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A dynamical inconsistency of Horava gravityDec 02 2009Dec 10 2009The dynamical consistency of the non-projectable version of Horava gravity is investigated by focusing on the asymptotically flat case. It is argued that for generic solutions of the constraint equations the lapse must vanish asymptotically. We then consider ... More

Counting supersymmetric branesSep 09 2011Dec 06 2011Maximal supergravity solutions are revisited and classified, with particular emphasis on objects of co-dimension at most two. This class of solutions includes branes whose tension scales with g_s^{-\sigma} for \sigma>2. We present a group theory derivation ... More

Lattice Vertex Algebras on General Even, Self-dual LatticesOct 30 2002Feb 11 2003In this note we analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices Gamma^{p,q} with p greater or equal to q. It is known that if the lattice is at most Lorentzian, the resulting Lie algebra ... More

Oxidizing Borcherds symmetriesJan 07 2013The tensor hierarchy of maximal supergravity in D dimensions is known to be closely related to a Borcherds (super)algebra that is constructed from the global symmetry group E(11-D). We here explain how the Borcherds algebras in different dimensions are ... More

Standard model fermions and K(E10)Apr 07 2015Jul 01 2015In recent work arXiv:1412.1715 it was shown how to modify Gell-Mann's proposal for identifying the 48 quarks and leptons of the Standard Model with the 48 spin-1/2 fermions of maximal SO(8) gauged supergravity that remain after the removal of eight Goldstinos, ... More

E10 and SO(9,9) invariant supergravityJul 13 2004We show that (massive) D=10 type IIA supergravity possesses a hidden rigid SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional reduction to one (time-like) dimension. We explicitly construct the associated locally supersymmetric ... More

Cancellation of divergences up to three loops in exceptional field theoryDec 07 2017We consider the tetrahedral three-loop diagram in $E_d$ exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the $\nabla^6 R^4$ term in the low-energy effective action ... More

Supergravity divergences, supersymmetry and automorphic formsJun 01 2015Jul 24 2015We investigate the occurrence of divergences in maximal supergravity in various dimensions from the point of view of supersymmetry constraints on the U-duality invariant threshold functions defining the higher derivative couplings in the effective action. ... More

Eisenstein series for infinite-dimensional U-duality groupsApr 13 2012May 29 2012We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E_n series of string duality ... More

On higher spin realizations of K(E10)Jul 01 2013Starting from the known unfaithful spinorial representations of the compact subalgebra K(E10) of the split real hyperbolic Kac-Moody algebra E10 we construct new fermionic `higher spin' representations of this algebra (for `spin-5/2' and `spin-7/2', respectively) ... More

E10 CosmologyNov 29 2005Jan 18 2006We construct simple exact solutions to the E10/K(E10) coset model by exploiting its integrability. Using the known correspondences with the bosonic sectors of maximal supergravity theories, these exact solutions translate into exact cosmological solutions. ... More

Gradient Representations and Affine Structures in AE(n)Jun 28 2005Oct 13 2005We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}. The interplay ... More

Modular graph functions and asymptotic expansions of Poincaré seriesMar 21 2019In this note we study $SL(2,\mathbb{Z})$-invariant functions such as modular graph functions or coefficient functions of higher derivative corrections in type IIB string theory. The functions solve inhomogeneous Laplace equations and we choose to represent ... More

Loops in exceptional field theoryOct 27 2015Jan 13 2016We study certain four-graviton amplitudes in exceptional field theory in dimensions $D\geq 4$ up to two loops. As the formulation is manifestly invariant under the U-duality group $E_{11-D}(\mathbb{Z})$, our resulting expressions can be expressed in terms ... More

Loops in exceptional field theoryOct 27 2015Dec 07 2017We study certain four-graviton amplitudes in exceptional field theory in dimensions $D\geq 4$ up to two loops. As the formulation is manifestly invariant under the U-duality group $E_{11-D}(\mathbb{Z})$, our resulting expressions can be expressed in terms ... More

Cosmological quantum billiardsDec 04 2009Feb 04 2010The mini-superspace quantization of D=11 supergravity is equivalent to the quantization of a E10/K(E10) coset space sigma model, when the latter is restricted to the E10 Cartan subalgebra. As a consequence, the wavefunctions solving the relevant mini-superspace ... More

On free Lie algebras and particles in electro-magnetic fieldsMay 16 2017The Poincar\'e algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electro-magnetic backgrounds and possibly including the backreaction due the presence of multipoles. ... More

Perturbative terms of Kac-Moody-Eisenstein seriesNov 22 2012Supersymmetric theories of gravity can exhibit surprising hidden symmetries when considered on manifolds that include a torus. When the torus is of large dimension these symmetries can become infinite-dimensional and of Kac-Moody type. When taking quantum ... More

Extended Symmetries in Supergravity: the Semi-simple CaseMay 16 2008Jul 04 2008The bosonic sector of various supergravity theories reduces to a homogeneous space G/H in three dimensions. The corresponding algebras g are simple for (half-)maximal supergravity, but can be semi-simple for other theories. We extend the existing literature ... More

IIA and IIB spinors from K(E10)Mar 27 2006Apr 11 2006We analyze the decomposition of recently constructed unfaithful spinor representations of K(E10) under its SO(9) x SO(9), and SO(9) x SO(2) subgroups, respectively, where K(E10) is the `maximal compact' subgroup of the hyperbolic Kac--Moody group E(10). ... More

IIB supergravity and E10Nov 24 2004We analyse the geodesic E10/K(E10) sigma-model in a level decomposition w.r.t. the A8xA1 subalgebra of E10, adapted to the bosonic sector of type IIB supergravity, whose SL(2,R) symmetry is identified with the A1 factor. The bosonic supergravity equations ... More

Higher spin representations of K(E10)Feb 12 2016We review the recently constructed non-trivial fermionic representations of the infinite-dimensional subalgebra K(E10) of the hyperbolic Kac--Moody algebra E10. These representations are all unfaithful (and more specifically, of finite dimension). In ... More

Tetrahedral modular graph functionsJun 06 2017Oct 04 2017The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams. These integrands are modular invariant and understanding the structure ... More

Higher spin fields from indefinite Kac-Moody algebrasOct 28 2004The emergence of higher spin fields in the Kac-Moody theoretic approach to M-theory is studied. This is based on work done by Schnakenburg, West and the second author. We then study the relation of higher spin fields in this approach to other results ... More

On unitary subsectors of polycritical gravitiesJun 29 2012Feb 08 2013We study higher-derivative gravity theories in arbitrary space-time dimension d with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to be dual to ... More

Hidden symmetries and the fermionic sector of eleven-dimensional supergravityDec 14 2005Feb 10 2006We study the hidden symmetries of the fermionic sector of D=11 supergravity, and the role of K(E10) as a generalised `R-symmetry'. We find a consistent model of a massless spinning particle on an E10/K(E10) coset manifold whose dynamics can be mapped ... More

An inverse scattering formalism for STU supergravityNov 27 2013STU supergravity becomes an integrable system for solutions that effectively only depend on two variables. This class of solutions includes the Kerr solution and its charged generalizations that have been studied in the literature. We here present an ... More

Heterotic-string amplitudes at one loop: modular graph forms and relations to open stringsNov 06 2018We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude, the integrals ... More

Supersymmetric quantum cosmological billiardsJul 17 2009Sep 18 2009D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic ... More

K(E10), Supergravity and FermionsJun 12 2006We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E(10,R) are studied and the supergravity equations are rewritten ... More

On spinorial representations of involutory subalgebras of Kac-Moody algebrasNov 28 2018The representation theory of involutory (or 'maximal compact') subalgebras of infinite-dimensional Kac-Moody algebras is largely terra incognita, especially with regard to fermionic (double-valued) representations. Nevertheless, certain distinguished ... More

Non-geometric branes are DFT monopolesJul 19 2016The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially ... More

An Inverse Scattering Construction of the JMaRT FuzzballSep 23 2014Dec 17 2014We present an inverse scattering construction in STU supergravity of the two-charge single-rotation JMaRT fuzzball. The key element in our construction is the fact that with appropriate changes in the parameters, the JMaRT fuzzball can be smoothly connected ... More

Very-extended Kac-Moody algebras and their interpretation at low levelsSep 19 2003We analyse the very-extended Kac-Moody algebras as representations in terms of certain A_d subalgebras and find the generators at low levels. Our results for low levels agree precisely with the bosonic field content of the theories containing gravity, ... More

Enhancement of hidden symmetries and Chern-Simons couplingsMay 27 2015We study the role of Chern--Simons couplings for the appearance of enhanced symmetries of Cremmer--Julia type in various theories. It is shown explicitly that for generic values of the Chern--Simons coupling there is only a parabolic Lie subgroup of symmetries ... More

Modular realizations of hyperbolic Weyl groupsOct 11 2010May 12 2011We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions. ... More

Symmetries of M-theory and free Lie superalgebrasSep 24 2018We study systematically various extensions of the Poincar\'e superalgebra. The most general structure starting from a set of spinorial supercharges $Q_\alpha$ is a free Lie superalgebra that we discuss in detail. We explain how this universal extension ... More

Heterotic-string amplitudes at one loop: modular graph forms and relations to open stringsNov 06 2018Mar 07 2019We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude, the integrals ... More

Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectorsDec 12 2013Mar 02 2015Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac-Moody groups. In particular, we analyse the Eisenstein series on $E_9(R)$, $E_{10}(R)$ and $E_{11}(R)$ ... More

Hyperbolic Weyl groups and the four normed division algebrasMay 20 2008We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral lattices of the ... More

Constraints and the E10 Coset ModelSep 17 2007We continue the study of the one-dimensional E10 coset model (massless spinning particle motion on E10/K(E10) whose dynamics at low levels is known to coincide with the equations of motion of maximal supergravity theories in appropriate truncations. We ... More

A note on gauge fixing in supergravity/Kac-Moody correspondencesMar 20 2006We explain how to achieve the traceless gauge for the spatial part of the spin connection in the framework of the recently proposed correspondence between the (appropriately truncated) bosonic sectors of maximal supergravities and the `geodesic' sigma-model ... More

K(E9) from K(E10)Nov 28 2006May 15 2007We analyse the M-theoretic generalisation of the tangent space structure group after reduction of the D=11 supergravity theory to two space-time dimensions in the context of hidden Kac-Moody symmetries. The action of the resulting infinite-dimensional ... More

Canonical structure of the E10 model and supersymmetryNov 21 2014Apr 28 2015A coset model based on the hyperbolic Kac-Moody algebra E10 has been conjectured to underly eleven-dimensional supergravity and M theory. In this note we study the canonical structure of the bosonic model for finite- and infinite-dimensional groups. In ... More

Some Algebraic Aspects of Half-BPS Bound States in M-TheoryNov 27 2009We revisit non-marginal half-BPS solutions of M-theory in the framework of the possible existence of an underlying E11 Kac-Moody symmetry. In this context, non-marginal BPS solutions of M-theory can be described as exact solutions of the brane sigma-model ... More

Supersymmetric Domain WallsJun 25 2012We classify the half-supersymmetric "domain walls", i.e. branes of codimension one, in toroidally compactified IIA/IIB string theory and show to which gauged supergravity theory each of these domain walls belong. We use as input the requirement of supersymmetric ... More

Inverse Scattering and the Geroch GroupNov 13 2012Sep 26 2013We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the ... More

Sugawara-type constraints in hyperbolic coset modelsDec 17 2009In the conjectured correspondence between supergravity and geodesic models on infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the constraints play a central role. We present a Sugawara-type construction in terms of the E10 ... More

Real forms of extended Kac-Moody symmetries and higher spin gauge theoriesOct 20 2011May 07 2012We consider the relation between higher spin gauge fields and real Kac-Moody Lie algebras. These algebras are obtained by double and triple extensions of real forms g_0 of the finite-dimensional simple algebras g arising in dimensional reductions of gravity ... More

An M-theory solution from null roots in E11Jan 14 2011We find a purely gravitational classical solution of M-theory/eleven-dimensional supergravity which corresponds to a solution of the E10 brane sigma-model involving a null root. This solution is not supersymmetric and is regularly embedded into E11.

Remarks on Gauge Invariance and First-Class ConstraintsApr 21 2010Gauge symmetries lead to first-class constraints. This assertion is of course true only for non trivial gauge symmetries, i.e., gauge symmetries that act non trivially on-shell on the dynamical variables. We illustrate this well-appreciated fact for time ... More

Hyperbolic Weyl groups and the four normed division algebrasMay 20 2008Jul 14 2017We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral lattices of the ... More

Representations of G+++ and the role of space-timeDec 19 2003We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find ... More

On the E10/Massive Type IIA Supergravity CorrespondenceNov 26 2008Mar 04 2009In this paper we investigate in detail the correspondence between E10 and Romans' massive deformation of type IIA supergravity. We analyse the dynamics of a non-linear sigma model for a spinning particle on the coset space E10/K(E10) and show that it ... More

The different faces of branes in Double Field TheoryMar 13 2019We show how the Wess-Zumino terms of the different branes in string theory can be embedded within double field theory. Crucial ingredients in our construction are the identification of the correct brane charge tensors {and the use of the} double field ... More

The different faces of branes in Double Field TheoryMar 13 2019Mar 27 2019We show how the Wess-Zumino terms of the different branes in string theory can be embedded within double field theory. Crucial ingredients in our construction are the identification of the correct brane charge tensors and the use of the double field theory ... More

Generalised diffeomorphisms for E$_9$Aug 29 2017Dec 06 2017We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a generalised diffeomorphism ... More

Numerical Evaluation of Feynman Loop Integrals by Reduction to Tree GraphsDec 17 2009We present a new method for the numerical evaluation of loop integrals which is based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be performed alongside ... More

Curvature corrections and Kac-Moody compatibility conditionsApr 20 2006We study possible restrictions on the structure of curvature corrections to gravitational theories in the context of their corresponding Kac--Moody algebras, following the initial work on E10 in Class. Quant. Grav. 22 (2005) 2849. We first emphasize that ... More

Small automorphic representations and degenerate Whittaker vectorsDec 17 2014We investigate Fourier coefficients of automorphic forms on split simply-laced Lie groups G. We show that for automorphic representations of small Gelfand-Kirillov dimension the Fourier coefficients are completely determined by certain degenerate Whittaker ... More

Massive Type IIA Supergravity and E10Jan 30 2009In this talk we investigate the symmetry under E10 of Romans' massive type IIA supergravity. We show that the dynamics of a spinning particle in a non-linear sigma model on the coset space E10/K(E10) reproduces the bosonic and fermionic dynamics of massive ... More

Exotic branes in Exceptional Field Theory: the SL(5) duality groupOct 26 2017Aug 11 2018We study how exotic branes, i.e. branes whose tensions are proportional to $g_s^{-\alpha}$, with $\alpha>2$, are realised in Exceptional Field Theory (EFT). The generalised torsion of the Weitzenb\"ock connection of the $\operatorname{SL}(5)$ EFT which, ... More

An E9 multiplet of BPS statesMar 30 2007We construct an infinite E9 multiplet of BPS states for 11D supergravity. For each positive real root of E9 we obtain a BPS solution of 11D supergravity, or of its exotic counterparts, depending on two non-compact transverse space variables. All these ... More

The gauge structure of generalised diffeomorphismsAug 29 2012Oct 24 2012We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show ... More

Eisenstein series and automorphic representationsNov 13 2015Jul 06 2016We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles ... More

E$_9$ exceptional field theory I. The potentialNov 09 2018We construct the scalar potential for the exceptional field theory based on the affine symmetry group E$_9$. The fields appearing in this potential live formally on an infinite-dimensional extended spacetime and transform under E$_9$ generalised diffeomorphisms. ... More

Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$Jul 27 2017We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit ... More

Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4May 28 2009Sep 07 2009We study the symmetries of pure N=2 supergravity in D=4. As is known, this theory reduced on one Killing vector is characterised by a non-linearly realised symmetry SU(2,1) which is a non-split real form of SL(3,C). We consider the BPS brane solutions ... More

Dual Gravity and MatterMar 13 2008Mar 27 2008We consider the problem of finding a dual formulation of gravity in the presence of non-trivial matter couplings. In the absence of matter a dual graviton can be introduced only for linearised gravitational interactions. We show that the coupling of linearised ... More

Beyond E11Mar 03 2017May 07 2017We study the non-linear realisation of E11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations ... More

Fourier coefficients and small automorphic representationsNov 14 2018In this paper we analyze Fourier coefficients of automorphic forms on adelic reductive groups $G(\mathbb{A})$. Let $\pi$ be an automorphic representation of $G(\mathbb{A})$. It is well-known that Fourier coefficients of automorphic forms can be organized ... More

E10 and Gauged Maximal SupergravityOct 31 2008Jan 08 2009We compare the dynamics of maximal three-dimensional gauged supergravity in appropriate truncations with the equations of motion that follow from a one-dimensional E10/K(E10) coset model at the first few levels. The constant embedding tensor, which describes ... More

Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantonsMay 26 2010Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2,1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the ... More

Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1)Sep 24 2009Jun 09 2010The hypermultiplet moduli space in Type IIA string theory compactified on a rigid Calabi-Yau threefold X, corresponding to the "universal hypermultiplet", is described at tree-level by the symmetric space SU(2,1)/(SU(2) x U(1)). To determine the quantum ... More

Stellar mixing length theory with entropy rainApr 13 2015Aug 22 2016The effects of a nongradient flux term originating from the motion of convective elements with entropy perturbations of either sign are investigated and incorporated into a modified version of stellar mixing length theory (MLT). Such a term, first studied ... More

Fixed points of involutive automorphisms of the Bruhat orderMar 04 2004Oct 14 2004Applying a classical theorem of Smith, we show that the poset property of being Gorenstein$^*$ over $\mathbb{Z}_2$ is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in ... More

Two Exterior Algebras for orthogonal and symplectic Quantum GroupsJun 08 1999Let \Gamma be one of the N^2-dimensional bicovariant first order differential calculi on the orthogonal or symplectic quantum group O_q(N) or Sp_q(N). The parameter q is not a root of unity. We show that the second antisymmetrizer exterior algebra is ... More

Why coronal mass ejections are necessary for the dynamoJan 03 2007Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that ... More

The helicity issue in large scale dynamosJul 18 2002The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable forms of the ... More

The solar dynamo: old, recent, and new problemsNov 30 2000A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between ... More

The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulenceJun 13 2000Dec 07 2000A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the alpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action with an additional large ... More

Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theoryApr 05 2007Apr 13 2007The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in ... More

Muonium spectrum beyond the nonrelativistic limitJan 09 2008A generalization of the Gell-Mann-Low theorem is applied to the antimuon-electron system. The bound state spectrum is extracted numerically. As a result, fine and hyperfine structure are reproduced correctly near the nonrelativistic limit (and for arbitrary ... More

Hydrogen dissociation on metal surfaces - a model system for reactions on surfacesAug 24 1998Reactions on surfaces play an important role in many technological applications. Since these processes are often rather complex, one tries to understand single steps of these complicated reactions by investigating simpler system. In particular the hydrogen ... More

The finite antichain property in Coxeter groupsDec 09 2005Jan 19 2006We prove that the weak order on an infinite Coxeter group contains infinite antichains if and only if the group is not affine.

Sparse Blind Deconvolution and Demixing Through $\ell_{1,2}$-MinimizationSep 08 2016Apr 13 2017This paper concerns solving the sparse deconvolution and demixing problem using $\ell_{1,2}$-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and Strohmer [Self ... More

Soft Recovery Through $\ell_{1,2}$ Minimization with Applications in Recovery of Simultaneously Sparse and Low-Rank MatriceSep 08 2016This article provides a new type of analysis of a compressed-sensing based technique for recovering column-sparse matrices, namely minimization of the $\ell_{1,2}$-norm. Rather than providing conditions on the measurement matrix which guarantees the solution ... More

Relativistic Bound StatesAug 27 2003In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe-Salpeter equation, various quasi-potential equations, the Feynman-Schwinger ... More

Bloch-Wilson Hamiltonian and a Generalization of the Gell-Mann-Low TheoremNov 25 1999The effective Hamiltonian introduced many years ago by Bloch and generalized later by Wilson, appears to be the ideal starting point for Hamiltonian perturbation theory in quantum field theory. The present contribution derives the Bloch-Wilson Hamiltonian ... More

Distributed versus tachocline dynamosDec 29 2005Arguments are presented in favor of the idea that the solar dynamo may operate not just at the bottom of the convection zone, i.e. in the tachocline, but it may operate in a more distributed fashion in the entire convection zone. The near-surface shear ... More

Numerical simulations of turbulent dynamosOct 24 2000Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta_t quenchings that are equally ... More

Magnetic helicity in primordial and dynamo scenarios of galaxiesJan 23 2006Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large ... More

On the Faddeev-Popov operator eigenspectrum in topological background fieldsMar 10 2006During the last years significant progress has been made in the understanding of the confinement of quarks and gluons. However, this progress has been made in two directions, which are at first sight very different. On the one hand, topological configurations ... More

On the spectrum of the Faddeev-Popov operator in topological background fieldsNov 30 2005In the Gribov-Zwanziger scenario the confinement of gluons is attributed to an enhancement of the spectrum of the Faddeev-Popov operator near eigenvalue zero. This has been observed in functional and also in lattice calculations. The linear rise of the ... More

The quenched SU(2) scalar-gluon vertex in minimal Landau gaugeFeb 27 2019The question of whether confining effects are visible in correlation functions is a long-standing one. Complementing investigations on the propagators of fundamental and adjoint scalar matter particles here the quenched scalar-gluon vertex is investigated. ... More

Algorithms for Non-Linear and Stochastic Resource Constrained Shortest PathsApr 29 2015Feb 15 2017Resource constrained shortest path problems are usually solved thanks to a smart enumeration of all the non-dominated paths. Recent improvements of these enumeration algorithms rely on the use of bounds on path resources to discard partial solutions. ... More

Nonautonomous Conley Index Theory: The Connecting HomomorphismJan 10 2018Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical system. To give ... More

Equilibrium-Like Solutions of Asymptotically Autonomous Differential EquationsDec 21 2017Jan 30 2018We analyze the chain recurrent set of skew product semiflows obtained from nonautonomous differential equations -- ordinary differential equations or semilinear parabolic differential equations. For many gradient-like dynamical systems, Morse-Smale dynamical ... More

Towards Distortion-Predictable Embedding of Neural NetworksAug 01 2015Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation produced by ... More

On the hierarchies of higher order mKdV and KdV equationsSep 16 2009Oct 28 2009The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces $\hat{H}^r_s(\R)$ defined by the norm $$\n{v_0}{\hat{H}^r_s(\R)} := \n{< \xi > ^s\hat{v_0}}{L^{r'}_{\xi}},\quad < \xi >=(1+\xi^2)^{\frac12}, ... More