A comparative study of non-Gaussianity in ILC-7yr CMB map

A detection or non detection of primordial non--Gaussianity (NG) by using the cosmic microwave background radiation (CMB) is a possible way to break the degeneracy of early universe models. Since a single statistical estimator hardly can be sensitive to all possible forms of NG which may be present in the data, it is important to use different statistical estimators to study NG in CMB. Recently, two new large-angle NG indicators based on skewness and kurtosis of spherical caps or spherical cells of CMB sky have been proposed and used in both CMB data and simulated maps. Here, we make a comparative study of these two different procedures by examining the NG in the WMAP seven years ILC map. We show that the spherical cells procedure detects a higher level of NG than that obtained by the method with overlapping spherical caps.Comment: 8 pages, 3 figures; V2: Typos correcte

Filter-linkedness and its effect on preservation of cardinal characteristics

We introduce the property ``$F$-linked'' of subsets of posets for a given free filter $F$ on the natural numbers, and define the properties ``$\mu$-$F$-linked'' and ``$\theta$-$F$-Knaster'' for posets in a natural way. We show that $\theta$-$F$-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. Concerning iterations of such posets, we develop a general technique to construct $\theta$-$\mathrm{Fr}$-Knaster posets (where $\mathrm{Fr}$ is the Frechet ideal) via matrix iterations of ${<}\theta$-ultrafilter-linked posets (restricted to some level of the matrix). This is applied to prove consistency results about Cicho\'n's diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal invariants associated with it are pairwise different. At the end, we show that three strongly compact cardinals are enough to force that Cicho\'n's diagram can be separated into $10$ different values.Comment: 30 pages, 7 figure

On Gieseker stability for Higgs sheaves

We review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. We prove some basic properties that are similar to the classical ones for torsion-free coherent sheaves over projective algebraic manifolds. In particular, we show that Gieseker stability for torsion-free Higgs sheaves can be defined using only Higgs subsheaves with torsion-free quotients; and we show that a classical relation between Gieseker stability and Mumford-Takemoto stability extends naturally to Higgs sheaves. We also prove that a direct sum of two Higgs sheaves is Gieseker semistable if and only if the Higgs sheaves are both Gieseker semistable with equal normalized Hilbert polynomial and we prove that a classical property of morphisms between Gieseker semistable sheaves also holds in the Higgs case; as a consequence of this and the existing relation between Mumford-Takemoto stability and Gieseker stability, we obtain certain properties concerning the existence of Hermitian-Yang-Mills metrics, simplesness and extensions in the Higgs context. Finally, we make some comments about Jordan-H\"older and Harder-Narasimhan filtrations for Higgs sheaves.Comment: 16 pages, some minor corrections, last section has been shortene

Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops

We discuss the relation between correlation functions of twist-two large spin operators and expectation values of Wilson loops along light-like trajectories. After presenting some heuristic field theoretical arguments suggesting this relation, we compute the divergent part of the correlator in the limit of large 't Hooft coupling and large spins, using a semi-classical worldsheet which asymptotically looks like a GKP rotating string. We show this diverges as expected from the expectation value of a null Wilson loop, namely, as $(\ln{\mu^{-2}})^ 2$, $\mu$ being a cut-off of the theory.Comment: 16+3 pages, 3 figures. Computation in section 4.1 has been clarified. Some comments on the vertex contributions has been added in section 4.2. Some other minor corrections. Version to appear in Nucl. Phys.