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A note on symplectic and Poisson linearization of semisimple Lie algebra actionsMar 12 2015In this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields in a neighbourhood of a common ... More

A singular Poincare lemmaMay 23 2004We prove a Poincare lemma for a set of r smooth functions on a 2n-dimensional smooth manifold satisfying a commutation relation determined by r singular vector fields associated to a Cartan subalgebra of $\frak{sp}(2r,\mathbb R)$. This result has a natural ... More

Action-angle coordinates for integrable systems on Poisson manifoldsMay 12 2008Jun 14 2008We prove the action-angle theorem in the general, and most natural, context of integrable systems on Poisson manifolds, thereby generalizing the classical proof, which is given in the context of symplectic manifolds. The topological part of the proof ... More

Cotangent models for group actions on $b$-Poisson manifoldsNov 29 2018Dec 13 2018In this article we give a normal form of a $b$-symplectic form in the neighborhood of a compact orbit of a Lie group action on a $b$-symplectic manifold. We establish cotangent models for Poisson actions on $b$-Poisson manifolds and a $b$-symplectic slice ... More

Equivariant classification of $b^m$-symplectic surfaces and Nambu structuresJul 06 2016Mar 09 2017In this paper we extend the classification scheme in [S] for $b^m$-symplectic surfaces and, more generally, $b^m$-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this ... More

Non-commutative integrable systems on $b$-symplectic manifoldsJun 08 2016In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics ... More

On a Poincare lemma for foliationsJan 24 2013Apr 16 2013In this paper we revisit a Poincare lemma for foliated forms, with respect to a regular foliation, and compute the foliated cohomology for local models of integrable systems with singularities of nondegenerate type. A key point in this computation is ... More

The geometry of E-manifoldsFeb 08 2018Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting generalizes the study ... More

Integrable systems and closed one formsDec 21 2017Dec 27 2017In the first part of this paper we revisit a classical topological theorem by Tischler and deduce a topological result about compact manifolds admitting a set of independent closed forms proving that the manifold is a fibration over a torus. As an application ... More

Geometric Quantization of real polarizations via sheavesJan 11 2013Aug 06 2013In this article we develop tools to compute the Geometric Quantization of a symplectic manifold with respect to a regular Lagrangian foliation via sheaf cohomology and obtain important new applications in the case of real polarizations. The starting point ... More

A Poincare lemma in Geometric QuantisationJul 11 2013Jan 07 2014This article presents a Poincare lemma for the Kostant complex, used to compute geometric quantisation, when the polarisation is given by a Lagrangian foliation defined by an integrable system with nondegenerate singularities.

Cotangent models for integrable systemsJan 19 2016May 23 2016We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on a special class called $b$-Poisson/$b$-symplectic manifolds. The semilocal equivalence with such models uses the corresponding action-angle ... More

On the volume elements of a manifold with transverse zeroesDec 10 2018Dec 18 2018Moser proved in 1965 in his seminal paper that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if their associated cohomology classes in the top cohomology group of a manifold ... More

Equivariant classification of $b^m$-symplectic surfaces and Nambu structuresJul 06 2016In this paper we extend the classification scheme in [S] for $b^m$-symplectic surfaces, and more generally, $b^m$-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this ... More

Contact structures with singularitiesJun 14 2018We study singular contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential forms, called $b^m$-contact ... More

Rigidity of infinitesimal momentum mapsOct 20 2014Sep 11 2015In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. ... More

Coupling symmetries with Poisson structuresJan 07 2013We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's splitting theorem for ... More

Zeroth Poisson homology, foliated cohomology and perfect Poisson manifoldsSep 04 2017We prove that for regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group and we give some applications. In particular, we show that for regular unimodular Poisson manifolds top Poisson and foliated cohomology ... More

Geometric quantization of integrable systems with hyperbolic singularitiesAug 03 2008Feb 04 2009We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the ... More

Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systemsFeb 24 2003Jul 30 2004We consider an integrable Hamiltonian system with n-degrees of freedom whose first integrals are invariant under the symplectic action of a compact Lie group G. We prove that the singular Lagrangian foliation associated to this Hamiltonian system is symplectically ... More

Weakly Hamiltonian actionsFeb 10 2016May 03 2016In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian ... More

A note on equivariant normal forms of Poisson structuresOct 25 2005Mar 17 2006We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse structure has ... More

Rigidity of Hamiltonian actions on Poisson manifoldsFeb 01 2011Oct 16 2011This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of SCI-type. This ... More

On geometric quantization of $b$-symplectic manifoldsAug 30 2016We study a notion of pre-quantization for $b$-symplectic manifolds. We use it to construct a formal geometric quantization of $b$-symplectic manifolds equipped with Hamiltonian torus actions with nonzero modular weight. We show that these quantizations ... More

Singular fibers of the Gelfand--Cetlin system on $\mathfrak{u}(n)^*$Mar 22 2018Apr 01 2018In this paper, we show that every singular fiber of the Gelfand--Cetlin system on coadjoint orbits of unitary groups is a smooth isotropic submanifold which is diffeomorphic to a $2$-stage quotient of a compact Lie group by free actions of two other compact ... More

Action-angle variables and a KAM theorem for b-Poisson manifoldsFeb 11 2015Mar 02 2015In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for ... More

Euler flows and singular geometric structuresJan 31 2019Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting $k$ independent closed one-forms fibers over a torus $T^k$. In this article we explain a version of this construction for manifolds ... More

On geometric quantization of $b^m$-symplectic manifoldsJan 11 2018We study the formal geometric quantization of $b^m$-symplectic manifolds equipped with Hamiltonian actions of a torus $T$ with nonzero leading modular weight. The resulting virtual $T-$modules are finite dimensional when $m$ is odd, as in \cite{gmw2}; ... More

Convexity of the moment map image for torus actions on $b^m$-symplectic manifoldsJan 03 2018We prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a $b^m$-symplectic manifold.

Desingularizing $b^m$-symplectic structuresDec 16 2015May 16 2017A $2n$-dimensional Poisson manifold $(M ,\Pi)$ is said to be $b^m$-symplectic if it is symplectic on the complement of a hypersurface $Z$ and has a simple Darboux canonical form at points of $Z$ which we will describe below. In this paper we will discuss ... More

Codimension one symplectic foliations and regular Poisson structuresSep 06 2010Jun 21 2011In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. ... More

Desingularizing $b^m$-symplectic structuresDec 16 2015A Poisson manifold $(M^{2n} ,\Pi)$ is said to be $b^m$-symplectic if it is symplectic on the complement of a hypersurface $Z$ and has a simple Darboux canonical form at points of $Z$ (which we will describe below). In this paper we will discuss a desingularization ... More

Symplectic and Poisson geometry on b-manifoldsJun 10 2012Feb 06 2014Let $M^{2n}$ be a Poisson manifold with Poisson bivector field $\Pi$. We say that $M$ is b-Poisson if the map $\Pi^n:M\to\Lambda^{2n}(TM)$ intersects the zero section transversally on a codimension one submanifold $Z\subset M$. This paper will be a systematic ... More

Examples of integrable and non-integrable systems on singular symplectic manifoldsDec 28 2015We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes ... More

Geometric quantization of semitoric systems and almost toric manifoldsMay 02 2017May 23 2017Kostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations given by integrable systems ... More

A note on symplectic topology of $b$-manifoldsDec 27 2013Nov 11 2015A Poisson manifold $(M^{2n},\p)$ is $b$-symplectic if $\bigwedge^n\p$ is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions pertaining to $b$-symplectic manifolds. We provide constructions ... More

Eigenvalue Asymptotics for a Schrödinger Operator with Non-Constant Magnetic Field Along One DirectionJan 20 2015Oct 16 2015We consider the discrete spectrum of the two-dimensional Hamiltonian $H=H_0+V$, where $H_0$ is a Schr\"odinger operator with a non-constant magnetic field $B$ that depends only on one of the spatial variables, and $V$ is an electric potential that decays ... More

Torsion Sections of Semistable Elliptic SurfacesAug 21 1992Let S be a torsion section of an elliptic surface with only I_n fibers. This article addresses the question: which components of singular fibers can S pass through? We give necessary criteria for the "component numbers", and show an equidistribution result ... More

Characterization of arbitrage-free marketsMar 23 2005The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem \refMainTheoremCharNA, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) ... More

Large deviations for cascades of diffusions arising in oscillating systems of interacting Hawkes processesSep 27 2017We consider oscillatory systems of interacting Hawkes processes introduced in Ditlevsen and Loecherbach (2017) to model multi-class systems of interacting neurons together with the diffusion approximations of their intensity processes. This diffusion, ... More

Newton strata in the loop group of a reductive groupMay 31 2010May 04 2011We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that elements of the ... More

Regeneration for interacting particle systems with interactions of infinite rangeNov 24 2009Feb 27 2011We consider an interacting particle system on $\Z^d$ with finite state space and interactions of infinite range in a high-noise regime. Assuming that the rate of change is continuous and that a Dobrushin-like condition holds, we show that the process ... More

Absolute continuity of the invariant measure in Piecewise Deterministic Markov Processes having degenerate jumpsJan 26 2016We consider piecewise deterministic Markov processes with degenerate transition kernels of the "house-of-cards"-type. We use a splitting scheme based on jump times to prove the absolute continuity, as well as some regularity, of the invariant measure ... More

The global structure of moduli spaces of polarized p-divisible groupsMar 28 2007We study the global structure of moduli spaces of quasi-isogenies of polarized p-divisible groups introduced by Rapoport and Zink. Using the corresponding results for non-polarized p-divisible groups from a previous paper, we determine their dimensions ... More

Connected components of closed affine Deligne-Lusztig varietiesJul 26 2006Jul 30 2007We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. Especially, we show that such an affine Deligne-Lusztig variety has isolated points if and ... More

Rack invariants of links in $L(p,1)$Mar 01 2017Dec 18 2017We describe a presentation for the augmented fundamental rack of a link in the lens space $L(p,1)$. Using this presentation, the (enhanced) counting rack invariants that have been defined for the classical links are applied to the links in $L(p,1)$. In ... More

Moduli spaces of p-divisible groupsFeb 15 2005Apr 27 2007We study the global structure of moduli spaces of quasi-isogenies of p-divisible groups introduced by Rapoport and Zink. We determine their dimensions and their sets of connected components and of irreducible components. If the isocrystals of the p-divisible ... More

Singular Riemannian Foliations: Exceptional Leaves; TautnessDec 17 2008For a singular Riemannian foliation whose leaves are properly embedded, we show in the first part of this article the existence of global tubular neighbourhoods, and we develop a global description of the foliation as stratification by types of leaves. ... More

A model for the parabolic slices Per_1(e^{2πi p/q}) in moduli space of quadratic rational mapsJan 26 2010The notion of relatedness loci in the parabolic slices Per_1(e^{2\pi i p/q}) in moduli space of quadratic rational maps is introduced. They are counterparts of the disconnectedness or escape locus in the slice of quadratic polynomials. A model for these ... More

Duality, Compactification, and $e^{-1/λ}$ Effects in the Heterotic String TheoryNov 24 1996Two classes of stringy instanton effects, stronger than standard field theory instantons, are identified in the heterotic string theory. These contributions are established using type IIA/heterotic and type I/heterotic dualities. They provide examples ... More

Gradient flow for the Boltzmann entropy and Cheeger's energy on time-dependent metric measure spacesNov 29 2016We introduce notions of dynamic gradient flows on time-dependent metric spaces as well as on time-dependent Hilbert spaces. We prove existence of solutions for a class of time dependent energy functionals in both settings. In particular we are interested ... More

Constructing biquandlesOct 06 2018We define biquandle structures on a given quandle, and show that any biquandle is given by some biquandle structure on its underlying quandle. We characterize all biquandles with a given underlying quandle. Using this characterization, we obtain a relationship ... More

Neuroevolutionary optimizationApr 20 2010This paper presents an application of evolutionary search procedures to artificial neural networks. Here, we can distinguish among three kinds of evolution in artificial neural networks, i.e. the evolution of connection weights, of architectures, and ... More

Constructive decomposition of functions of two variables using functions of one variableFeb 27 2007Given a compact set K in the plane, which contains no triple of points forming a vertical and a horizontal segment, and a continuous real-valued map f on K, we give a construction of real-valued continuous maps of one variable g,h such that f(x,y)=g(x)+h(y) ... More

The dimension of some affine Deligne-Lusztig varietiesMar 28 2006Jul 21 2006We prove Rapoport's dimension conjecture for affine Deligne-Lusztig varieties for GL_h and superbasic b. From this case the general dimension formula for affine Deligne-Lusztig varieties for special maximal compact subgroups of split groups follows, as ... More

Toric actions on b-symplectic manifoldsSep 07 2013Mar 05 2014We study Hamiltonian actions on $b$-symplectic manifolds with a focus on the effective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classifies these manifolds using polytopes that reside in a certain ... More

An Invitation to Singular Symplectic GeometryMay 10 2017In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure. At the end of ... More

Convexity for Hamiltonian torus actions on $b$-symplectic manifoldsDec 08 2014May 11 2016In [GMPS] we proved that the moment map image of a $b$-symplectic toric manifold is a convex $b$-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on $b$-symplectic manifolds. The modular ... More

Miracle at the Gepner PointMar 23 1995Mar 26 1995A four-point function of $E_6$ singlets, of interest in elucidating the moduli space of (0,2) deformations of the quintic string vacuum, is computed using analytic and numerical methods. The conformal field theory amplitude satisfies the requisite selection ... More

Structural Stability and Immunogenicity of PeptidesApr 19 2010We investigated the role of peptide folding stability in peptide immunogenicity. It was the aim of this thesis to implement a stability criterion based on energy computations using an AMBER force field, and to test the implementation with a large dataset. ... More

Stability for the determination of unknown boundary and impedance with a Robin boundary conditionApr 13 2010We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the boundary.

Cell decomposition and definable functions for weak p-adic structuresMay 18 2012We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted addition.

A Cartan-Eilenberg spectral sequence for a non-normal extensionNov 13 2018Jan 19 2019Let $\Phi\to \Gamma\to \Sigma$ be a conormal extension of Hopf algebras over a commutative ring $k$, and let $M$ be a $\Gamma$-comodule. The Cartan-Eilenberg spectral sequence $$ E_2 = \mathrm{Ext}_\Phi(k,\mathrm{Ext}_\Sigma(k,M)) \implies \mathrm{Ext}_\Gamma(k,M)$$ ... More

Radix Representations, Self-Affine Tiles, and Multivariable WaveletsFeb 22 2010We investigate the connection between radix representations for Z^n and self-affine tilings of R^n. We apply our results to show that Haar-like multivariable wavelets exist for all dilation matrices that are sufficie

Knot symmetries and the fundamental quandleJul 16 2017We establish a relationship between the knot symmetries and the automorphisms of the knot quandle. We identify the homeomorphisms of the pair $(S^{3},K)$ that induce the (anti)automorphisms of the fundamental quandle $Q(K)$. We show that every quandle ... More

Twisted Alexander Modules of Complex Essential Hyperplane Arrangement ComplementsOct 18 2017We study the torsion properties of the twisted Alexander modules of the affine complement M of complex essential hyperplane arrangements, as well as those of punctured stratified tubular neighborhoods of complex essential hyperplane arrangements. We investigate ... More

Large-Small Equivalence in String TheoryJan 08 1992The simplest toroidally compactified string theories exhibit a duality between large and small radii: compactification on a circle, for example, is invariant under R goes to 1/R. Compactification on more general Lorentzian lattices (i.e. toroidal compactification ... More

Dimensional Mutation and Spacelike SingularitiesOct 05 2005Feb 27 2006I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield the consistent ... More

Propagation of Gravitational Waves in Generalized TeVeSJan 11 2010Efforts are underway to improve the design and sensitivity of gravitational waves detectors, with the hope that the next generation of these detectors will observe a gravitational wave signal. Such a signal will not only provide information on dynamics ... More

Minimal geodesics and topological entropy on T^2Jul 04 2007Let (T^2, g) be a two-dimensional Riemannian torus. In this paper we prove that the topological entropy of the geodesic flow restricted to the set of initial conditions of minimal geodesics vanishes, independent of the choice of the Riemannian metric. ... More

AdS and dS Entropy from String JunctionsAug 26 2003Flux compactifications of string theory exhibiting the possibility of discretely tuning the cosmological constant to small values have been constructed. The highly tuned vacua in this discretuum have curvature radii which scale as large powers of the ... More

TASI/PiTP/ISS Lectures on Moduli and MicrophysicsMay 09 2004I review basic forces on moduli that lead to their stabilization, for example in the supercritical and KKLT models of de Sitter space in string theory, as well as an $AdS_4\times S^3\times S^3$ model I include which is not published elsewhere. These forces ... More

Localization-induced Griffiths phase of disordered Anderson latticesMar 13 2000Jan 05 2001We demonstrate that local density of states fluctuations in disordered Anderson lattice models universally lead to the emergence of non-Fermi liquid (NFL) behavior. The NFL regime appears at moderate disorder (W = W_c) and is characterized by power-law ... More

Dynamical mean-field theories of correlation and disorderDec 28 2011We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe the standard DMFT approach, which is exact in the limit of large coordination, ... More

Localization effects in disordered Kondo latticesAug 11 1998We investigate the role of localization effects in the Kondo disorder mechanism for non-Fermi liquid behavior in disordered Kondo lattices. We find that the distribution of Kondo temperatures is strongly affected by fluctuations of the conduction electron ... More

Substructures in lens galaxies: PG1115+080 and B1555+375, two fold configurationsSep 24 2007Sep 27 2007We study the anomalous flux ratio which is observed in some four-image lens systems, where the source lies close to a fold caustic. In this case two of the images are close to the critical curve and their flux ratio should be equal to unity, instead in ... More

Z-dark search with the ATLAS detectorAug 30 2016The search of the "hidden sector" via new neutral light bosons Z-dark ($Z_{d}$) could be revealed by the study of the decay of the discovered Higgs-like boson or any other undiscovered Higgs boson. After the LHC concluded a successful first period of ... More

Linear Systems on Edge-Weighted GraphsMay 02 2011Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are R-valued functions on the set of vertices and graph edges are permitted to have nonegative weights in R. Using this generalization, we provide ... More

Quantum Cohomology of Rational SurfacesOct 27 1994In this article formulas for the quantum product of a rational surface are given, and used to give an algebro-geometric proof of the associativity of the quantum product for strict Del Pezzo surfaces, those for which $-K$ is very ample. An argument for ... More

Degenerations of Planar Linear SystemsFeb 21 1997Apr 03 1998Fixing $n$ general points $p_i$ in the plane, what is the dimension of the space of plane curves of degree $d$ having multiplicity $m_i$ at $p_i$ for each $i$? In this article we propose an approach to attack this problem, and demonstrate it by successfully ... More

Inflationary Steps in the Planck DataDec 03 2013We extend and improve the modeling and analysis of large-amplitude, sharp inflationary steps for second order corrections required by the precision of the Planck CMB power spectrum and for arbitrary Dirac-Born-Infeld sound speed. With two parameters, ... More

What lies between a free adiabatic expansion and a quasi-static one?Sep 26 2012An expression is found that relates the initial and final volumes and temperatures for any adiabatic process. It is given in terms of a parameter r that smoothly interpolates between a free adiabatic expansion (r = 0) and a quasi-static one (r = 1). The ... More

How to transform, with a capacitor, thermal energy into usable workAug 10 2012The temperature dependence of the dielectric permittivity is taken into account to study the energy change in a capacitor that follows a cycle between a cold and a hot thermal reservoirs. There is a net energy gain in the process that, in principle, can ... More

Possible Relevance of Odd Frequency Pairing to Heavy Fermion SuperconductivityOct 07 1994What is the character of the gapless quasiparticles in heavy fermion superconductors (HFSC)? We discuss an odd-frequency pairing interpretation of HFSC which leads to a two component model for the quasiparticle excitations. In this picture, line zeroes ... More

Non-uniform phases in metals with local momentsJan 14 2005The two-dimensional Kondo lattice model with both nearest and next-nearest neighbor exchange interactions is studied within a mean-field approach and its phase diagram is determined. In particular, we allow for lattice translation symmetry breaking. We ... More

Homogeneous interpolation on ten pointsNov 29 2008In this paper we prove that for all pairs $(d,m)$ with $d/m \geq 174/55$, the linear system of plane curves of degree $d$ with ten general base points of multiplicity $m$ has the expected dimension.

Theory of tangential idealizers and tangentially free idealsAug 06 2009Jun 20 2017We generalize the theory of logarithmic derivations through a self-contained study of modules here dubbed tangential idealizers. We establish reflexiveness criteria for such modules, provided the ring is a factorial domain. As a main consequence, necessary ... More

Formal Equivalence Between Normal Forms of Reversible and Hamiltonian Dynamical SystemsMar 02 2011We show the existence of formal equivalences between reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory.

Discrete Spectrum of Quantum Hall Effect Hamiltonians II. Periodic Edge PotentialsJan 05 2011May 27 2011We consider the unperturbed operator $H_0: = (-i \nabla - {\bf A})^2 + W$, self-adjoint in $L^2({\mathbb R}^2)$. Here ${\bf A}$ is a magnetic potential which generates a constant magnetic field $b>0$, and the edge potential $W = \bar{W}$ is a ${\mathcal ... More

K3 Surfaces, N=4 Dyons, and the Mathieu Group M24May 28 2010Jun 03 2010A close relationship between K3 surfaces and the Mathieu groups has been established in the last century. Furthermore, it has been observed recently that the elliptic genus of K3 has a natural interpretation in terms of the dimensions of representations ... More

The Spectra of Supersymmetric States in String TheoryJul 19 2008In this thesis we study the spectra of supersymmetric states in string theory compactifications with eight and sixteen supercharges, with special focus placed on the quantum states of black holes and the phenomenon of wall-crossing in these theories. ... More

On non-smooth vector fields having a torus or a sphere as the sliding manifoldJul 02 2012In this paper we consider a non-smooth vector field $Z=(X,Y)$, where $X,Y$ are linear vector fields in dimension 3 and the discontinuity manifold $\Sigma$ of $Z$ is or the usual embedded torus or the unitary sphere at origin. We suppose that $\Sigma$ ... More

Note on the representation of the gap formation probability for real and quaternion Wishart matricesJul 16 2016Wishart random matrices are often used to model multivariate systems in physics, finance, biology and wireless communication. Extreme value statistics, such as those of the smallest eigenvalue, can be used to test the accuracy of the model. In this article ... More

Exact bounds of the M{ö}bius inverse of monotone set functionsMar 30 2015We give the exact upper and lower bounds of the M{\"o}bius inverse of monotone and normalized set functions (a.k.a. normalized capacities) on a finite set of n elements. We find that the absolute value of the bounds tend to 4 n/2 $\sqrt$ $\pi$n/2 when ... More

Internal Kinematics of Microstructures and ImplicationsOct 14 2003High resolution images at different wavelengths show the common presence of structures and microstructures in planetary nebulae (PNe), which are not well incorporated to the existing models for the formation of these objects. We summarize how studies ... More

Entropy generation in a chemical reactionAug 10 2012Entropy generation in a chemical reaction is analyzed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic equation of an ... More

Adiabatic reversible compression: a molecular viewAug 13 2012The adiabatic compression (or expansion) of an ideal gas has been analysed. Using the kinetic theory of gases the usual relation between temperature and volume is obtained, while textbooks follow a thermodynamic approach. In this way we show once again ... More

Theoretical method for the study of the excited states of a systemJun 21 2012A novel, exact, theoretical method for the study of the excited states of a system is presented. It is demonstrated how to transform the excited state problem of one Hamiltonian into the ground state problem of an auxiliary one. From this, a new exact ... More

Stringy Model of Cosmological Dark EnergyOct 16 2007A string field theory(SFT) nonlocal model of the cosmological dark energy providing w<-1 is briefly surveyed. We summarize recent developments and open problems, as well as point out some theoretical issues related with others applications of the SFT ... More

QGP time formation in holographic shock waves model of heavy ion collisionsMar 07 2015We estimate the thermalization time in two colliding shock waves holographic model of heavy-ion collisions. For this purpose we model the process by the Vaidya metric with a horizon defined by the trapped surface location. We consider two bottom-up AdS/QCD ... More