upper limits are set on the cross-section times branching ratio for a broad colour-octet resonance with Γ/m = 15% decaying to tt¯. These range from 4.8 pb to 0.03 pb for masses from 0.4 TeV to 3.0 TeV. A Kaluza-Klein excitation of the gluon in a Randall-Sundrum model is excluded for masses below 2.2 TeV.

Search for a new resonance decaying to a W or Z boson and a Higgs boson in the ℓℓ/ℓν/νν+bb¯final states with the ATLAS detector

A search for a new resonance decaying to a W or Z boson and a Higgs boson in the ℓℓ/ℓν/νν+bb¯ final states is performed using 20.3 fb−1 of pp collision data recorded at s√= 8 TeV with the ATLAS detector at the Large Hadron Collider. The search is conducted by examining the WH/ZH invariant mass distribution for a localized excess. No significant deviation from the Standard Model background prediction is observed. The results are interpreted in terms of constraints on the Minimal Walking Technicolor model and on a simplified approach based on a phenomenological Lagrangian of Heavy Vector Triplets.

Reproductive ecology of the invader species gekkonid lizard Hemidactylus mabouia in an area of southeastern Brazil

Hemidactylus mabouia Moreau de Jonnés, 1818 is a "fixed" clutch size exotic species well established in Brazil. In this paper we investigate some reproductive strategies adopted to minimize the costs of invariant clutch size to this invader species living in an environment with marked climatic seasonality in Southeastern Brazil (22°56’S; 46°55’W). The study was carried out from April 2002 to March 2003. Females and males attain maturity at 47.9mm and 46.9mm SVL, respectively. Larger females tended to produce larger eggs. The reproduction occurred throughout the year, but only at the wet season the females increase the clutch frequency. There was a significant variation in mean testis volume among the months throughout the year and the largest means were recorded between August and December. Maternal investment on egg size, increase on clutch frequency and seasonal increase on testis volume can represent important reproductive strategies of this invader species living in an non-urban habitat whit climatic seasonality (dry and cold weather season).

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

RECASTING THE ELLIOTT CONJECTURE

Let A be a simple, unital, finite, and exact C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomor phism, and prove the conjecture in several cases. In these same cases - Z-stable algebras all - we prove that the Elliott conjecture in its strongest form is equivalent to a conjecture which appears much weaker. Outside the class of Z-stable C*-algebras, this weaker conjecture has no known counterexamples, and it is plausible that none exist. Thus, we reconcile the still intact principle of Elliott's classification conjecture -that K-theoretic invariants will classify separable and nuclear C*-algebras- with the recent appearance of counterexamples to its strongest concrete form.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

Lipschitz harmonic capacity and Bilipschitz images of cantor sets

For bilipschitz images of Cantor sets in Rd we estimate the Lipschitz harmonic capacity and show this capacity is invariant under bilipschitz homeomorphisms.

The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-Algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C¤-algebras. In particular, our results apply to the largest class of simple C¤-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the usual form of the Elliott conjecture is equivalent, among Z-stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C¤-algebras. We also prove in passing that the Kuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for all simple unital C¤-algebras of interest.

On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

Invariants de matrius Hadamard en MAGMA

L'objectiu d'aquest projecte ha estat generalitzar i integrar la funcionalitat de dos projectes anteriors que ampliaven el tractament que oferia el Magma respecte a les matrius de Hadamard. Hem implementat funcions genèriques que permeten construir noves matrius Hadamard de qualsevol mida per a cada rang i dimensió de nucli, i així ampliar la seva base de dades. També hem optimitzat la funció que calcula el nucli, i hem desenvolupat funcions que calculen la invariant Symmetric Hamming Distance Enumerator (SH-DE) proposada per Kai-Tai Fang i Gennian Gei que és més sensible per a la detecció de la no equivalència de les matrius Hadamard.