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Face-centered cubic crystallization of atomistic configurationsJul 02 2014We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level, phenomena such ... More

Asymptotic Analysis of the Ginzburg-Landau Functional on Point CloudsApr 17 2016Nov 10 2016The Ginzburg-Landau functional is a phase transition model which is suitable for clustering or classification type problems. We study the asymptotics of a sequence of Ginzburg-Landau functionals with anisotropic interaction potentials on point clouds ... More

Rescaled Objective Solutions of Fokker-Planck and Boltzmann equationsMay 25 2018Dec 11 2018We study the long-time behavior of symmetric solutions of the nonlinear Boltzmann equation and a closely related nonlinear Fokker-Planck equation. If the symmetry of the solutions corresponds to shear flows, the existence of stationary solutions can be ... More

Long Range Particle Dynamics and the Linear Boltzmann EquationDec 12 2017This paper gives the first full proof of the justification of the linear Boltzmann equation from an underlying long range particle evolution. We suppose that a tagged particle is interacting with a background via a two body potential that is decaying ... More

Asymptotic Analysis of the Ginzburg-Landau Functional on Point CloudsApr 17 2016The Ginzburg-Landau functional is a phase transition model which is suitable for clustering or classification type problems. We study the asymptotics of a sequence of Ginzburg-Landau functionals with anisotropic interaction potentials on point clouds ... More

The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas Particle ModelMar 24 2016Apr 02 2017A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with background ... More

The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas Particle ModelMar 24 2016A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with background ... More

Energy transport by acoustic modes of harmonic latticesNov 21 2006We study the large scale evolution of a scalar lattice excitation which satisfies a discrete wave-equation in three dimensions. We assume that the dispersion relation associated to the elastic coupling constants of the wave-equation is acoustic, i.e., ... More

Surface energy and boundary layers for a chain of atoms at low temperatureApr 12 2019We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ ... More

Convergence of the $k$-Means Minimization Problem using $Γ$-ConvergenceJan 06 2015Apr 03 2015The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is possible to apply ... More

Efficient Tabling of Structured Data with Enhanced Hash-ConsingOct 04 2012Current tabling systems suffer from an increase in space complexity, time complexity or both when dealing with sequences due to the use of data structures for tabled subgoals and answers and the need to copy terms into and from the table area. This symptom ... More

Thermalization of rate-independent processes by entropic regularizationSep 17 2012We consider the effective behaviour of a rate-independent process when it is placed in contact with a heat bath. The method used to "thermalize" the process is an interior-point entropic regularization of the Moreau--Yosida incremental formulation of ... More

Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard HamiltonianMar 29 2019We study mathematically the equilibrium properties of the Bose-Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the microcanonical and ... More

Optimal uncertainty quantification for legacy data observations of Lipschitz functionsFeb 09 2012Apr 13 2013We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not ... More

Nonlinear Elasticity from Atomistic MechanicsFeb 17 2012Apr 06 2012We present sharp convergence results for the Cauchy--Born approximation of general classical atomistic interactions, for both static and dynamic problems, for small data.

Recursion Relations for Long-Range Integrable Spin Chains with Open Boundary ConditionsJan 04 2012Apr 26 2012It is well known that integrable charges for short-range (e.g. nearest-neighbor) spin chains with periodic boundary conditions can be recursively generated by a so-called boost operator. In the past, this iterative construction has been generalized to ... More

On the Structure of Monodromy Algebras and Drinfeld DoublesSep 18 1996Oct 11 1996We give a review and some new relations on the structure of the monodromy algebra (also called loop algebra) associated with a quasitriangular Hopf algebra H. It is shown that as an algebra it coincides with the so-called braided group constructed by ... More

Local cohomology and F-stabilityApr 28 2009Jun 25 2009We study the relationship between the Frobenius stability of an Artinian module over an F-injective ring and its stable part.

Standard Model statistics of a Type II orientifoldDec 15 2005Dec 22 2005We analyse four-dimensional, supersymmetric intersecting D-brane models in a toroidal orientifold background from a statistical perspective. The distribution and correlation of observables, like gauge groups and couplings, are discussed. We focus on models ... More

Statistics in the Landscape of Intersecting Brane ModelsOct 12 2007Mar 24 2008An approach towards a statistical survey of four dimensional supersymmetric vacua in the string theory landscape is described and illustrated with three examples of ensembles of intersecting D-brane models. The question whether it is conceivable to make ... More

On not testing the foreign-language effect: A comment on Costa, Foucart, Arnon, Aparici, and Apesteguia (2014)Jun 25 2015In their first five studies, Costa, Foucart, Arnon, Aparici, and Apesteguia (2014) fail to provide a statistical test of the foreign-language effect. Instead, the authors employ a procedure in which they test the framing effects separately for the native ... More

Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ringJun 16 2015We show that two blocks of generalized quaternion defect with three simple modules over a sufficiently large $2$-adic ring $\mathcal O$ are Morita-equivalent if and only if the corresponding blocks over the residue field of $\mathcal O$ are Morita-equivalent. ... More

Superfluidity in driven non-equilibrium Bose-Einstein condensates due to balanced forcesNov 10 2016In this letter an analytical proof of the existence and suppression of superfluidity in open Bose- Einstein condensates (BEC) such as those of Exciton-Polaritons (Polaritons) or the atom laser is given. To test superfluidity in the mean-field regime of ... More

Automatic Calculation of supersymmetric Renormalization Group Equations and Self EnergiesFeb 03 2010Jan 11 2011SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. Those information can be used by \SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. ... More

Automation of non-SUSY two-loop RGEs with PyR@TE: latest developmentsOct 29 2015In light of the conspicuous absence of SUSY in the energy range explored by the LHC during run I, non-supersymmetric BSM scenarios are becoming more and more attractive. One key ingredient in exploring such BSM physics are the renormalization group equations ... More

On the impact of kinetic mixing in beta functions at two-loopAug 25 2016Sep 06 2016Kinetic mixing is a fundamental property of models with a gauge symmetry involving several $\mathrm{U}(1)$ group factors. In this paper, we perform a numerical study of the impact of kinetic mixing on beta functions at two-loop. To do so, we use the recently ... More

Lectures on Yangian SymmetryJun 09 2016Jul 26 2016In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional ... More

A closer look at non-decoupling D-TermsMar 18 2016May 09 2016Non-Decoupling D-Terms are an attractive possibility to enhance the tree-level mass of the standard model like Higgs boson in supersymmetric models. We discuss here for the case of a new Abelian gauge group two effects usually neglected in literature: ... More

Analytical calculation of the axis angle 2V from extinction measurements on the spindle stageFeb 27 2017A concise derivation of the "Joel equations", which allow for the determination of the axis angle 2V from measurements of extinction directions on a spindle stage, is provided starting from the wave-equation. Only analytic methods and no geometric arguments ... More

Lower bounds on the size of general Schrödinger-cat states from experimental dataOct 11 2016Mar 20 2017Experimental progress with meso- and macroscopic quantum states (i.e., general Schrodinger-cat states) was recently accompanied by theoretical proposals on how to measure the merit of these efforts. So far, experiment and theory were disconnected as theoretical ... More

Instantaneous non-local computation of low T-depth quantum circuitsNov 09 2015Sep 26 2016Instantaneous non-local quantum computation requires multiple parties to jointly perform a quantum operation, using pre-shared entanglement and a single round of simultaneous communication. We study this task for its close connection to position-based ... More

Beyond superfluidity in driven non-equilibrium Bose-Einstein condensatesNov 10 2016Apr 04 2017The phenomenon of superfluidity in open Bose-Einstein condensates (BEC) is analysed numerically and analytically. It is found that a superfluid phase is feasible even above the speed of sound, when forces due to inhomogeneous non-equilibrium processes ... More

Levine's motivic comparison theorem revisitedJan 22 2007For a field of characteristic zero, M. Levine has proved that his category of triangulated motives is equivalent to the one constructed by V. Voevodsky. In this paper we show that the strategy of Levine's proof can be applied on every perfect field to ... More

Elementary equivalence versus IsomorphismSep 20 2001How does the first order language of fields encode birational invariants of varieties?... This question is related to rational points on varieties and effectiveness in algebraic/arithmetic geometry.

Dealing with cross-country heterogeneity in panel VARs using finite mixture modelsApr 04 2018In this paper, we provide a parsimonious means to estimate panel VARs with stochastic volatility. We assume that coefficients associated with domestic lagged endogenous variables arise from a Gaussian mixture model. Shrinkage on the cluster size is introduced ... More

Vector Field Twisting of Lie-AlgebrasJul 11 2006Aug 10 2006In quantum groups coproducts of Lie-algebras are twisted in terms of generators of the corresponding universal enveloping algebra. If representations are considered, twists also serve as starproducts that accordingly quantize representation spaces. In ... More

Update of the flavour-physics constraints in the NMSSMDec 07 2015We consider the impact of several flavour-changing observables in the $B$- and the Kaon sectors on the parameter space of the NMSSM, in a minimal flavour violating version of this model. Our purpose consists in updating our previous results in arXiv:0710.3714 ... More

Topological Entropy of Formal LanguagesJan 22 2018In this thesis we will introduce topological automata and the topological entropy of a topological automaton, which is the topological entropy of the dynamical system contained in the automaton. We will use these notions to define a measure of complexity ... More

Refined enumerations of alternating sign trianglesApr 27 2018This article introduces and investigates a refinement of alternating sign trapezoids by means of Catalan objects and Motzkin paths. Alternating sign trapezoids are a generalisation of alternating sign triangles that were recently introduced by Ayyer, ... More

Index Search Algorithms for Databases and Modern CPUsJun 20 2017Over the years, many different indexing techniques and search algorithms have been proposed, including CSS-trees, CSB+ trees, k-ary binary search, and fast architecture sensitive tree search. There have also been papers on how best to set the many different ... More

Ranking Functions for Vector Addition SystemsOct 23 2017Vector addition systems are an important model in theoretical computer science and have been used for the analysis of systems in a variety of areas. Termination is a crucial property of vector addition systems and has received considerable interest in ... More

The shortest way to visit all metro lines in a citySep 13 2017Apr 10 2018What if $\{$a tourist, a train addict, Dr. Sheldon Cooper, somebody who likes to waste time$\}$ wants to visit all metro lines or carriages in a given network in a minimum number of steps? We study this problem with an application to the metro network ... More

Perturbations in the relaxation mechanism for a large cosmological constantSep 11 2009Jan 12 2010Recently, a mechanism for relaxing a large cosmological constant (CC) has been proposed [arxiv:0902.2215], which permits solutions with low Hubble rates at late times without fine-tuning. The setup is implemented in the LXCDM framework, and we found a ... More

The Cosmological Constant and Discrete Space-TimesOct 16 2006In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations of scaling ... More

The Picard Group of Various Families of $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant Quartic K3 SurfacesNov 05 2015Jul 18 2017The subject of this paper is the study of various families of quartic K3 surfaces which are invariant under a certain $(\mathbb{Z}/2\mathbb{Z})^{4}$ action. In particular, we describe families whose general member contains $8,16,24$ or $32$ lines as well ... More

On the Monodromy and Galois Group of Conics Lying on Heisenberg Invariant Quartic K3 SurfacesNov 04 2015In "Curves on Heisenberg invariant quartic surfaces in projective 3-space", Eklund showed that a general $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant quartic K3 surface contains at least $320$ conics. In this paper we analyse the field of definition of those ... More

A projector based convergence proof of the Ginelli algorithm for covariant Lyapunov vectorsFeb 23 2018Linear perturbations of solutions of dynamical systems exhibit different asymptotic growth rates, which are naturally characterized by so-called covariant Lyapunov vectors (CLVs). Due to an increased interest of CLVs in applications, several algorithms ... More

Sharp estimates of the Kobayashi metric and Gromov hyperbolicityJan 03 2008Let D be a smooth relatively compact and strictly J-pseudoconvex domain in a four dimensional almost complex manifold (M,J). We give sharp estimates of the Kobayashi metric. Our approach is based on an asymptotic quantitative description of both the domain ... More

Refined enumerations of alternating sign trianglesApr 27 2018May 23 2019This article introduces and investigates a refinement of alternating sign trapezoids by means of Catalan objects and Motzkin paths. Alternating sign trapezoids are a generalisation of alternating sign triangles, which were recently introduced by Ayyer, ... More

xSLHA: an Les Houches Accord reader for Python and MathematicaDec 11 2018The format defined by the SUSY Les Houches Accord (SLHA) is widely used in high energy physics to store and exchange information. It is no longer applied only to a few supersymmetric models, but the general structure is adapted to all kind of models. ... More

Special subvarieties of Drinfeld modular varietiesMar 22 2005Feb 28 2009We explore an analogue of the Andr\'e-Oort conjecture for subvarieties of Drinfeld modular varieties. The conjecture states that a subvariety $X$ of a Drinfeld modular variety contains a Zariski-dense set of complex multiplication (CM) points if and only ... More

On the 2-Abelian Complexity of the Thue-Morse WordApr 15 2014Jun 02 2015We show that the 2-abelian complexity of the infinite Thue-Morse word is 2-regular, and other properties of the 2-abelian complexity, most notably that it is a concatenation of palindromes of increasing length. We also show sharp bounds for the length ... More

Improved Delsarte bounds for spherical codes in small dimensionsJan 27 2005Mar 10 2008We present an extension of the Delsarte linear programming method. For several dimensions it yields improved upper bounds for kissing numbers and for spherical codes. Musin's recent work on kissing numbers in dimensions three and four can be viewed in ... More

The Galois action on M-Origamis and their Teichmüller curvesAug 28 2014We consider a rather special class of translation surfaces (called M-Origamis in this work) that are obtained from dessins by a construction introduced by Martin M\"oller. We give a new proof with a more combinatorial flavour of M\"oller's theorem that ... More

A Probabilistic Look at Conservative Growth-Fragmentation EquationsSep 08 2016Nov 02 2016In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates. We prove the ... More

Random colorings and automorphism breaking in locally finite graphsApr 24 2013A colouring of a graph G is called distinguishing if its stabiliser in Aut G is trivial. It has been conjectured that, if every automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We study ... More

Bounds for the annealed return probability on large finite percolation clustersNov 30 2008Aug 26 2012Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation and the associated ... More

Optimal regularity for two-dimensional Pfaffian systems and the fundamental theorem of surface theoryApr 16 2019We prove that a Pfaffian system with coefficients in the critical space $L^2_\mathrm{loc}$ on a simply connected open subset of $\mathbb{R}^2$ has a non-trivial solution in $W^{1,2}_\mathrm{loc}$ if the coefficients are antisymmetric and satisfy a compatibility ... More

Invariance of the BFV-complexDec 12 2008Nov 21 2010The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold $S$ of a Poisson manifold $(M,\Pi)$. However the assignment (coisotropic submanifold) ... More

The MMT API: A Generic MKM SystemJun 13 2013The MMT language has been developed as a scalable representation and interchange language for formal mathematical knowledge. It permits natural representations of the syntax and semantics of virtually all declarative languages while making MMT-based MKM ... More

A Framework for an Ego-centered and Time-aware Visualization of Relations in Arbitrary Data RepositoriesSep 27 2010Understanding constellations in large data collections has become a common task. One obstacle a user has to overcome is the internal complexity of these repositories. For example, extracting connected data from a normalized relational database requires ... More

p-Adic Lifting Problems and Derived EquivalencesFeb 08 2011Jan 08 2012For two derived equivalent $k$-algebras $\bar\Lambda$ and $\bar\Gamma$, we introduce a correspondence between $\OO$-orders reducing to $\bar\Lambda$ and $\OO$-orders reducing to $\bar\Gamma$. We outline how this may be used to transfer properties like ... More

Reverse mathematics of the finite downwards closed subsets of $\mathbb{N}^k$ ordered by inclusionOct 04 2016Oct 05 2016We show that the well-partial orderedness of the finite downwards closed subsets of $\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $\omega^{\omega^\omega}$. This was conjectured to be the case by Hatzikiriakou ... More

Vortex formation and dynamics in two-dimensional driven-dissipative condensatesJul 23 2016We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We derive the generalization of the truncated Wigner approximation for open quantum many-body systems ... More

The Distribution of Optimal Strategies in Symmetric Zero-sum GamesNov 18 2016Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is given by the ... More

The integral polytope groupMay 04 2016We show that the Grothendieck group associated to integral polytopes in $\mathbb{R}^n$ is free-abelian by providing an explicit basis. Moreover, we identify the involution on this polytope group given by reflection about the origin as a sum of Euler characteristic ... More

Electroweak Symmetry Breaking without the $μ^2$ TermApr 01 2015May 12 2015We demonstrate that from a low energy perspective a viable electroweak symmetry breaking can be achieved without the (negative sign) $\mu^2$ mass term in the Higgs potential, thereby avoiding completely the appearance of relevant operators. We show that ... More

A Logic-Independent IDEOct 30 2014The author's MMT system provides a framework for defining and implementing logical systems. By combining MMT with the jEdit text editor, we obtain a logic-independent IDE. The IDE functionality includes advanced features such as context-sensitive auto-completion, ... More

Thoughts on the Vacuum Energy in the Quantum N-PortraitAug 25 2014Oct 21 2015An application of the quantum N-portrait to the Universe is discussed, wherein the space-time geometry is understood as a Bose-Einstein condensate of N soft gravitons. If near or at the critical point of a quantum phase transition, indications are found ... More

An Indirect Handle on the Down-Quark Yukawa CouplingMay 31 2014To measure the Yukawa couplings of the up and down quarks, Y_{u,d}, seems to be far beyond the capabilities of current and (near) future experiments in particle physics. By performing a general analysis of the potential misalignment between quark masses ... More

Introduction to SARAH and related toolsSep 22 2015Mar 17 2016I give in this lecture an overview of the features of the Mathematica package SARAH, and explain how it can be used together with other codes to study all aspects of a BSM model. The focus will be on the description of the analytical calculations which ... More

A Supermanifold structure on Spaces of Morphisms between SupermanifoldsJun 29 2014The aim of this work is the construction of a "supermanifold of morphisms $X \rightarrow Y$", given two finite-dimensional supermanifolds $X$ and $Y$. More precisely, we will define an object $\underline{SC}^\infty(X,Y)$ in the category of supermanifolds ... More

Poisson Brackets in Kontsevich's "Lie World"Aug 31 2016In this note the notion of Poisson brackets in Kontsevich's "Lie World" is developed. These brackets can be thought of as "universally" defined classical Poisson structures, namely formal expressions only involving the structure maps of a quadratic Lie ... More

Vortex formation and dynamics in two-dimensional driven-dissipative condensatesJul 23 2016Nov 21 2016We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum ... More

Gaussian impurity moving through a Bose-Einstein superfluidOct 13 2016Apr 04 2017In this paper a Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial ... More

Fully packed loop configurations: polynomiality and nested archesFeb 24 2017This article proves a conjecture by Zuber about the enumeration of fully packed loops (FPLs). The conjecture states that the number of FPLs whose link pattern consists of two noncrossing matchings which are separated by $m$ nested arches is a polynomial ... More

On $α$-largeness and the Paris-Harrington principle in $\mathrm{RCA}$ and $\mathrm{RCA}_0^{\displaystyle{*}}$Nov 28 2016We examine, within $\mathrm{RCA}$, the treatment by Ketonen and Solovay on the use of $\alpha$-largeness for giving an upper bound for the Paris-Harrington principle. We also show how to modify the arguments to work within $\mathrm{RCA}_0^{\displaystyle{*}}$. ... More

A new method to identify water masses -- a network-based analysis of oceanographic point measurement time seriesAug 23 2012This is a statistical analysis of the oceanographic time series measured across Fram Strait at a latitude of 78{\deg}50'N. Fram Strait is the deepest passage between the Arctic Ocean and the North Atlantic. There are up to 16 mooring lines with instruments ... More

The $L^2$-torsion polytope of amenable groupsApr 24 2017Feb 19 2019We introduce the notion of groups of polytope class and show that torsion-free amenable groups satisfying the Atiyah Conjecture possess this property. A direct consequence is the homotopy invariance of the $L^2$-torsion polytope among $G$-CW-complexes ... More

Reverse mathematics of the relativised fast growing hierarchyAug 18 2016A short note on the reverse mathematical status of the totality of the relativised fast growing hierarchy.

Monomial ideals and independence of $\mathrm{I}Σ_2$Mar 11 2016We show that a miniaturised version of Maclagan's theorem on monomial ideals is equivalent to $\mathrm{1}{-}\mathrm{Con}(\mathrm{I}\Sigma_2)$ and classify a phase transition threshold for this theorem. This work highlights the combinatorial nature of ... More

The XL-mHG Test For Enrichment: A Technical ReportJul 28 2015Sep 24 2015The minimum hypergeometric test (mHG) is a powerful nonparametric hypothesis test to detect enrichment in ranked binary lists. Here, I provide a detailed review of its definition, as well as the algorithms used in its implementation, which enable the ... More

On spanning tree packings of highly edge connected graphsSep 30 2011Sep 18 2013We prove a refinement of the tree packing theorem by Tutte/Nash-Williams for finite graphs. This result is used to obtain a similar result for end faithful spanning tree packings in certain infinite graphs and consequently to establish a sufficient Hamiltonicity ... More

Kershaw closures for linear transport equations in slab geometry I: model derivationNov 09 2015Aug 02 2016This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability property, that is the fact that the underlying closure is non-negative. ... More

CM points on products of Drinfeld modular curvesJul 20 2004Let X be a product of Drinfeld modular curves over a general base ring A of odd characteristic. We classify those subvarieties of X which contain a Zariski-dense set of CM points. This is an analogue of the Andr\'e-Oort conjecture. As an application, ... More

On the $k$-Semispray of Nonlinear Connections in $k$-Tangent Bundle GeometryJan 05 2016In this paper we present a method by which is obtained a sequence of $k$-semisprays and two sequences of nonlinear connections on the $k$-tangent bundle $T^kM$, starting from a given one. Interesting particular cases appear for Lagrange and Finsler spaces ... More

Breaking graph symmetries by edge colouringsApr 27 2016The distinguishing index $D'(G)$ of a graph $G$ is the least number of colours needed in an edge colouring which is not preserved by any non-trivial automorphism. Broere and Pil\'sniak conjectured that if every non-trivial automorphism of a countable ... More

Almost complex structures on the cotangent bundleJul 04 2005Jan 04 2006We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric ... More

Algebraic approximation of Kähler threefoldsDec 07 2011In the present work, we investigate existence of deformations and algebraic approximability for certain uniruled K\"ahler threefolds. In the first part, we establish existence of infinitesimal deformations for all conic bundles with relative Picard number ... More

The unirationality of Hurwitz spaces of 6-gonal curves of small genusSep 16 2011Nov 16 2012In this short note we prove the unirationality of Hurwitz spaces of 6-gonal curves of genus $g$ with $5\leq g\leq 28$ or $g=30,31,33,35,36,40,45$. Key ingredient is a liaison construction in $\PP^1 \times \PP^2$. By semicontinuity, the proof of the dominance ... More

Counterexamples to the topological Tverberg conjectureFeb 01 2015Nov 13 2015The "topological Tverberg conjecture" by B\'ar\'any, Shlosman and Sz\H{u}cs (1981) states that any continuous map of a simplex of dimension $(r-1)(d+1)$ to $\mathbb{R}^d$ maps points from $r$ disjoint faces of the simplex to the same point in $\mathbb{R}^d$. ... More

BFV-complex and higher homotopy structuresNov 29 2006Oct 14 2008We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the so-called strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can ... More

On the intriguing search for good permutationsJun 14 2018Jul 27 2018The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri's 80th birthday we aim to survey (some ... More

On an explicit lower bound for the star discrepancy in three dimensionsFeb 03 2016Oct 05 2016Following a result of D.~Bylik and M.T.~Lacey from 2008 it is known that there exists an absolute constant $\eta>0$ such that the (unnormalized) $L^{\infty}$-norm of the three-dimensional discrepancy function, i.e, the (unnormalized) star discrepancy ... More

An Application of Fixed-point Theory to Probabilistic Social ChoiceOct 22 2014Nov 26 2014The purpose of this note is to prove the existence of a randomized mechanism, a social decision scheme (SDS), with desirable fairness, efficiency, and strategyproofness properties unmatched by all known SDSs. In particular, we disprove a conjecture by ... More

Warum Astrologie nicht funktionieren kannAug 28 2011There exists many different versions of astrology that are different from each other and sometimes even in conflict with each other. But the basis of every astrological system is the assumption of a connection between the motion of celestial bodies and ... More

Schwinger effect in inhomogeneous electric fieldsJun 29 2011The vacuum of quantum electrodynamics is unstable against the formation of many-body states in the presence of an external electric field, manifesting itself as the creation of electron-positron pairs (Schwinger effect). This effect has been a long-standing ... More

Gaussian impurity moving through a Bose-Einstein superfluidOct 13 2016In this paper a Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial ... More

Cosmology with the 6-degree Field Galaxy SurveyMar 13 2013This thesis presents the analysis of the clustering of galaxies in the 6dF Galaxy Survey (6dFGS). At large separation scales the baryon acoustic oscillation (BAO) signal is detected which allows to make an absolute distance measurement at $z_{\rm eff} ... More

The p-adic group ring of SL_2(p^f)Jan 31 2013In this article we show that the $\Z_p[\zeta_{p^f-1}]$-order $\Z_p[\zeta_{p^f-1}]\SL_2(p^f)$ can be recognized among those orders whose reduction modulo $p$ is isomorphic to $\F_{p^f}\SL_2(p^f)$ using only ring-theoretic properties (in other words we ... More