Results for "Fabian Böttcher"

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Transient supersolid properties in an array of dipolar quantum dropletsJan 23 2019Mar 08 2019We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent ... More
The low-energy Goldstone mode in a trapped dipolar supersolidJun 11 2019A supersolid is a counter-intuitive state of matter that combines the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid. Since the first prediction in the 1950s, experimental efforts to realize this state have ... More
Embedded Markov chain approximations in Skorokhod topologiesSep 16 2014Jan 30 2018In order to approximate a continuous time stochastic process by discrete time Markov chains one has several options to embed the Markov chains into continuous time processes. On the one hand there is the Markov embedding, which uses exponential waiting ... More
Quantum correlations in dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equationApr 23 2019Dipolar quantum droplets are exotic quantum objects that are self-bound due to the subtle balance of attraction, repulsion and quantum correlations. Here we present a systematic study of the critical atom number of these self-bound droplets, comparing ... More
Polarized Parton DensitiesDec 31 2002In this talk we summarize main results of a recent determination of the polarized deeply inelastic parton distributions to NLO from the world data. In the analysis the LO and NLO parton densities and their $1\sigma$ statistical errors were derived and ... More
The Euler scheme for Feller processesNov 27 2009Jun 30 2010We consider the Euler scheme for stochastic differential equations with jumps, whose intensity might be infinite and the jump structure may depend on the position. This general type of SDE is explicitly given for Feller processes and a general convergence ... More
QCD Analysis of Polarized Deep Inelastic Scattering DataMay 18 2010Aug 09 2010A QCD analysis of the world data on polarized deep inelastic scattering is presented in next--to--leading order, including the heavy flavor Wilson coefficient in leading order in the fixed flavor number scheme. New parameterizations are derived for the ... More
Energy stable discretization of Allen-Cahn type problems modeling the motion of phase boundariesMar 08 2017We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an associated energy ... More
Parity anomaly driven topological transitions in magnetic fieldJul 26 2016Jan 20 2019Recent developments in solid state physics give a prospect to observe the parity anomaly in (2+1)D massive Dirac systems. Here we show, that the quantum anomalous Hall (QAH) state in orbital magnetic fields originates from the Dirac mass term and induces ... More
Reverberation mapping of the central regions of active galactic nuclei using high-energy gamma-ray observationsApr 20 1995We calculate the time- and energy-dependent opacity of high-energy gamma-rays attenuated by pair production interaction with accretion-flare photons that are scattered by gas and dust surrounding thenuclei of active galaxies. We show that the temporal ... More
Self-bound droplets of a dilute magnetic quantum liquidJul 25 2016Self-bound many-body systems occur in different scenarios all across the fields of physics. For example in the astrophysical context the stellar classification is based on a detailed balance of attractive self-gravitating forces and repulsive terms e.g. ... More
Anisotropic Superfluid Behavior of a Dipolar Bose-Einstein CondensateApr 12 2018Jul 18 2018We present transport measurements on a dipolar superfluid using a Bose-Einstein condensate of Dy-162 with strong magnetic dipole-dipole interactions. By moving an attractive laser beam through the condensate we observe an anisotropy in superfluid flow. ... More
Striped states in a many-body system of tilted dipolesJun 28 2017Nov 28 2017We study theoretically and experimentally the behaviour of a strongly confined dipolar Bose-Einstein condensate, in the regime of quantum-mechanical stabilization by beyond-mean-field effects. Theoretically, we demonstrate that self-organized striped ... More
Onset of a modulational instability in trapped dipolar Bose-Einstein condensatesNov 20 2017Jan 23 2018We explore the phase diagram of a finite-sized dysprosium dipolar Bose-Einstein condensate in a cylindrical harmonic trap. We monitor the final state after the scattering length is lowered from the repulsive BEC regime to the quantum droplet regime. Either ... More
Transient supersolid properties in an array of dipolar quantum dropletsJan 23 2019We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent ... More
Scissors mode of dipolar quantum droplets of dysprosium atomsDec 19 2017Mar 25 2018We report on the observation of the scissors mode of a single dipolar quantum droplet. The existence of this mode is due to the breaking of the rotational symmetry by the dipole-dipole interaction, which is fixed along an external homogeneous magnetic ... More
The Fate of the Higgs Mode in a Trapped Dipolar SupersolidJul 22 2019We theoretically investigate the spectrum of elementary excitations of a trapped dipolar quantum gas across the BEC-supersolid phase transition. Our calculations reveal the existence of distinct Higgs and Nambu-Goldstone modes that emerge from the softening ... More
Self-bound droplets of a dilute magnetic quantum liquidJul 25 2016Nov 10 2016Self-bound many-body systems are formed through a balance of attractive and repulsive forces and occur in many physical scenarios. Liquid droplets are an example of a self-bound system, formed by a balance of the mutual attractive and repulsive forces ... More
Non-Singlet QCD Analysis of the Structure Function F_2 in 3-LoopsJul 07 2004Jul 09 2004First results of a non--singlet QCD analysis of the structure function $F_2(x,Q^2)$ in 3--loop order based on the non--singlet world data are presented. Correlated errors are determined and their propagation through the evolution equations is performed ... More
Embedding into bipartite graphsJul 23 2009The conjecture of Bollob\'as and Koml\'os, recently proved by B\"ottcher, Schacht, and Taraz [Math. Ann. 343(1), 175--205, 2009], implies that for any $\gamma>0$, every balanced bipartite graph on $2n$ vertices with bounded degree and sublinear bandwidth ... More
Temporal dynamics of online petitionsMay 11 2017Online petitions are an important avenue for direct political action, yet the dynamics that determine when a petition will be successful are not well understood. Here we analyze the temporal characteristics of online-petition signing behavior in order ... More
On the convergence rate of the three operator splitting schemeOct 25 2016The three operator splitting scheme was recently proposed by [Davis and Yin, 2015] as a method to optimize composite objective functions with one convex smooth term and two convex (possibly non-smooth) terms for which we have access to their proximity ... More
On the convergence rate of the three operator splitting schemeOct 25 2016Oct 29 2016The three operator splitting scheme was recently proposed by [Davis and Yin, 2015] as a method to optimize composite objective functions with one convex smooth term and two convex (possibly non-smooth) terms for which we have access to their proximity ... More
Topological order of mixed states in quantum many-body systemsSep 08 2016Jan 16 2017Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical ensembles. ... More
Moments of Spinor L-Functions and symplectic Kloosterman sumsMay 29 2018We compute the second moment of spinor $L$-functions at central points of Siegel modular forms on congruence subgroups of large prime level $N$ and give applications to non-vanishing.
Theoretical Investigation of C_60 IR SpectrumFeb 16 1996Feb 19 1996A semi-empirical model of the infrared (IR) spectrum of the C$_{60}$ molecule is proposed. The weak IR-active modes seen experimentally in a C$_{60}$ crystalline sample are argued to be combination modes caused by anharmonicity. The origin of these 2-mode ... More
Cosmological Simulations of Normal-Branch Braneworld GravityOct 01 2009Aug 01 2018We introduce a cosmological model based on the normal branch of DGP braneworld gravity with a smooth dark energy component on the brane. The expansion history in this model is identical to LambdaCDM, thus evading all geometric constraints on the DGP cross-over ... More
A Quantum Kirwan Map, II: BubblingJun 09 2011Sep 27 2012Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,\omega)$. Under suitable assumptions, counting gauge equivalence classes of (symplectic) vortices on the plane $R^2$ conjecturally gives rise to ... More
A Quantum Kirwan Map, I: Fredholm TheoryMay 25 2009Sep 27 2012Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,\omega)$. Under some assumptions on $(M,\omega)$ and the action, D. A. Salamon conjectured that counting gauge equivalence classes of symplectic ... More
The Invariant Symplectic Action and Decay for VorticesNov 24 2006Sep 08 2008The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It is defined ... More
Remarks on a quasi-linear model of the Navier-Stokes EquationsSep 19 2004Dinaburg and Sinai recently proposed a quasi-linear model of the Navier-Stokes equations. Their model assumes that nonlocal interactions in Fourier space are dominant, contrary to the Kolmogorov turbulence phenomenology where local interactions prevail. ... More
Algebraic Characters of Harish-Chandra Modules and ArithmeticityOct 25 2013These are expanded notes from lectures at the Workshop "Representation Theory and Applications" held at Yeditepe University, Istanbul, in honor of Roger E. Howe. They are supplemented by the application of algebraic character theory to the construction ... More
Almost every vector valued modular form is an oldformJan 23 2014Jan 27 2014In this article we show that 'most' of the vector valued modular forms w.r.t. the Weil representation on the groups rings $\mathbb{C}[D]$ of discriminant forms D are oldforms. The precise meaning of oldform is that the form can be represented as a sum ... More
Searches for Lorentz-Violating Signals with Astrophysical Polarization MeasurementsJul 15 2019Astrophysical observations are a powerful tool to constrain effects of Lorentz-invariance violation in the photon sector. Objects at high redshifts provide the longest possible baselines, and gamma-ray telescopes allow us to observe some of the highest ... More
The cubo-cubic transformation and K3 surfacesAug 15 2019In this note we observe that the Cremona transformation in Oguiso's example of Cremona isomorphic but not projectively equivalent quartic K3 surfaces in three-dimensional projective space is the classical cubo-cubic transformation.
Rate-optimal estimation of the Blumenthal-Getoor index of a Lévy processJun 19 2019The Blumenthal-Getoor (BG) index characterizes the jump measure of an infinitely active L\'evy process. It determines sample path properties and affects the behavior of various econometric procedures. If the process contains a diffusion term, existing ... More
Topological order of mixed states in quantum many-body systemsSep 08 2016Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical ensembles. ... More
Modulus of continuity of averages of SRB measures for a transversal family of piecewise expanding unimodal mapsApr 12 2016Let $f_t:[0,1] \to [0,1]$ be a family of piecewise expanding unimodal maps with a common critical point that is dense for almost all $t \in [a,b]$. If $\mu_t$ is the corresponding SRB measure for $f_t$, we study the regularity of $\Gamma(t)=\int \phi ... More
Polynomial Separating Algebras and Reflection GroupsJul 29 2013This note considers a finite algebraic group $G$ acting on an affine variety $X$ by automorphisms. Results of Dufresne on polynomial separating algebras for linear representations of $G$ are extended to this situation. For that purpose, we show that the ... More
Leafwise fixed points for $C^0$-small Hamiltonian flows and local coisotropic Floer homologyAug 20 2014Sep 10 2015Consider a closed coisotropic submanifold $N$ of a symplectic manifold $(M,\omega)$ and a Hamiltonian diffeomorphism $\phi$ on $M$. The main result of this article is that $\phi$ has a leafwise fixed point with respect to $N$, provided that it is the ... More
Hilbert-Samuel multiplicities of certain deformation ringsDec 20 2012Mar 31 2014We compute presentations of crystalline framed deformation rings of a two dimensional representation $\bar{\rho}$ of the absolute Galois group of $\mathbb{Q}_p$, when $\bar{\rho}$ has scalar semi-simplification, the Hodge-Tate weights are small and $p>2$. ... More
Distributed Graph AutomataApr 25 2014Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the regular languages ... More
Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetryOct 21 2008In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation the universal ... More
The final log canonical model of $\bar{M}_6$Mar 27 2013We describe the birational model of $\bar{M}_6$ given by quadric hyperplane sections of the degree 5 del Pezzo surface. In the spirit of the genus 4 case treated by Fedorchuk, we show that it is the last non-trivial space in the log minimal model program ... More
Hadron Physics at the COMPASS ExperimentDec 08 2014Quantum Chromodynamics (QCD), the theory of strong interactions, in principle describes the interaction of quark and gluon fields. However, due to the self-coupling of the gluons, quarks and gluons are confined into hadrons and cannot exist as free particles. ... More
The effect of relative velocity and density perturbations between baryons and dark matter on the clustering of galaxiesFeb 29 2016Aug 24 2016Pre-recombination acoustic oscillations induce non-adiabatic perturbations between baryons and dark matter, corresponding to a constant relative-density $\delta_{bc}$ and decaying relative-velocity perturbation $\vec{v}_{bc}$. Due to their significant ... More
Towards a self-consistent halo model for the nonlinear large-scale structureNov 06 2015Feb 17 2016The halo model is a theoretically and empirically well-motivated framework for predicting the statistics of the nonlinear matter distribution in the Universe. However, current incarnations of the halo model suffer from two major deficiencies: $(i)$ they ... More
A remark on a relation between foliations and number theoryMay 07 2006We interpret a formula for meromorphic functions on foliations by Riemann surfaces as an analogue to the product formula of valuations in algebraic number theory.
Estimation of state-dependent jump activity and drift for Markovian semimartingalesNov 15 2018Jun 26 2019The jump behavior of an infinitely active It\^o semimartingale can be conveniently characterized by a jump activity index of Blumenthal-Getoor type, typically assumed to be constant in time. We study Markovian semimartingales with a non-constant, state-dependent ... More
Recent progress in the partial-wave analysis of the diffractively produced $π^-π^+π^-$ final state at COMPASSAug 28 2018The COMPASS spectrometer at CERN has collected a large data set for diffractive three-pion production of $46\times10^6$ exclusive events. Based on previous conventional Partial-Wave Analyses (PWA), we performed a `freed-isobar PWA' on the same data, removing ... More
Improved tuning methods for Monte Carlo generatorsJan 22 2018The Monte Carlo event generators (MC) are used for the simulation of different processes in high energy physics. To achieve the best description of the data, the parameters of simulations are adjusted (tuned) with different methods. In this thesis extensions ... More
Note on local coisotropic Floer homology and leafwise fixed pointsJul 14 2017I outline a construction of a local Floer homology for a coisotropic submanifold of a symplectic manifold and explain how it can be used to show that leafwise fixed points of Hamiltonian diffeomorphisms exist.
Separating Invariants of Finite GroupsApr 13 2017This paper studies separating invariants of finite groups acting on affine varieties through automorphisms. Several results, proved by Serre, Dufresne, Kac-Watanabe and Gordeev, and Jeffries and Dufresne exist that relate properties of the invariant ring ... More
Monodromic Dark EnergySep 05 2017Oct 06 2017Since the discovery of the accelerated expansion of the Universe, the constraints on the equation of state $w_\text{DE}$ of dark energy, the stress-energy component responsible for the acceleration, have tightened significantly. These constraints generally ... More
Evolving neural networks with genetic algorithms to study the String LandscapeJun 21 2017Aug 10 2017We study possible applications of artificial neural networks to examine the string landscape. Since the field of application is rather versatile, we propose to dynamically evolve these networks via genetic algorithms. This means that we start from basic ... More
The stochastic nonlinear Schrödinger equation in unbounded domains and manifoldsJun 20 2019In this article, we construct a global martingale solution to a general nonlinear Schr\"{o}dinger equation with linear multiplicative noise in the Stratonovich form. Our framework includes many examples of spatial domains like $\mathbb{R}^d$, non-compact ... More
Stable Frames in Model CategoriesFeb 15 2010We develop a stable analogue to the theory of cosimplicial frames in model cagegories; this is used to enrich all homotopy categories of stable model categories over the usual stable homotopy category and to give a different description of the smash product ... More
Fourier coefficients of half-integral weight cusp forms and Waring's problemJun 28 2017Extending the approach of Iwaniec and Duke, we present strong uniform bounds for Fourier coefficients of half-integral weight cusp forms of level $N$. As an application, we consider a Waring-type problem with sums of mixed powers.
Valuations on Log-Concave FunctionsJul 20 2017A classification of $\operatorname{SL}(n)$ and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs ... More
Gravitational Infall onto Molecular FilamentsApr 16 2013Two aspects of filamentary molecular cloud evolution are addressed: (1) Exploring analytically the role of the environment for the evolution of filaments demonstrates that considering them in isolation (i.e. just addressing the fragmentation stability) ... More
The Maxflow problem and a generalization to simplicial complexesDec 05 2012The problem of Maxflow is a widely developed subject in modern mathematics. Efficient algorithms exist to solve this problem, that is why a good generalization may permit these algorithms to be understood as a particular instance of solutions in a wider ... More
A Deligne pairing for Hermitian Azumaya modulesJan 21 2015In this short note we want to give a definition of a generalized Deligne pairing for modules over an Azumaya algebra on an arithmetic surface $X$. We do this by defining Hermitian metrics on the Azumaya algebra and on the modules in question. Then we ... More
Highlights from COMPASS in hadron spectroscopyDec 31 2014Since Quantum Choromdynamics allows for gluon self-coupling, quarks and gluons cannot be observed as free particles, but only their bound states, the hadrons. This so-called confinement phenomenon is responsible for $98\%$ of the mass in the visible universe. ... More
An all-coupling theory for the Fröhlich polaronSep 29 2015The Fr\"ohlich model describes the interaction of a mobile impurity with a surrounding bath of phonons which leads to the formation of a quasiparticle, the polaron. In this article an efficient renormalization group approach is presented which provides ... More
The Vacuum Structure of Vector Mesons in QCDApr 14 2015We study the chiral dynamics of vector mesons in two-flavor QCD in vacuum by utilizing a functional renormalization group approach. This allows us to capture the dynamical transition from the quark-gluon phase at high energies to the hadronic phase at ... More
Asynchronous Distributed Automata: A Characterization of the Modal Mu-FragmentNov 25 2016We establish the equivalence on finite directed graphs between a class of asynchronous distributed automata and a small fragment of least fixpoint logic. More specifically, the logic we consider is (a variant of) the fragment of modal $\mu$-calculus that ... More
Majorana QubitsApr 03 2014Contribution to the 44th IFF Spring School held at the Forschungszentrum J\"ulich in 2013 on "Quantum Information Processing". The notes include a pedagogic (but incomplete) introduction to Majorana fermions; especially paying attention to the usefulness ... More
The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimatesNov 22 2016We consider the stochastic NLS with linear multiplicative noise in $L^2(\mathbb{R}^d)$ and prove the existence and uniqueness of a global solution in the subcritical and a local solution in the critical case, respectively. In particular, we relax the ... More
Towards the Integration of an Intuitionistic First-Order Prover into CoqJun 20 2016An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix characterization ... More
Light-Meson Spectroscopy at COMPASSNov 04 2016The goal of the COMPASS experiment at CERN is to study the structure and spectroscopy of hadrons. The two-stage spectrometer has large acceptance and covers a wide kinematic range for charged as well as neutral particles allowing to access a wide range ... More
Integral Brauer-Manin obstructions for sums of two squares and a powerApr 03 2013We use Brauer-Manin obstructions to explain failures of the integral Hasse principle and strong approximation away from infinity for the equation x^2+y^2+z^k=m with fixed integers k>=3 and m. Under Schinzel's hypothesis (H), we prove that Brauer-Manin ... More
Non-Gaussian Halo Bias Beyond the Squeezed LimitApr 05 2013Jun 13 2013Primordial non-Gaussianity, in particular the coupling of modes with widely different wavelengths, can have a strong impact on the large-scale clustering of tracers through a scale-dependent bias with respect to matter. We demonstrate that the standard ... More
Measurements of the Muon Content of UHECR Air Showers with the Pierre Auger ObservatoryFeb 26 2009The Pierre Auger Observatory, recently completed, has been operational since 2004. As a hybrid experiment, it allows for a wide range of measurements of UHECR-induced extensive air showers (EAS), including measurements of the EAS particle content on ground ... More
Algebraic Characters for Harish-Chandra modulesJan 12 2012Oct 25 2013We give a cohomological treatment of a character theory for (g,K)-modules. This leads to a nice formalism extending to large categories of not necessarily admissible (g,K)-modules. Due to results of Hecht, Schmid and Vogan the classical results of Harish-Chandra's ... More
Rank one sheaves over quaternion algebras on Enriques surfacesSep 09 2019Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra A on X. Then we study the moduli scheme of torsion free A-modules of rank one. Finally we prove that this moduli scheme is an \'{e}tale ... More
Cosmological Simulations of Normal-Branch Braneworld GravityOct 01 2009Nov 30 2009We introduce a cosmological model based on the normal branch of DGP braneworld gravity with a smooth dark energy component on the brane. The expansion history in this model is identical to LambdaCDM, thus evading all geometric constraints on the DGP cross-over ... More
spikeSlabGAM: Bayesian Variable Selection, Model Choice and Regularization for Generalized Additive Mixed Models in RMay 26 2011The R package spikeSlabGAM implements Bayesian variable selection, model choice, and regularized estimation in (geo-)additive mixed models for Gaussian, binomial, and Poisson responses. Its purpose is to (1) choose an appropriate subset of potential covariates ... More
On Period Relations for Automorphic L-functions IIApr 14 2016We study Hecke algebras for pairs (g,K) over arbitrary fields E of characteristic 0, define the Bernstein functor and give another definition of the Zuckerman functor over E. Building on this we show that hard duality remains valid over E and apply this ... More
A local proof of the Breuil-Mézard conjecture in the scalar semi-simplification caseJun 03 2015We give a new local proof of the Breuil-M\'ezard conjecture in the case of a reducible representation of the absolute Galois group of $\mathbb{Q}_p$, $p>2$, that has scalar semi-simplification, via a formalism of Pa\v{s}k\=unas.
Reverse Reconciliation Continuous Variable Quantum Key Distribution Based on the Uncertainty PrincipleMay 23 2014Nov 18 2014A big challenge in continuous variable quantum key distribution is to prove security against arbitrary coherent attacks including realistic assumptions such as finite-size effects. Recently, such a proof has been presented in [Phys. Rev. Lett. 109, 100502 ... More
Dust in the Early (z>1) UniverseApr 01 2009Although dust emission at cosmological distances has only been detected a little more than a decade ago, remarkable progress has been achieved since then in characterizing the far-infrared emission of high-redshift systems. The mere fact that dust can ... More
Leafwise fixed points for $C^0$-small Hamiltonian flowsAug 20 2014Jul 14 2017Consider a closed coisotropic submanifold $N$ of a symplectic manifold $(M,\omega)$ and a Hamiltonian diffeomorphism $\phi$ on $M$. The main result of this article states that $\phi$ has at least the cup-length of $N$ many leafwise fixed points w.r.t. ... More
Relative Hofer Geometry and the Asymptotic Hofer-Lipschitz ConstantFeb 24 2011Mar 25 2011Let $(M,\omega)$ be a symplectic manifold and $U\subseteq M$ an open subset. I study the natural inclusion of the group of Hamiltonian diffeomorphisms of $U$ into the group of Hamiltonian diffeomorphisms of $M$. The main result is an upper bound for this ... More
Large-scale Velocities and Primordial Non-GaussianityMay 21 2010Jun 01 2010We study the peculiar velocities of density peaks in the presence of primordial non-Gaussianity. Rare, high density peaks in the initial density field can be identified with tracers such as galaxies and clusters in the evolved matter distribution. The ... More
Self-Consistent Cosmological Simulations of DGP Braneworld GravityMay 06 2009Sep 16 2009We perform cosmological N-body simulations of the Dvali-Gabadadze-Porrati braneworld model, by solving the full non-linear equations of motion for the scalar degree of freedom in this model, the brane bending mode. While coupling universally to matter, ... More
Weak Lensing Probes of Modified GravityMay 30 2008Jul 14 2008We study the effect of modifications to General Relativity on large scale weak lensing observables. In particular, we consider three modified gravity scenarios: f(R) gravity, the DGP model, and TeVeS theory. Weak lensing is sensitive to the growth of ... More
Dynamical Masses in Modified GravityMar 01 2010Mar 11 2010Differences in masses inferred from dynamics, such as velocity dispersions or X-rays, and those inferred from lensing are a generic prediction of modified gravity theories. Viable models however must include some non-linear mechanism to restore General ... More
Hermitian Azumaya modules and arithmetic Chern classesJul 27 2016We compute arithmetic Chern classes of sheaves on an arithmetic surface X associated to a Hermitian Azumaya algebra.
An extension of the Siegel space of complex abelian varieties and conjectures on stability structuresAug 20 2018We study semi--algebraic domains associated with symplectic tori and conjecturally identified with spaces of stability conditions on the Fukaya categories of these tori. Our motivation is to test which results from the theory of flat surfaces could hold ... More
First results from an extended freed-isobar analysis at COMPASSNov 29 2017One of the goals of the COMPASS experiment is the precision study of light-meson spectroscopy with data for various final states. With $46\times10^6$ exclusive events, the process $\pi^- p\to\pi^-\pi^+\pi^- p$ constitutes the flagship channel. Based on ... More
Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-valuesAug 08 2017Oct 30 2018We prove new congruences between special values of Rankin-Selberg $L$-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$ over arbitrary number fields. This allows us to control the behavior of $p$-adic $L$-functions under Tate twists and to prove the ... More
An example for a nontrivial irreducible geodesic net in the planeFeb 21 2019We construct a geodesic net in the plane with four unbalanced (boundary) vertices that has 16 balanced vertices and does not contain proper geodesic subnets. This is the first example of an irreducible geodesic net in the Euclidean plane with 4 boundary ... More
On the strict Arnold chord property and coisotropic submanifolds of complex projective spaceSep 01 2014Jan 19 2015Let $\alpha$ be a contact form on a manifold $M$, and $L\subseteq M$ a closed Legendrian submanifold. I prove that $L$ intersects some characteristic for $\alpha$ at least twice if all characteristics are closed and of the same period, and $\alpha$ embeds ... More
Existence of Minimizers in Restricted Hartree-Fock TheoryJun 21 2012In this note we establish the existence of ground states for atoms within several restricted Hartree-Fock theories. It is shown, for example, that there exists a ground state for closed shell atoms with $N$ electrons and nuclear charge $Z \geq N-1$. This ... More
Rational Structures on Automorphic RepresentationsNov 12 2014May 23 2017This paper proves the existence of global rational structures on spaces of cusp forms of general reductive groups. We identify cases where the constructed rational structures are optimal, which includes the case of GL($n$). As an application, we deduce ... More
On the Lojasiewicz-Simon gradient inequality on submanifoldsJul 22 2019We provide sufficient conditions for the Lojasiewicz-Simon gradient inequality to hold on a submanifold of a Banach space and discuss the optimality of our assumptions. Our result provides a tool to study asymptotic properties of quasilinear parabolic ... More
Rank one sheaves over quaternion algebras on Enriques surfacesSep 09 2019Sep 10 2019Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra A on X. Then we study the moduli scheme of torsion free A-modules of rank one. Finally we prove that this moduli scheme is an \'{e}tale ... More
Measurement of the charge asymmetry in top quark pair production in pp collision data at sqrt(s) = 7 TeV using the ATLAS detectorApr 04 2012A measurement of the charge asymmetry in the production of top quark pairs in the semileptonic decay channel has been performed. A dataset corresponding to an integrated luminosity of 1.04 inverse femtobarn, obtained at a centre-of-mass energy of 7 TeV ... More
Yangians in Integrable Field Theories, Spin Chains and Gauge-String DualitiesJan 09 2012In the following paper, which is based on the authors PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in ... More
State-dependent jump activity estimation for Markovian semimartingalesNov 15 2018The jump behavior of an infinitely active It\^o semimartingale can be conveniently characterized by a jump activity index of Blumenthal-Getoor type, typically assumed to be constant in time. We study Markovian semimartingales with a non-constant, state-dependent ... More