Results for "Benjamin Erk"

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Implicit Argument Prediction with Event KnowledgeFeb 20 2018Apr 13 2018Implicit arguments are not syntactically connected to their predicates, and are therefore hard to extract. Previous work has used models with large numbers of features, evaluated on very small datasets. We propose to train models for implicit argument ... More
Relations such as Hypernymy: Identifying and Exploiting Hearst Patterns in Distributional Vectors for Lexical EntailmentMay 18 2016Sep 23 2016We consider the task of predicting lexical entailment using distributional vectors. We perform a novel qualitative analysis of one existing model which was previously shown to only measure the prototypicality of word pairs. We find that the model strongly ... More
Implicit Argument Prediction as Reading ComprehensionNov 08 2018Implicit arguments, which cannot be detected solely through syntactic cues, make it harder to extract predicate-argument tuples. We present a new model for implicit argument prediction that draws on reading comprehension, casting the predicate-argument ... More
Coulomb explosion imaging of concurrent CH$_{2}$BrI photodissociation dynamicsOct 06 2017The dynamics following laser-induced molecular photodissociation of gas-phase CH$_{2}$BrI at 271.6 nm were investigated by time-resolved Coulomb explosion imaging using intense near-IR femtosecond laser pulses. The observed delay-dependent photofragment ... More
Discriminants of stable rank two sheaves on some general type surfacesDec 05 2018Jan 10 2019We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We ... More
Distributional Modeling on a Diet: One-shot Word Learning from Text OnlyApr 14 2017Oct 13 2017We test whether distributional models can do one-shot learning of definitional properties from text only. Using Bayesian models, we find that first learning overarching structure in the known data, regularities in textual contexts and in properties, helps ... More
Photophysics of indole upon x-ray absorptionFeb 08 2018Jul 19 2018A photofragmentation study of gas-phase indole (C$_8$H$_7$N) upon single-photon ionization at a photon energy of 420 eV is presented. Indole was primarily inner-shell ionized at its nitrogen and carbon $1s$ orbitals. Electrons and ions were measured in ... More
Photophysics of indole upon x-ray absorptionFeb 08 2018A photofragmentation study of gas-phase indole (C$_8$H$_7$N) upon single-photon ionization at a photon energy of 420 eV is presented. Indole was primarily inner-shell ionized at its nitrogen and carbon $1s$ orbitals. Electrons and ions were measured in ... More
A bound for the splitting of smooth Fano polytopes with many verticesSep 25 2014Aug 10 2015The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex ... More
Modeling Semantic Plausibility by Injecting World KnowledgeApr 02 2018Apr 10 2018Distributional data tells us that a man can swallow candy, but not that a man can swallow a paintball, since this is never attested. However both are physically plausible events. This paper introduces the task of semantic plausibility: recognizing plausible ... More
Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noiseJul 11 2018We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu, ... More
Quantum spin pumping with adiabatically modulated magnetic barrier'sMar 29 2003Dec 09 2003A quantum pump device involving magnetic barriers produced by the deposition of ferro magnetic stripes on hetero-structure's is investigated. The device for dc- transport does not provide spin-polarized currents, but in the adiabatic regime, when one ... More
On smooth Gorenstein polytopesMar 08 2013A Gorenstein polytope of index r is a lattice polytope whose r-th dilate is a reflexive polytope. These objects are of interest in combinatorial commutative algebra and enumerative combinatorics, and play a crucial role in Batyrev's and Borisov's computation ... More
The Cartan-Hadamard Theorem for Metric Spaces with Local Geodesic BicombingsSep 23 2015Nov 07 2016Local-to-global principles are spread all-around in mathematics. The classical Cartan-Hadamard Theorem from Riemannian geometry was generalized by W. Ballmann for metric spaces with non-positive curvature, and by S. Alexander and R. Bishop for locally ... More
Long wave approximation for water waves under a Coriolis forcing and the Ostrovsky equationMar 29 2016Sep 09 2016This paper is devoted to the study of the long wave approximation for water waves under the influence of the gravity and a Coriolis forcing. We start by deriving a generalization of the Boussinesq equations in 1D (in space) and we rigorously justify them ... More
Blue hypertext is a perfect design decision: No perceptual disadvantage in reading and successful highlighting of relevant informationJan 13 2016Highlighted text in the Internet (i.e. Hypertext) is predominantly blue and underlined. The percept of these hypertext characteristics were heavily questioned by applied research and empirical tests resulted in inconclusive results. The ability to identify ... More
Coriolis effect on water wavesNov 23 2015Sep 09 2016This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We prove a local wellposedness ... More
Entropic fluctuations of XY quantum spin chainsMar 08 2015We consider an XY quantum spin chain that consists of a left, center and right part initially at thermal equilibrium at temperatures $T_l$, $T_c$, and $T_r$, respectively. The left and right systems are infinitely extended thermal reservoirs and the central ... More
Investigating the Quantum Properties of Jets and the Search for a Supersymmetric Top Quark Partner with the ATLAS DetectorSep 12 2016Quarks and gluons are the fundamental building blocks of matter responsible for most of the visible energy density in the universe. However, they cannot be directly observed due to the confining nature of the strong force. The LHC uses pp collisions to ... More
Szego\H o-Widom asymptotics of Chebyshev Polynomials on Circular ArcsJul 25 2016Thiran and Detaille give an explicit formula for the asymptotics of the sup-norm of the Chebyshev polynomials on a circular arc. We give the so-called $\textrm{Szeg\H o}$-Widom asymptotics for this domain, i.e., explicit expressions for the asymptotics ... More
SLIC in a defined mask with applications to medical imagingJun 30 2016Supervoxel methods are effective for reducing an image or volume into a set of locally similar regions which has a number of advantages to pixel based methods for segmentation and graph based methods. Simple linear iterative clustering (SLIC) is an effective ... More
Universality Conjectures for Curvature Flow on Graphs, and Limits of Embedded Cell ComplexesMay 29 2016Curvature flow on embedded graphs and cell complexes embedded in $\mathbb{R}^n$ is of great mathematical interest, and has important physical applications in materials science. In order to formalize universality conjectures about the long term behavior ... More
Turaev-Viro invariants as an extended TQFT IIIDec 02 2010Aug 30 2011In the third paper in this series, we examine the Reshetikhin-Turaev and Turaev-Viro TQFTs at the level of surfaces. In particular, we show that for a closed surface $\Sigma$, $Z_{TV, \mathcal{C}}(\Sigma) \cong Z_{RT, Z(\C)}(\Sigma)$, thus extending the ... More
Geometrizing the Quantum - A Toy ModelApr 19 2010It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum mechanics as ... More
Quantizing Geometry or Geometrizing the Quantum?Apr 16 2010Apr 19 2010The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an approach the quantum ... More
Nonequilibrium density matrix for thermal transport in quantum field theoryDec 05 2012In these notes I explain how to describe one-dimensional quantum systems that are simultaneously near to, but not exactly at, a critical point, and in a far-from-equilibrium steady state. This description uses a density matrix on scattering states (of ... More
Conformal loop ensembles and the stress-energy tensorSep 07 2012We give a construction of the stress-energy tensor of conformal field theory (CFT) as a local "object" in conformal loop ensembles CLE_\kappa, for all values of \kappa in the dilute regime 8/3 < \kappa <= 4 (corresponding to the central charges 0 < c ... More
Factorisation of conformal maps on finitely connected domainsJul 04 2011Let $U$ be a multiply connected domain of the Riemann sphere $\hat{C}$ whose complement $\hat{C}\setminus U$ has $N<\infty$ components. We show that every conformal map on $U$ can be written as a composition of $N$ maps conformal on simply connected domains. ... More
The Cartan-Hadamard Theorem for Metric Spaces with Local BicombingsSep 23 2015The classical Cartan-Hadamard Theorem was generalized by W. Ballmann for metric spaces with non-positive curvature and by S. Alexander and R. Bishop for locally convex metric spaces. In this paper, we prove the Cartan-Hadamard Theorem in a more general ... More
On the endomorphism monoid of a profinite semigroupMar 19 2010Necessary and sufficient conditions are given for the endomorphism monoid of a profinite semigroup to be profinite. A similar result is established for the automorphism group.
On Even Linear Indexed Languages with a Reduction to the Learning of Context-Free LanguagesDec 01 2013Aug 23 2014This paper presents a restricted form of linear indexed grammars, called even linear indexed grammars, which yield the even linear indexed languages. These languages properly contain the context-free languages and are contained in the set of linear indexed ... More
Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loopsJul 17 2015Sep 14 2016We consider the general spin-1 SU(2) invariant Heisenberg model with a two-body interaction. A random loop model is introduced and relations to quantum spin systems is proved. Using this relation it is shown that for dimensions 3 and above N\'eel order ... More
Central derivatives of L-functions in Hida familiesFeb 28 2012We prove a result of the following type: given a Hida family of modular forms, if there exists a weight two form in the family whose L-function vanishes to exact order one at s=1, then all but finitely many weight two forms in the family enjoy this same ... More
Complex multiplication cycles and Kudla-Rapoport divisorsMar 03 2013We study the intersections of special cycles on a unitary Shimura variety of signature (n-1,1), and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of conjectures ... More
Intersection theory on Shimura surfaces IIFeb 28 2012This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed the Shimura curve over Q associated to a rational quaternion ... More
Twisted Gross-Zagier theoremsFeb 28 2012The theorems of Gross-Zagier and Zhang relate the N\'eron-Tate heights of complex multiplication points on the modular curve X_0(N) (and on Shimura curve analogues) with the central derivatives of automorphic L-functions. We extend these results to include ... More
Chaotic Brane InflationNov 16 2012Mar 18 2014We illustrate a framework for constructing models of chaotic inflation where the inflaton is the position of a D3 brane along the universal cover of a string compactification. In our scenario, a brane rolls many times around a non-trivial one-cycle, thereby ... More
Stochastic energetics of a Brownian motor and refrigerator driven by non-uniform temperatureJul 05 2009Jun 02 2014The energetics of a Brownian heat engine and heat pump driven by position dependent temperature, known as the B\"uttiker-Landauer heat engine and heat pump, is investigated by numerical simulations of the inertial Langevin equation. We identify parameter ... More
Assessing Wikipedia-Based Cross-Language Retrieval ModelsJan 10 2014This work compares concept models for cross-language retrieval: First, we adapt probabilistic Latent Semantic Analysis (pLSA) for multilingual documents. Experiments with different weighting schemes show that a weighting method favoring documents of similar ... More
A logical treatment of special relativity, with and without faster-than-light observersJun 25 2013There are three goals of this thesis. First: to present a concise yet accessible description of basic mathematical logic and model theory. Second: to develop an axiomatization of special relativity using only two undefined predicates. Ideally, these axioms ... More
Finding Rational Periodic Points on Wehler K3 SurfacesJan 23 2008Mar 12 2010This article examines dynamical systems on a class of K3 surfaces in $\mathbb{P}^{2} \times \mathbb{P}^{2}$ with an infinite automorphism group. In particular, this article develops an algorithm to find $\mathbb{Q}$-rational periodic points using information ... More
On background-independent renormalization of spin foam modelsJul 29 2014Sep 09 2014In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the notion of cylindrical ... More
On knottings in the physical Hilbert space of LQG as given by the EPRL modelJun 03 2010We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the ... More
Sparse arrays of signatures for online character recognitionAug 01 2013Dec 01 2013In mathematics the signature of a path is a collection of iterated integrals, commonly used for solving differential equations. We show that the path signature, used as a set of features for consumption by a convolutional neural network (CNN), improves ... More
A general approach of least squares estimation and optimal filteringMay 27 2013The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the method as ... More
A proof that tidal heating in a synchronous rotation is always larger than in an asymptotic nonsynchronous rotation stateOct 30 2007In a recent paper, Wisdom (2007, Icarus, in press) derived concise expressions for the rate of tidal dissipation in a synchronously rotating body for arbitrary orbital eccentricity and obliquity. He provided numerical evidence than the derived rate is ... More
Monodromy Invariants and Polarization Types of Generalized Kummer FibrationsJun 29 2016Aug 31 2016In this paper a monodromy invariant for isotropic classes on generalized Kummer type manifolds is constructed. This invariant is used to determine the polarization type of Lagrangian fibrations on such manifolds - a notion which was introduced in an earlier ... More
Progress on Asymptotics of Klazar-type Set Partition Pattern AvoidanceSep 20 2016We consider asymptotics of set partition pattern avoidance in the sense of Klazar. The main result of this paper extends work of Alweiss, and finds a classification for $\pi$ such that the number of set partitions avoiding $\pi$ grows more slowly than ... More
On a combinatorial problem of Erdos, Kleitman and LemkeOct 25 2010Aug 12 2012In this paper, we study a combinatorial problem originating in the following conjecture of Erdos and Lemke: given any sequence of n divisors of n, repetitions being allowed, there exists a subsequence the elements of which are summing to n. This conjecture ... More
On the existence of zero-sum subsequences of distinct lengthsMar 20 2009May 25 2012In this paper, we obtain a characterization of short normal sequences over a finite Abelian p-group, thus answering positively a conjecture of Gao for a variety of such groups. Our main result is deduced from a theorem of Alon, Friedland and Kalai, originally ... More
Redefining $π$Nov 19 2016This paper revisits formulas for $\pi$ involving nested radicals in iterative forms by discussing a method of deriving an infinite number of them.This method involves deriving a limit for $\pi$ from the formula expression, circumference, $C=2r k$. In ... More
Families of mutually isospectral Riemannian orbifoldsSep 02 2013In this paper we consider three arithmetic families of isospectral non-isometric Riemannian orbifolds and in each case derive an upper bound for the size of the family which is polynomial as a function of the volume of the orbifolds. The first family ... More
Toric Symplectic StacksMar 13 2019We give an intrinsic definition of toric symplectic stacks, and show that they are classified by simple convex polytopes equipped with some additional combinatorial data. This generalizes Delzant's classification of toric symplectic manifolds. As an application, ... More
Generating subgroups of ray class groups with small prime idealsJul 04 2018Explicit bounds are given on the norms of prime ideals generating arbitrary subgroups of ray class groups of number fields, assuming the Extended Riemann Hypothesis. These are the first explicit bounds for this problem, and are significantly better than ... More
Periods and algebraic deRham cohomologyJun 07 2005It is known that the algebraic \deRham cohomology group $\hDR{i}(X_0/\Q)$ of a nonsingular variety $X_0/\Q$ has the same rank as the rational singular cohomology group $\h^i\sing(\Xh;\Q)$ of the complex manifold $\Xh$ associated to the base change $X_0\times_{\Q}\C$. ... More
Weighted Persistent Homology Sums of Random Čech ComplexesJul 18 2018Sep 06 2018We study the asymptotic behavior of random variables of the form \begin{equation*} E_{\alpha}^i\left(x_1,\ldots,x_n\right)=\sum_{\left(b,d\right)\in \mathit{PH}_i\left(x_1,\ldots,x_n\right)} \left(d-b\right)^{\alpha} \end{equation*} where $\left\{x_j\right\}_{j\in\mathbb{N}}$ ... More
Analogues of Complex GeometryJul 10 2001May 10 2006We prove that there are no pseudoholomorphic theories of anything other than curves, even if one allows more general spaces than almost complex manifolds. The proof is elementary, except for theories of pseudoholomorphic hypersurfaces, where topological ... More
Optimal Nash Equilibria for Bandwidth AllocationApr 06 2019In bandwidth allocation, competing agents wish to transmit data along paths of links in a network, and each agent's utility is equal to the minimum bandwidth she receives among all links in her desired path. Recent market mechanisms for this problem have ... More
Braid group actions on the $n$-adic integersMar 15 2019We construct an infinite tower of covering spaces over the configuration space of $n-1$ distinct non-zero points in the complex plane. This results in an action of the affine braid group $\mathbb{B}_{n-1}^{aff}$ on the $n$-adic integers $\mathbb{Z}_n$ ... More
Pre- and post-quantum Diffie-Hellman from groups, actions, and isogeniesSep 13 2018Sep 20 2018Diffie-Hellman key exchange is at the foundations of public-key cryptography, but conventional group-based Diffie-Hellman is vulnerable to Shor's quantum algorithm. A range of 'post-quantum Diffie-Hellman' protocols have been proposed to mitigate this ... More
Android Tapjacking VulnerabilityJul 30 2015Android is an open source mobile operating system that is developed mainly by Google. It is used on a significant portion of mobile devices worldwide. In this paper, I will be looking at an attack commonly known as tapjacking. I will be taking the attack ... More
Almost Morawetz estimates and global well-posedness for the defocusing $L^2$-critical nonlinear Schr{ö}dinger equation in higher dimensionsSep 23 2009In this paper, we consider the global well-posedness of the defocusing, $L^{2}$ - critical nonlinear Schr{\"o}dinger equation in dimensions $n \geq 3$. Using the I-method, we show the problem is globally well-posed in $n = 3$ when $s > {2/5}$, and when ... More
Summary of progress on the Blaschke conjectureSep 05 2013Nov 15 2016The Blaschke conjecture claims that every compact Riemannian manifold whose injectivity radius equals its diameter is, up to constant rescaling, a compact rank one symmetric space. We summarize the intuition behind this problem, the proof that such manifolds ... More
Holomorphic Parabolic Geometries and Calabi-Yau ManifoldsDec 09 2008Sep 20 2011We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact K\"ahler manifolds.
Norm bounds for Ehrhart polynomial rootsFeb 21 2006Sep 09 2006M. Beck, J. De Loera, M. Develin, J. Pfeifle and R. Stanley found that the roots of the Ehrhart polynomial of a d-dimensional lattice polytope are bounded above in norm by 1+(d+1)!. We provide an improved bound which is quadratic in d and applies to a ... More
Wavelets in function spaces on cellular domainsFeb 15 2013Nowadays the theory and application of wavelet decompositions plays an important role not only for the study of function spaces (of Lebesgue, Hardy, Sobolev, Besov, Triebel-Lizorkin type) but also for its applications in signal and numerical analysis, ... More
Dynamics of Bose-Einstein CondensatesApr 05 2007We report on some recent results concerning the dynamics of Bose-Einstein condensates, obtained in a series of joint papers with L. Erdos and H.-T. Yau. Starting from many body quantum dynamics, we present a rigorous derivation of a cubic nonlinear Schroedinger ... More
Discontinuity propagation in delay differential-algebraic equationsMar 12 2018The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencil, a complete characterization of the different ... More
Lifting locally homogeneous geometric structuresAug 16 2011We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.
Topological Field Theories and Harrison HomologyFeb 16 2011Nov 19 2012The tools and arguments developed by Kevin Costello are adapted to families of "Outer Spaces" or spaces of graphs. This allows us to prove a version of Deligne's conjecture: the Harrison homology associated to a homotopy commutative algebra is naturally ... More
Gorenstein toric Fano varietiesMay 24 2004We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular ... More
Testing spherical transitivity in iterated wreath products of cyclic groupsJul 22 2006We give a partial solution a question of Grigorchuk, Nekrashevych, Sushchanskii and \v{S}uni\'k by giving an algorithm to test whether a finite state element of an infinite iterated (permutational) wreath product $\hat G = \mathbb Z/k\mathbb Z\wr \mathbb ... More
Dual curves and pseudoholomorphic curvesJan 02 2001Aug 06 2005A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with, and yields ... More
Random attractors for singular stochastic partial differential equationsNov 01 2011The existence of random attractors for singular stochastic partial differential equations (SPDE) perturbed by general additive noise is proven. The drift is assumed only to satisfy the standard assumptions of the variational approach to SPDE with compact ... More
Shape, Scale, and Minimality of Matrix RangesMar 25 2018Jul 18 2018We study containment and uniqueness problems concerning matrix convex sets. First, to what extent is a matrix convex set determined by its first level? Our results in this direction quantify the disparity between two product operations, namely the product ... More
Rank two sheaves with maximal third Chern character in three-dimensional projective spaceNov 29 2018We give a complete classification of semistable rank two sheaves on three-dimensional projective space with maximal third Chern character. This implies an explicit description of their moduli spaces. As an open subset they contain rank two reflexive sheaves ... More
Counterexample to the Generalized Bogomolov-Gieseker Inequality for ThreefoldsFeb 16 2016We give a counterexample to the generalized Bogomolov-Gieseker inequality for threefolds conjectured by Bayer, Macr\`i and Toda using the blow up of a point over three dimensional projective space.
Bridgeland Stability on Threefolds - Some Wall CrossingsSep 15 2015Following up on the construction of Bridgeland stability condition on $\mathbb{P}^3$ by Macr\`i, we compute first examples of wall crossing behaviour. In particular, for Hilbert schemes of curves such as twisted cubics or complete intersections of the ... More
Brauer's Height Zero Conjecture for metacyclic defect groupsApr 30 2012We prove that Brauer's Height Zero Conjecture holds for p-blocks of finite groups with metacyclic defect groups. If the defect group is nonabelian and contains a cyclic maximal subgroup, we obtain the distribution into p-conjugate and p-rational irreducible ... More
Blocks with defect group D_{2^n} x C_{2^m}Feb 21 2011May 25 2011We determine the numerical invariants of blocks with defect group D_{2^n}\times C_{2^m}, where D_{2^n} denotes a dihedral group of order 2^n and C_{2^m} denotes a cyclic group of order 2^m. This generalizes Brauer's results for m=0. As a consequence, ... More
Free Actions on C*-algebra Suspensions and Joins by Finite Cyclic GroupsOct 14 2015Mar 11 2017We present a proof for certain cases of the noncommutative Borsuk-Ulam conjectures proposed by Baum, D\k{a}browski, and Hajac. When a unital $C^*$-algebra $A$ admits a free action of $\mathbb{Z}/k\mathbb{Z}$, $k \geq 2$, there is no equivariant map from ... More
Cooperads as Symmetric SequencesOct 07 2013We give a brief overview of the basics of cooperad theory using a new definition which lends itself to easy example creation and verification. We also apply our definition to build the parenthesization and cosimplicial structures exhibited by cooperads ... More
Periodic cyclic homology and derived de Rham cohomologyAug 15 2018We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the Hodge-completion of the ... More
Quadrilaterals inscribed in convex curvesJan 05 2018Jan 30 2018We classify the set of quadrilaterals that can be inscribed in convex Jordan curves, in the continuous as well as in the smooth case. This answers a question of Makeev in the special case of convex curves. The difficulty of this problem comes from the ... More
Smooth Surfaces in Smooth Fourfolds with Vanishing First Chern ClassOct 13 2016Jan 24 2018According to a conjecture attributed to Hartshorne and Lichtenbaum and proven by Ellingsrud and Peskine, the smooth rational surfaces in $\mathbb{P}^4$ belong to only finitely many families. We formulate and study a collection of analogous problems in ... More
Global well-posedness and scattering for the defocusing, mass - critical generalized KdV equationApr 30 2013In this paper we prove that the defocusing, mass - critical generalized KdV initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\mathbf{R})$. We prove this via a concentration compactness argument.
Global well - posedness and scattering for the focusing, energy - critical nonlinear Schrödinger problem in dimension $d = 4$ for initial data below a ground state thresholdSep 05 2014In this paper we prove global well - posedness and scattering for the focusing, energy - critical nonlinear Schr\"odinger initial value problem in four dimensions. Previous work proved this in five dimensions and higher using the double Duhamel trick. ... More
Global well-posedness and scattering for the defocusing, energy -critical, nonlinear Schr{ö}dinger equation in the exterior of a convex obstacle when $d = 4$Dec 04 2011May 11 2012In this paper we prove that the energy - critical nonlinear Schr{\"o}dinger equation in the domain exterior to a convex obstacle is globally well - posed and scattering for initial data having finite energy. To prove this we utilize frequency localized ... More
Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schrödinger equation when $d = 1$Oct 01 2010Mar 18 2011In this paper we prove that the defocusing, quintic nonlinear Schr\"odinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\mathbf{R})$. To do this, we will prove a frequency localized interaction Morawetz estimate similar ... More
Global well-posedness and scattering for the radial, defocusing, cubic wave equation with almost sharp initial dataApr 14 2016Aug 04 2017In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in a slightly supercritical Sobolev space, and a weighted Sobolev space.
Toric Symplectic StacksMar 13 2019Apr 03 2019We give an intrinsic definition of toric symplectic stacks, and show that they are classified by simple convex polytopes equipped with some additional combinatorial data. This generalizes Delzant's classification of toric symplectic manifolds. As an application, ... More
Quantum Dynamics, Coherent States and Bogoliubov TransformationsOct 04 2012Systems of interest in physics are usually composed by a very large number of interacting particles. At equilibrium, these systems are described by stationary states of the many-body Hamiltonian (at zero temperature, by the ground state). The reaction ... More
A new upper bound for the cross number of finite Abelian groupsDec 03 2007In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number valid in the general case of arbitrary finite Abelian groups. Given a finite ... More
Monodromy Invariants and Polarization Types of Generalized Kummer FibrationsJun 29 2016May 21 2018In this paper a monodromy invariant for isotropic classes on generalized Kummer type manifolds is constructed. This invariant is used to determine the polarization type of Lagrangian fibrations on such manifolds - a notion which was introduced in an earlier ... More
Matrix Factorisations Arising From Well-Generated Complex Reflection GroupsApr 20 2017In this note we discuss an interesting duality known to occur for certain complex reflection groups, we prove in particular that this duality has a concrete representation theoretic realisation. As an application, we construct matrix factorisations of ... More
Linear conjugacyJul 24 2018We say that two elements of a group or semigroup are $\Bbbk$-linear conjugates if their images under any linear representation over $\Bbbk$ are conjugate matrices. In this paper we characterize $\Bbbk$-linear conjugacy for finite semigroups (and, in particular, ... More
Random attractors for degenerate stochastic partial differential equationsJun 11 2012Mar 15 2013We prove the existence of random attractors for a large class of degenerate stochastic partial differential equations (SPDE) perturbed by joint additive Wiener noise and real, linear multiplicative Brownian noise, assuming only the standard assumptions ... More
Representation growth and representation zeta functions of groupsSep 13 2012We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic groups, such as ... More
Sur la présentation des représentations supersingulières de $\mathrm{GL}_2(F)$Jan 20 2012Feb 07 2012Let $F$ be a quadratic extension of $\mathbb{Q}_p$. We prove that smooth irreducible supersingular representations with central character of $\mathrm{GL}_2(F)$ are not of finite presentation.
Ideals of etale groupoid algebras and Exel's Effros-Hahn conjectureOct 24 2018Oct 30 2018We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal of an ample groupoid algebra over a field is an intersection of kernels of induced representations from isotropy groups, with a much shorter proof, by using the ... More