The overlap Dirac operator as a continued fraction

We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method and nested conjugate gradient procedures are avoided. We point out that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions.Comment: 7 pages, Talk given at the Third International Workshop on Numerical Analysis and Lattice QCD, Edinburgh, June 200

Plateau's problem for integral currents in locally non-compact metric spaces

The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective metric spaces and Hadamard spaces. We furthermore prove a weak$^*$-compactness theorem for integral currents in dual spaces of separable Banach spaces. Our theorems generalize results of Ambrosio-Kirchheim, Lang, the author, and recent results of Ambrosio-Schmidt

Filling invariants at infinity and the Euclidean rank of Hadamard spaces

In this paper we study a homological version of the higher-dimensional divergence invariants defined by Brady and Farb. We show that they are quasi-isometry invariants in the class of proper cocompact Hadamard spaces in the sense of Alexandrov and that they can moreover be used to detect the Euclidean rank of such spaces. We thereby extend results of Brady-Farb, Leuzinger, and Hindawi from the setting of symmetric spaces of non-compact type to that of singular Hadamard spaces. Finally, we exhibit the optimal power for the growth of the divergence above the rank for symmetric spaces of non-compact type and for Hadamard spaces with strictly negative upper curvature bound.Comment: In this new version we add a theorem which shows that the homological divergence functions are quasi-isometry invariants in the class of proper cocompact Hadamard spaces. This extends the corresponding theorem of Brady and Far

Compactness for manifolds and integral currents with bounded diameter and volume

By Gromov's compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance. Working in the class or oriented $k$-dimensional Riemannian manifolds (with boundary) and, more generally, integral currents in metric spaces in the sense of Ambrosio-Kirchheim and replacing the Hausdorff distance with the filling volume or flat distance, we prove an analogous compactness theorem in which we replace uniform compactness of the sequence with uniform bounds on volume and diameter.Comment: Some changes made to the introduction; some references adde

Flat convergence for integral currents in metric spaces

It is well known that in compact local Lipschitz neighborhood retracts in Euclidean space flat convergence for integer rectifiable currents amounts just to weak convergence. In the present paper we extend this result to integral currents in complete metric spaces admitting a local cone type inequality. These include in particular all Banach spaces as well as complete CAT(k)-spaces (metric spaces of curvature bounded above by k in the sense of Alexandrov). The main result can be used to prove the existence of minimal elements in a fixed Lipschitz homology class in compact metric spaces admitting local cone type inequalities or to conclude that integral currents which are weak limits of sequences of absolutely area minimizing integral currents are again absolutely area minimizing

The asymptotic rank of metric spaces

In this article we define and study a notion of asymptotic rank for metric spaces and show in our main theorem that for a large class of spaces, the asymptotic rank is characterized by the growth of the higher filling functions. For a proper, cocompact, simply-connected geodesic metric space of non-curvature in the sense of Alexandrov the asymptotic rank equals its Euclidean rank.Comment: Theorem 4.1 in Version 2 and its proof have been moved into a new paper, see reference in the new version. Some new references have been adde

Gromov hyperbolic spaces and the sharp isoperimetric constant

In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our results strengthen and generalize theorems of Gromov, Papasoglu and others.Comment: Improved exposition and structure, new introduction, which includes an outline of the proof; partially new proof, not relying on asymptotic cones anymor

Centrality Dependence of Delta-eta, Delta-phi Correlations in Heavy Ion Collisions

In these proceedings, a measurement of two-particle correlations with a high transverse momentum trigger particle (pT_trig > 2.5 GeV/c) is presented for Au+Au collisions at sqrt(s_NN) = 200 GeV over the uniquely broad longitudinal acceptance of the PHOBOS detector (-4 < Delta-eta < 2). As in p+p collisions, the near-side is characterized by a peak of correlated partners at small angle relative to the trigger. However, in central Au+Au collisions an additional correlation extended in Delta-eta and known as the 'ridge' is found to reach at least |Delta-eta| = 4. The ridge yield is largely independent of Delta-eta over the measured range, and it decreases towards more peripheral collisions. For the chosen pT_trig cut of 2.5 GeV/c, the ridge yield is consistent with zero for events with less than roughly 100 participating nucleons.Comment: 4 pages, 3 figures, proceedings for the 2009 QCD session of the Moriond conferenc

Nilpotent groups without exactly polynomial Dehn function

We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of Carnot groups. This class contains groups for which it is known that their Dehn function grows no faster than $n^2\log n$. We therefore obtain the existence of (finitely generated) nilpotent groups whose Dehn functions do not have exactly polynomial growth and we thus answer a well-known question about the possible growth rate of Dehn functions of nilpotent groups

Aperture optical antennas

This contribution reviews the studies on subwavelength aperture antennas in the optical regime, paying attention to both the fundamental investigations and the applications. Section 2 reports on the enhancement of light-matter interaction using three main types of aperture antennas: single subwavelength aperture, single aperture surrounded by shallow surface corrugations, and subwavelength aperture arrays. A large fraction of nanoaperture applications is devoted to the field of biophotonics to improve molecular sensing, which are reviewed in Section 3. Lastly, the applications towards nano-optics (sources, detectors and filters) are discussed in Section 4.Comment: Published as chapter in "Optical Antennas," editied by M. Agio qnd A. Alu, Cambridge University Press (Cambridge, 2013