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Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimatorJun 11 2019In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing the fracture ... More

A phase-field model for fractures in incompressible solidsJan 16 2019Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds on a mixed form ... More

A Semi-Lagrangian two-level preconditioned Newton-Krylov solver for constrained diffeomorphic image registrationApr 07 2016We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use an optimization formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. ... More

K3 en route From Geometry to Conformal Field TheoryMar 29 2015To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau manifolds and their ... More

An effective look at right-handed currents and quark flavour mixingNov 24 2010We present an effective theory approach for a model with a left-right symmetric flavour group broken only by the Yukawa couplings. An underlying SU(2)_L x SU(2)_R x U(1)_{B-L} global symmetry is assumed without specifying the fundamental theory. The model ... More

Orbifold Constructions of K3: A Link between Conformal Field Theory and GeometryDec 01 2001May 08 2002We discuss geometric aspects of orbifold conformal field theories in the moduli space of N=(4,4) superconformal field theories with central charge c=6. Part of this note consists of a summary of our earlier results on the location of these theories within ... More

Gauge Fields Out-Of-Equilibrium: A Gauge Invariant Formulation and the Coulomb GaugeJan 25 2001We study the abelian Higgs model out-of-equilibrium in two different approaches, a gauge invariant formulation, proposed by Boyanovsky et al. \cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches become equivalent in a consistent ... More

Kohomologie von Garben nichtabelscher GruppenJul 16 2015Sheaves of noncommutative groups are an essential tool especially in the context of vector bundles. As known there is no real cohomology theory with values in such sheaves. This work deals with the question of under what circumstances the cohomology set ... More

The Transformation Operator for One-Dimensional Schroedinger Operators on Almost Periodic Infinite-Gap BackgroundsJun 21 2010Apr 05 2011We investigate the kernels of the transformation operators for one-dimensional Schroedinger operators with potentials, which are asymptotically close to Bohr almost periodic infinite-gap potentials.

Snapshots of Conformal Field TheoryApr 11 2014May 27 2017In snapshots, this exposition introduces conformal field theory, with a focus on those perspectives that are relevant for interpreting superconformal field theory by Calabi-Yau geometry. It includes a detailed discussion of the elliptic genus as an invariant ... More

Strings, Black Holes and Conformal Field TheoryApr 25 1994The SL(2,R)/U(1) gauged Wess-Zumino-Witten model is an exact conformal field theory describing a black hole in two-dimensional space-time. The free field approach of Bershadsky and Kutasov is a suitable formulation of this CFT in order to compute physically ... More

Consistency of Orbifold Conformal Field Theories on K3Oct 30 2000Jan 20 2002We explicitly determine the locations of G orbifold conformal field theories, G=Z_M, M=2,3,4,6, G=\hat D_n, n=4,5, or G the binary tetrahedral group \hat T, within the moduli space M^{K3} of N=(4,4) superconformal field theories associated to K3. This ... More

Strongly transitive multiple treesOct 12 2011Oct 25 2011We give an amalgamation construction of free multiple trees with a strongly transitive automorphism group. The construction shows that any partial codistance function on a tuple of finite trees can be extended to yield multiple trees.

Banach space valued Cauchy-Riemann equations with totally real boundary conditionsJan 27 2004The main purpose of this paper is to give a general regularity result for Cauchy-Riemann equations in complex Banach spaces with totally real boundary conditions. The usual elliptic $L^p$-regularity results hold true under one crucial assumption: The ... More

Repellers for non-uniformly expanding maps with singular or critical pointsJun 16 2010Given an ergodic measure with positive entropy and only positive Lyapunov exponents, its dynamical quantifiers can be approximated by means of quantifiers of some family of uniformly expanding repellers. Here non-uniformly expanding maps are studied that ... More

Lagrangian boundary conditions for anti-self-dual instantons and the Atiyah-Floer conjectureJul 13 2006The purpose of this survey is to explain an approach to the Atiyah-Floer conjecture via a new instanton Floer homology with Lagrangian boundary conditions. This is a joint project with Dietmar Salamon. This paper also provides a rough guide to the analysis ... More

The free pseudospace is n-ample, but not (n+1)-ampleSep 29 2011Nov 01 2011We give a uniform construction of free pseudospaces of dimension n extending work by Baudisch and Pillay. This yields examples of $\omega$-stable theories which are n-ample, but not (n+1)-ample. The prime models of these theories are buildings associated ... More

A family of SCFTs hosting all "very attractive" relatives of the (2)^4 Gepner modelDec 19 2005Jan 23 2006This work gives a manual for constructing superconformal field theories associated to a family of smooth K3 surfaces. A direct method is not known, but a combination of orbifold techniques with a non-classical duality turns out to yield such models. A ... More

A Note on Compactifications on Spin(7)-Holonomy ManifoldsNov 13 2000Mar 19 2001In this note we consider compactifications of ${\cal M}$-theory on $Spin(7)$-holonomy manifolds to three-dimensional Minkowski space. In these compactifications a warp factor is included. The conditions for unbroken N=1 supersymmetry give rise to determining ... More

Testing M(atrix)-Theory at Two LoopsSep 04 1997I discuss the relation between M-theory and M(atrix)-theory in flat space by considering the effective potential for the scattering of two groups of D0-branes in both theories. An explicit calculation of this potential up to two loop order in M(atrix)-theory ... More

On Superconformal Field Theories Associated to Very Attractive QuarticsJul 07 2003Dec 18 2005We study N=(4,4) superconformal field theories with left and right central charge c=6 which allow geometric interpretations on specific quartic hypersurfaces in CP^3. Namely, we recall the proof that the Gepner model (2)^4 admits a geometric interpretation ... More

Fredholm notions in scale calculus and Hamiltonian Floer theorySep 18 2012Oct 25 2016We give an equivalent definition of the Fredholm property for linear operators on scale Banach spaces and introduce a (nonlinear) scale Fredholm property with respect to a splitting of the domain. The latter implies the Fredholm property introduced by ... More

Non-hyperbolic behavior of geodesic flows of rank 1 surfacesAug 02 2018We prove that for the geodesic flow of a rank 1 Riemannian surface which is expansive but not Anosov the Hausdorff dimension of the set of vectors with only zero Lyapunov exponents is large.

Horseshoes for diffeormorphisms preserving hyperbolic measuresNov 26 2014Jul 19 2017We give extensions of Katok's horseshoe constructions, comment on related results, and provide a self-contained proof. We consider either a $C^{1+\alpha}$ diffeomorphism preserving a hyperbolic measure or a $C^1$ diffeomorphism preserving a hyperbolic ... More

Equality of pressures for diffeomorphisms preserving hyperbolic measuresMar 11 2008For a diffeomorphism which preserves a hyperbolic measure the potential $\phi^u=-\log|{\rm Jac} df|_{E^u}|$ is studied. Various types of pressure of $\phi^u$ are introduced. It is shown that these pressures satisfy a corresponding variational principle. ... More

An inexact Newton-Krylov algorithm for constrained diffeomorphic image registrationAug 27 2014May 07 2015We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial differential equation ... More

Somersaults on unstable islandsNov 26 2014We give extensions of Katok's horseshoe constructions, comment on related results, and provide a self-contained proof. We consider either a $C^{1+\alpha}$ diffeomorphism preserving a hyperbolic measure or a $C^1$ diffeomorphism preserving a hyperbolic ... More

Hodge-elliptic genera and how they govern K3 theoriesMay 28 2017Mar 13 2018The Hodge-elliptic genus and its conformal field theoretic counterpart were recently introduced by Kachru and Tripathy, refining the traditional complex elliptic genus. We construct a different, so-called chiral Hodge-elliptic genus, which is expected ... More

Smooth structures on Morse trajectory spaces, featuring finite ends and associative gluingMay 03 2012We give elementary constructions of manifold with corner structures and associative gluing maps on compactifications of spaces of infinite, half infinite, and finite Morse flow lines.

Energy quantization and mean value inequalities for nonlinear boundary value problemsMay 26 2004We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal ... More

Infinite sharply multiply transitive groupsMar 07 2016The finite sharply $2$-transitive groups were classified by Zassenhaus in the 1930's. They essentially all look like the group of affine linear transformations $x\mapsto ax+b$ for some field (or at least near-field) $K$. However, the question remained ... More

Hodge-elliptic genera and how they govern K3 theoriesMay 28 2017Feb 15 2019The (complex) Hodge-elliptic genus and its conformal field theoretic counterpart were recently introduced by Kachru and Tripathy, refining the traditional complex elliptic genus. We construct a different, so-called chiral Hodge-elliptic genus, which is ... More

Floer Field PhilosophyFeb 16 2016Floer field theory is a construction principle for e.g. 3-manifold invariants via decomposition in a bordism category and a functor to the symplectic category, and is conjectured to have natural 4-dimensional extensions. This survey provides an introduction ... More

Anti-self-dual instantons with Lagrangian boundary conditions II: BubblingJan 27 2004Jan 29 2004We study bubbling phenomena of anti-self-dual instantons on $\H^2\times\S$, where $\S$ is a closed Riemann surface. The restriction of the instanton to each boundary slice $\{z\}\times\S$, $z\in\pd\H^2$ is required to lie in a Lagrangian submanifold of ... More

Anti-self-dual instantons with Lagrangian boundary conditions I : Elliptic theoryApr 11 2002Jan 27 2004We study a nonlocal boundary value problem for anti-self-dual instantons on 4-manifolds with a space-time splitting of the boundary. The model case is $\R \times Y$, where $Y$ is a compact oriented 3-manifold with boundary $\Sigma$. The restriction of ... More

Constrained $H^1$-regularization schemes for diffeomorphic image registrationMar 02 2015Sep 07 2016We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov ... More

Optimization Algorithms for Catching Data Manipulators in Power System Estimation LoopsAug 01 2016In this paper we develop a set of algorithms that can detect the identities of malicious data-manipulators in distributed optimization loops for estimating oscillation modes in large power system models. The problem is posed in terms of an averaging consensus ... More

Optimization Algorithms for Catching Data Manipulators in Power System Estimation LoopsAug 01 2016Mar 28 2017In this paper we develop a set of algorithms that can detect the identities of malicious data-manipulators in distributed optimization loops for estimating oscillation modes in large power system models. The estimation is posed in terms of a consensus ... More

A Lagrangian Gauss-Newton-Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image RegistrationMar 13 2017Jul 12 2017We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to ... More

A Semi-Lagrangian two-level preconditioned Newton-Krylov solver for constrained diffeomorphic image registrationApr 07 2016Feb 28 2018We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We ... More

Fredholm notions in scale calculus and Hamiltonian Floer theorySep 18 2012Jan 14 2013We give an equivalent definition of the Fredholm property for linear operators on scale Banach spaces and introduce a (nonlinear) scale Fredholm property with respect to a splitting of the domain. The latter implies the Fredholm property introduced by ... More

Snapshots of Conformal Field TheoryApr 11 2014In snapshots, this exposition introduces conformal field theory, with a focus on those perspectives that are relevant for interpreting superconformal field theory by Calabi-Yau geometry. It includes a detailed discussion of the elliptic genus as an invariant ... More

Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgroundsApr 04 2012We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.

Standard monomials for wonderful group compactificationsDec 01 2005Let X be the wonderful compactification of a semisimple adjoint algebraic group. Extending the standard monomials on the flag variety, Chirivi and Maffei constructed a basis of the space of global sections on X that is compatible with all closures of ... More

Privacy - an Issue for eLearning? A Trend Analysis Reflecting the Attitude of European eLearning UsersMay 04 2007Availing services provided via the Internet became a widely accepted means in organising one's life. Beside others, eLearning goes with this trend as well. But, while employing Internet service makes life more convenient, at the same time, it raises risks ... More

On restricted families of projections in R^3Feb 26 2013Jan 11 2014We study projections onto non-degenerate one-dimensional families of lines and planes in $\mathbb{R}^{3}$. Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most $1/2$-dimensional sets $B \subset ... More

Constancy results for special families of projectionsAug 09 2012Feb 08 2013Let {\mathbb{V} = V x R^l : V \in G(n-l,m-l)} be the family of m-dimensional subspaces of R^n containing {0} x R^l, and let \pi_{\mathbb{V}} : R^n --> \mathbb{V} be the orthogonal projection onto \mathbb{V}. We prove that the mapping V \mapsto Dim \pi_{\mathbb{V}}(B) ... More

Completely reducible subcomplexes of spherical buildingsSep 29 2010Feb 09 2011We generalize a result of Serre's to show that if every vertex of some fixed type of a convex subcomplex of an irreducible spherical building has an opposite, then the subcomplex is completely reducible.

A non-desarguesian projective planeOct 21 2015We construct a new non-desarguesian projective plane from a complex analytic structure. At the same time the construction can be explained in terms of so called Hrushovski's construction. This supports the hypothesis that in general structures produced ... More

Supersymmetry Breaking, M-Theory and FluxesJul 06 2001Jul 16 2001We consider warped compactifications of ${\cal M}$-theory to three-dimensional Minkowski space on compact eight-manifolds. Taking all the leading quantum gravity corrections of eleven-dimensional supergravity into account we obtain the solution to the ... More

Compactifying M-Theory to Four DimensionsOct 30 2000Nov 07 2000We consider compactifications of ${\cal M}$-theory to four-dimensional Minkowski space on seven-dimensional non-compact manifolds. These compactifications include a warp factor which is non-constant due to the presence of sources coming from fivebranes ... More

Quantum Gravity Corrections for Schwarzschild Black HolesOct 07 1998We consider the Matrix theory proposal describing eleven-dimensional Schwarzschild black holes. We argue that the Newtonian potential between two black holes receives a genuine long range quantum gravity correction, which is finite and can be computed ... More

A twist in the M24 moonshine storyMar 13 2013Mar 07 2015Prompted by the Mathieu Moonshine observation, we identify a pair of 45-dimensional vector spaces of states that account for the first order term in the massive sector of the elliptic genus of K3 in every Z2-orbifold CFT on K3. These generic states are ... More

Torsional Heterotic GeometriesMar 23 2009Apr 03 2009We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used ... More

A sufficient condition for subellipticity of the d-bar-Neumann operatorMar 10 2005We give a sufficient condition for subelliptic estimates for the d-bar-Neumann operator on smoothly bounded, pseudoconvex domains in $\mathbb{C}^n$. This condition is a quantified version of McNeal's condition ($\tilde{P}$) for compactness of the d-bar-Neumann ... More

A Polyfold Proof of the Arnold ConjectureOct 15 2018Jan 04 2019We give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds $M$ via a direct Piunikhin-Salamon-Schwarz morphism. Our constructions are based on a coherent polyfold description ... More

Pseudofinite groups with NIP theory and definability in finite simple groupsFeb 15 2012We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and shortens the proof ... More

On orbifolds and free fermion constructionsSep 02 2008Nov 15 2008This work develops the correspondence between orbifolds and free fermion models. A complete classification is obtained for orbifolds X/G with X the product of three elliptic curves and G an abelian extension of a group (Z_2)^2 of twists acting on X. Each ... More

Extremal Kaehler metrics and Ray-Singer analytic torsionApr 12 1999May 06 1999Let (X,[\omega]) be a compact Kaehler manifold with a fixed Kaehler class [\omega]. Let K_\omega be the set of all Kaehler metrics on X whose Kaehler class equals [\omega]. In this paper we investigate the critical points of the functional Q(g)= |v|_g ... More

On density of ergodic measures and generic pointsApr 02 2014Aug 25 2015We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of invariant measures ... More

Robustness of a bisimulation-type faster-than preorderNov 15 2009TACS is an extension of CCS where upper time bounds for delays can be specified. Luettgen and Vogler defined three variants of bismulation-type faster-than relations and showed that they all three lead to the same preorder, demonstrating the robustness ... More

Cluster deprojection with joint lensing, X-ray, and Sunyaev-Zeldovich dataSep 09 1999We propose a new cluster deprojection algorithm for recovering cluster structure along the line of sight (los) based on the Richardson-Lucy (RL) algorithm, which recovers a nonnegative theoretical distribution from a given projection. To optimize our ... More

Projection effects in mass-selected galaxy-cluster samplesFeb 10 1999Selection of galaxy clusters by mass is now possible due to weak gravitational lensing effects. It is an important question then whether this type of selection reduces the projection effects prevalent in optically selected cluster samples. We address ... More

Heterotic Strings with TorsionSep 09 2002Dec 04 2002In this paper we describe the heterotic dual of the type IIB theory compactified to four dimensions on a toroidal orientifold in the presence of fluxes. The type IIB background is most easily described in terms of an M-theory compactification on a four-fold. ... More

Geometric Aspects of D-branes and T-dualityAug 16 2009Sep 13 2009We explore the differential geometry of T-duality and D-branes. Because D-branes and RR-fields are properly described via K-theory, we discuss the (differential) K-theoretic generalization of T-duality and its application to the coupling of D-branes to ... More

Building-like geometries of finite Morley RankJun 20 2016Sep 25 2016For any $n\geq 6$ we construct almost strongly minimal geometries of type $\bullet \overset{n}{-} \bullet \overset{n}{-}\bullet$ which are $2$-ample but not $3$-ample.

Dominated Pesin theory: convex sum of hyperbolic measuresMar 19 2015Feb 22 2016In the uniformly hyperbolic setting it is well known that the measure supported on periodic orbits is dense in the convex space of all invariant measure. In this paper we consider the reverse question, in the non-uniformly hyperbolic setting: assuming ... More

Exceptional sets for nonuniformly hyperbolic diffeomorphismsDec 29 2017For a surface diffeomorphism, a compact invariant locally maximal set $W$ and some subset $A\subset W$ we study the $A$-exceptional set, that is, the set of points whose orbits do not accumulate at $A$. We show that if the Hausdorff dimension of $A$ is ... More

Exceptional sets for nonuniformly expanding mapsJun 01 2015Feb 15 2016Given a rational map of the Riemann sphere and a subset $A$ of its Julia set, we study the $A$-exceptional set, that is, the set of points whose orbit does not accumulate at $A$. We prove that if the topological entropy of $A$ is less than the topological ... More

A Maslov cocycle for unitary groupsJul 16 2007May 16 2009We introduce a 2-cocycle for symplectic and skew-hermitian hyperbolic groups over arbitrary fields and skew fields, with values in the Witt group of hermitian forms. This cocycle has good functorial properties: it is natural under extension of scalars ... More

Symmetry-surfing the moduli space of Kummer K3sMar 12 2013Jan 23 2015A maximal subgroup of the Mathieu group M24 arises as the combined holomorphic symplectic automorphism group of all Kummer surfaces whose Kaehler class is induced from the underlying complex torus. As a subgroup of M24, this group is the stabilizer group ... More

The PI Property of Graded Hecke AlgebrasAug 14 2006We show that graded Hecke algebras are PI algebras if and only if they are finitely generated over their centres if and only if the deformation parameters $t_{i}$ are zero for all $i=1,\ldots,N$. This generalises a result for symplectic reflection algebras ... More

New simple groups with a BN-pairJun 02 2013We show that there are simple groups with a spherical BN-pair of rank 2 which are non-Moufang and hence not of algebraic origin.

Kuranishi atlases with trivial isotropy - the 2013 state of affairsAug 07 2012Aug 11 2015Kuranishi structures were introduced to symplectic topology by Fukaya and Ono and recently refined by Joyce, in order to extract homological data from compactified moduli spaces of holomorphic maps in cases where geometric regularization approaches such ... More

The Lyapunov spectrum of some parabolic systemsSep 18 2007We study the Hausdorff dimension spectrum for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, ... More

Orientations for pseudoholomorphic quiltsMar 26 2015Jun 07 2017We construct orientations on moduli spaces of pseudoholomorphic quilts with seam conditions in Lagrangian correspondences equipped with relative spin structures and determine the effect of various gluing operations on the orientations. We also investigate ... More

Exact triangle for fibered Dehn twistsMar 26 2015Mar 05 2019We use quilted Floer theory to generalize Seidel's long exact sequence in symplectic Floer theory to fibered Dehn twists. We then apply it to construct versions of the Floer and Khovanov-Rozansky exact triangles in Lagrangian Floer theory of moduli spaces ... More

Orientations for pseudoholomorphic quiltsMar 26 2015Aug 09 2016We construct coherent orientations on moduli spaces of pseudoholomorphic quilts and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the orientations under composition of Lagrangian correspondences. ... More

Exact triangle for fibered Dehn twistsMar 26 2015Jun 02 2016We use quilted Floer theory to generalize Seidel's long exact sequence in symplectic Floer theory to fibered Dehn twists. We then apply it to construct versions of the Floer and Khovanov-Rozansky exact triangles in Lagrangian Floer theory of moduli spaces ... More

Decoding the geometry of conformal field theoriesMar 05 2008To certain geometries, string theory associates conformal field theories. We discuss techniques to perform the reverse procedure: To recover geometrical data from abstractly defined conformal field theories. This is done by introducing appropriate notions ... More

Limits and Degenerations of Unitary Conformal Field TheoriesAug 21 2003Jan 11 2004In the present paper, degeneration phenomena in conformal field theories are studied. For this purpose, a notion of convergent sequences of CFTs is introduced. Properties of the resulting limit structure are used to associate geometric degenerations to ... More

Many Faces of Mimetic GravityDec 30 2015We consider the recently introduced mimetic gravity, which is a Weyl-symmetric extension of the General Relativity and which can play a role of an imperfect fluid-like Dark Matter with a small sound speed. In this paper we discuss in details how this ... More

Low functions of realsMar 09 2009Sep 26 2010We introduce a new notion of computable function on $\R^N$ and prove some basic properties. We give two applications, first a short proof of Yoshinaga's theorem that periods are \el (they are actually low). We also show that the low complex numbers form ... More

M-Theory on Eight-ManifoldsMay 08 1996We show that in certain compactifications of ${\cal M}$-theory on eight-manifolds to three-dimensional Minkowski space-time the four-form field strength can have a non-vanishing expectation value, while an $N=2$ supersymmetry is preserved. For these compactifications ... More

Fivebrane Gravitational AnomaliesNov 18 1999Dec 03 1999Freed, Harvey, Minasian and Moore have proposed a mechanism to cancel the gravitational anomaly of the M-theory fivebrane coming from diffeomorphisms acting on the normal bundle. This procedure is based on a modification of the conventional M-theory Chern-Simons ... More

Instanton Action for Type II HypermultipletsJan 25 1999Apr 08 1999We analyze the hypermultiplet moduli space describing the universal sector of type IIA theory compactified on a Calabi-Yau threefold. The classical moduli space is described in terms of the coset $SU(2,1)/U(2)$. The flux quantization condition of the ... More

Complete Solution for M(atrix) Theory at Two LoopsJul 23 1998The complete result for the effective potential for two graviton exchange at two loops in M(atrix) theory can be expressed in terms of a generalized hypergeometric function.

Asymptotic cones and ultrapowers of Lie groupsNov 07 2003Jan 21 2004Asymptotic cones of metric spaces were first invented by Gromov. They are metric spaces which capture the 'large-scale structure' of the underlying metric space. Later, van den Dries and Wilkie gave a more general construction of asymptotic cones using ... More

Affine $Λ$-buildings, ultrapowers of Lie groups and Riemannian symmetric spaces: an algebraic proof of the Margulis conjectureSep 11 2002Oct 24 2002In this paper, we give a general group-theoretic construction of affine $\RR$-buildings, and more generally, of affine $\Lambda$-buildings, associated to semisimple Lie groups over nonarchimedean real closed fields. The construction of Kleiner-Leeb using ... More

The isometry group of the bounded Urysohn space is simpleNov 26 2012We show that the isometry group of the bounded Urysohn space is simple. This extends previous work by the authors.

The symmetries of the tetrahedral Kummer surface in the Mathieu group M_24Aug 05 2010Jul 20 2011We provide a method, based on Nikulin's lattice gluing techniques, which identifies the symplectic automorphisms of Kummer surfaces as permutation groups on 24 elements preserving the Golay code. In other words, we explicitly realise these symplectic ... More

\emph{Addendum to} Sharply $2$-transitive groups of characteristic~$0$ [arXiv:1604.00573]Mar 07 2017In this short note we show how to modify the construction of non-split sharply $2$-transitive groups of characteristic~$0$ given by Rips and Tent [arXiv:1604.00573] to allow for arbitrary fields of characteristic 0

Simple factor dressing and the Lopez-Ros deformation of minimal surfaces in Euclidean 3-spaceSep 18 2014The aim of this paper is to give a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps. Since a minimal surface in 3-space ... More

On weak Fraisse limitsNov 25 2017Using the natural action of $S_\infty$ we show that a countable hereditary class $\cC$ of finitely generated structures has the joint embedding property (JEP) and the weak amalgamation property (WAP) if and only if there is a structure $M$ whose isomorphism ... More

Symmetries and multipeakon solutions for the modified two-component Camassa-Holm systemApr 20 2017Compared with the two-component Camassa-Holm system, the modified two-component Camassa-Holm system introduces a regularized density which makes possible the existence of solutions of lower regularity, and in particular of multipeakon solutions. In this ... More

Quilted Floer CohomologyMay 09 2009Aug 13 2010We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations ... More

The general peakon-antipeakon solution for the Camassa-Holm equationFeb 26 2015We compute explicitly the peakon-antipeakon solution of the Camassa-Holm equation $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ in the non-symmetric and $\alpha$-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution ... More

Context Models for OOV Word Translation in Low-Resource LanguagesJan 26 2018Out-of-vocabulary word translation is a major problem for the translation of low-resource languages that suffer from a lack of parallel training data. This paper evaluates the contributions of target-language context models towards the translation of ... More

Topological pressure for one-dimensional holomorphic dynamical systemsMay 31 2007For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials h the topological pressure is entirely determined by the values of h on the repelling periodic points of f. This is a version of a classical ... More

Mirror Symmetry on Kummer Type K3 SurfacesJun 13 2001Oct 02 2003We investigate both geometric and conformal field theoretic aspects of mirror symmetry on N=(4,4) superconformal field theories with central charge c=6. Our approach enables us to determine the action of mirror symmetry on (non-stable) singular fibers ... More