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Computationally-secure and composable remote state preparationApr 12 2019We introduce a protocol between a classical polynomial-time verifier and a quantum polynomial-time prover that allows the verifier to securely delegate to the prover the preparation of certain single-qubit quantum states. The protocol realizes the following ... More

Rigidity of quantum steering and one-sided device-independent verifiable quantum computationDec 23 2015Sep 29 2016The relationship between correlations and entanglement has played a major role in understanding quantum theory since the work of Einstein, Podolsky and Rosen (1935). Tsirelson (1980) proved that Bell states, shared among two parties, when measured suitably, ... More

Verification of quantum computation: An overview of existing approachesSep 20 2017Jul 09 2018Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can check whether ... More

Robustness and device independence of verifiable blind quantum computingFeb 09 2015Apr 28 2015Recent advances in theoretical and experimental quantum computing bring us closer to scalable quantum computing devices. This makes the need for protocols that verify the correct functionality of quantum operations timely and has led to the field of quantum ... More

A Theoretical Approach for Dynamic Modelling of Sustainable DevelopmentFeb 28 2011This article presents a theoretical model for a dynamic system based on sustainable development. Due to the relatively absence of theoretical studies and practical issues in the area of sustainable development, Romania aspires to the principles of sustainable ... More

Macrostate Parameter and Investment Risk Diagrams for 2008 and 2009Jan 24 2011In this paper are made some considerations of the application of phenomenological thermodynamics in risk analysis for the transaction on financial markets, using the concept of economic entropy and the macrostate parameter introduced by us in a previous ... More

Economic Amplifier - A New Econophysics ModelJul 25 2007Most of the econometric and econophysics models have been borrowed from the statistical physics, and as a cosequence, a new interdisciplinary science called econophysics has emerged. In this paper we planned to extend the analogy between different economic ... More

Quantum cryptanalysis of symmetric, public-key and hash-based cryptographic schemesFeb 06 2019Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum ... More

Entanglement transformations using separable operationsMay 02 2007Sep 19 2007We study conditions for the deterministic transformation $\ket{\psi}\longrightarrow\ket{\phi}$ of a bipartite entangled state by a separable operation. If the separable operation is a local operation with classical communication (LOCC), Nielsen's majorization ... More

Surface plasmon resonances of clustered nanoparticlesApr 29 2011Linear clusters made by tightly connecting two or more metallic nanoparticles have new types of surface plasmon resonances as compared to isolated nanoparticles. These new resonances are related to the size of the junction and to the number of interconnected ... More

Universal Uncertainty RelationsApr 23 2013Dec 11 2013Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs \emph{entropic ... More

Quantum circuit optimizations for NISQ architecturesApr 03 2019Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum circuit describing ... More

Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs EffectsNov 21 2013Jan 09 2015We argue that generic off-diagonal vacuum and nonvacuum solutions for Einstein manifolds mimic physical effects in modified gravity theories (MGTs) and encode certain models of the $f(R,T,...)$, Ho\v{r}ava type with dynamical Lorentz symmetry breaking, ... More

Fault tolerant resource estimation of quantum random-access memoriesFeb 04 2019Quantum random-access look-up of a string of classical bits is a necessary ingredient in several important quantum algorithms. In some cases, the cost of such quantum random-access memory (qRAM) is the limiting factor in the implementation of the algorithm. ... More

Entering New Markets-a Challenge in Times of CrisisOct 28 2010After September 2008, the advanced economies severe decline caused demand for emerging economies' exports to drop and the crisis became truly global, much deeper and broader than expected. In these times of global depression, most countries and companies ... More

A Geometric View of the Sieve of EratosthenesDec 25 2011Feb 07 2012We study the geometry of the Sieve of Eratosthenes. We introduce some concepts as Focals and Extremes. We find a symmetry in the distribution of the Focals (all the information about the primes is contained into a small set of numbers). We find that there ... More

Uniform Model of Geometric SpacesNov 02 2010Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of uniform equations ... More

Sharp Uncertainty Principles on Finsler Manifolds: the effect of curvatureNov 25 2013Nov 28 2013In this paper we investigate the validity of uncertainty principles (Heisenberg-Pauli-Weyl inequality, Hardy inequality and their interpolation inequality) on non-compact, complete Finsler manifolds with vanishing mean covariation. The present study is ... More

Gauge freeness for Cuntz-Pimsner algebrasMay 31 2018To every $C^*$ correspondence over a $C^*$-algebra one can associate a Cuntz-Pimsner algebra generalizing crossed product constructions, graph $C^*$-algebras, and a host of other classes of operator algebras. Cuntz-Pimsner algebras come equipped with ... More

Spinors as automorphisms of the tangent bundleOct 27 2002Apr 11 2003We show that, on a 4-manifold M endowed with a spin^c structure induced by an almost-complex structure, a self-dual (= positive) spinor field \phi \in \Gamma(W^+) is the same as a bundle morphism \phi: TM \to TM acting on the fiber by self-dual conformal ... More

On the scattering for the $\bar{\partial}$- equation and reconstruction of convection termsMar 26 2004In this paper we reconstruct convection terms from boundary measurements.We reduce the Beals and Coifman inverse scattering scattering formalism from a first order system to a formalism for the $\bar{\partial}$ equation.

Characteristic varieties and logarithmic differential 1-formsMay 28 2008Nov 13 2008We introduce in this paper a hypercohomology version of the resonance varieties and obtain some relations to the characteristic varieties of rank one local systems on a smooth quasi-projective complex variety $M$, see Theorem (3.1) and Corollaries (3.2) ... More

Calabi-Yau structures on cotangent bundlesOct 28 2013Oct 31 2013Starting with an orientable compact real-analytic Riemannian manifold $(L,g)$ with $\chi(L)=0$, we show that a small neighbourhood $ \textrm{Op}(L) $ of the zero section in the cotangent bundle $T^{*}L$ carries a Calabi-Yau structure such that the zero ... More

Veronese Algebras and Modules of Rings with Straightening LawsJan 13 2012Do the Veronese rings of an algebra with straightening laws (ASL) still have an ASL structure? We give positive answers to this question in some particular cases, namely for the second Veronese algebra of Hibi rings and of discrete ASLs. We also prove ... More

Non-crossing linked partitions, the partial order << on NC(n), and the S-transformJan 09 2009Jan 29 2009The paper establishes a connection between two recent combinatorial developments in free probability: the non-crossing linked partitions introduced by Dykema in 2007 to study the S-transform, and the partial order << on NC(n) introduced by Belinschi and ... More

Gauge freeness for Cuntz-Pimsner algebrasMay 31 2018Apr 04 2019To every $C^*$ correspondence over a $C^*$-algebra one can associate a Cuntz-Pimsner algebra generalizing crossed product constructions, graph $C^*$-algebras, and a host of other classes of operator algebras. Cuntz-Pimsner algebras come equipped with ... More

A survey of Floer homology for manifolds with contact type boundary or Symplectic homologyMar 22 2004The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for manifolds with ... More

Ricci identities of the Liouville d-vector fields z^2 and z^2Jul 07 2009Jul 30 2012It is the purpose of the present paper to outline an introduction in theory of embeddings in the manifold Osc^{2}M. First, we recall the notion of 2-osculator bundle. The second section is dedicated to the notion of submanifold in the total space of the ... More

Quantum rigidity of negatively curved manifoldsMar 27 2015We show that an isometric action of a compact quantum group on the underlying geodesic metric space of a compact connected Riemannian manifold $(M,g)$ with strictly negative curvature is automatically classical, in the sense that it factors through the ... More

On quantum symmetries of compact metric spacesJul 03 2014Jul 04 2014An action of a compact quantum group on a compact metric space $(X,d)$ is (D)-isometric if the distance function is preserved by a diagonal action on $X\times X$. We show that an isometric action in this sense has the following additional property: The ... More

Grothendieck rings of universal quantum groupsJun 17 2010We determine the Grothendieck ring of finite-dimensional comodules for the free Hopf algebra on a matrix coalgebra, and similarly for the free Hopf algebra with bijective antipode and other related universal quantum groups. The results turn out to be ... More

Existence of foliations on 4-manifoldsFeb 25 2003Dec 14 2003We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures on most 4-manifolds. ... More

Circular CNOT Circuits: Definition, Analysis and Application to Fault-Tolerant Quantum CircuitsApr 11 2016The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the starting point ... More

Curvature on the integers, IIDec 08 2015In a prequel to this paper \cite{curvature1} a notion of curvature on the integers was introduced, based on the technique of "analytic continuation between primes", introduced in \cite{laplace}. In this paper, which is essentially independent of its prequel, ... More

On the Milnor monodromy of the irreducible complex reflection arrangementsJun 13 2016Jun 22 2016Using recent results by A. Macinic, S. Papadima and R. Popescu, and a refinement of an older construction of ours, we determine the monodromy action on $H^1(F(G),C)$, where $F(G)$ denotes the Milnor fiber of a hyperplane arrangement associated to an irreducible ... More

Jacobian syzygies, stable reflexive sheaves, and Torelli properties for projective hypersurfaces with isolated singularitiesAug 10 2014Mar 04 2015We investigate the relations between the syzygies of the Jacobian ideal of the defining equation for a projective hypersurface $V$ with isolated singularities and the Torelli properties of $V$ (in the sense of Dolgachev-Kapranov). We show in particular ... More

SurfBraid: A concept tool for preparing and resource estimating quantum circuits protected by the surface codeFeb 06 2019The first generations of quantum computers will execute fault-tolerant quantum circuits, and it is very likely that such circuits will use surface quantum error correcting codes. To the best of our knowledge, no complete design automation tool for such ... More

Transient one-dimensional diffusions conditioned to converge to a different limit pointOct 01 2015Let $(X_t)_{t\geq 0}$ be a regular one-dimensional diffusion that models a biological population. If one assumes that the population goes extinct in finite time it is natural to study the $Q$-process associated to $(X_t)_{t\geq 0}$. This is the process ... More

Differential operators on modular forms (mod p)Jun 29 2018Jul 30 2018We give a survey of recent work on the construction of differential operators on various types of modular forms (mod p). We also discuss a framework for determining the effect of such operators on the mod p Galois representations attached to Hecke eigenforms. ... More

Siegel modular forms (mod p) and algebraic modular formsJun 13 2003In a letter to Tate, Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions on an adelic double coset space constructed from the endomorphism algebra of a supersingular ... More

Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangementsDec 07 2010May 10 2011The order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and sufficient condition for the triviality of this monodromy operator is given. It is known that ... More

Morse theory, closed geodesics, and the homology of free loop spacesJun 12 2014This is a survey paper on Morse theory and the existence problem for closed geodesics. The free loop space plays a central role, since closed geodesics are critical points of the energy functional. As such, they can be analyzed through variational methods. ... More

Three results on representations of Mackey Lie algebrasMar 11 2014I. Penkov and V. Serganova have recently introduced, for any non-degenerate pairing $W\otimes V\to\mathbb C$ of vector spaces, the Lie algebra $\mathfrak{gl}^M=\mathfrak{gl}^M(V,W)$ consisting of endomorphisms of $V$ whose duals preserve $W\subseteq V^*$. ... More

Centers, cocenters and simple quantum groupsDec 19 2012Sep 15 2013We define the notion of a (linearly reductive) center for a linearly reductive quantum group, and show that the quotient of a such a quantum group by its center is simple whenever its fusion semiring is free in the sense of Banica and Vergnioux. We also ... More

Categorical aspects of compact quantum groupsAug 26 2012We show that either of the two reasonable choices for the category of compact quantum groups is nice enough to allow for a plethora of universal constructions, all obtained "by abstract nonsense" via the adjoint functor theorem. This approach both recovers ... More

Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebrasOct 31 2011Mar 07 2014The question of whether or not a Hopf algebra $H$ is faithfully flat over a Hopf subalgebra $A$ has received positive answers in several particular cases: when $H$ (or more generally, just $A$) is commutative, or cocommutative, or pointed, or when $K$ ... More

Ranks of overpartitions: asymptotics and inequalitiesApr 15 2019In this paper we compute asymptotics for $ \overline{N}(a,c,n), $ the number of overpartitions of $ n $ with rank congruent to $ a $ modulo $ c. $ As an application we prove, among others, some inequalities conjectured by Ji, Zhang and Zhao (2018), and ... More

A quick survey of foliations on 4-manifoldsFeb 26 2003Apr 15 2003We present a few general results on foliations of 4-manifolds by surfaces: existence, tautness, relations to minimal genus of embedded surfaces; as well as some open problems. We hope to stimulate interest in this area.

Location of quantum information in additive graph codesDec 10 2009Mar 27 2010The location of quantum information in various subsets of the qudit carriers of an additive graph code is discussed using a collection of operators on the coding space which form what we call the information group. It represents the input information ... More

Arithmetic analogues of some basic concepts from Riemannian geometryMar 09 2015Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are stated to the effect ... More

Differential calculus with integersAug 23 2013Ordinary differential equations have an arithmetic analogue in which functions are replaced by numbers and the derivation operator is replaced by a Fermat quotient operator. In this survey we explain the main motivations, constructions, results, applications, ... More

Freeness versus maximal global Tjurina number for plane curvesAug 20 2015Dec 08 2015We give a characterization of nearly free plane curves in terms of their global Tjurina numbers, similar to the characterization of free curves as curves with a maximal Tjurina number, due to A. A. du Plessis and C.T.C. Wall. It is also shown that an ... More

The Poincaré-Deligne polynomial of Milnor fibers of triple point line arrangements is combinatorially determinedSep 15 2014Using a recent result by S. Papadima and A. Suciu, we show that the equivariant Poincar\'e-Deligne polynomial of the Milnor fiber of a projective line arrangement having only double and triple points is combinatorially determined.

Geometric aspects of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds with applicationsFeb 05 2015Feb 17 2015In this paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform estimates via Gromov's covering ... More

On the irreducible components of characteristic varietiesMar 09 2007This is a quick survey on the characteristic varieties associated to rank one local systems on a smooth, irreducible, quasi-projective complex variety $M$. A key new result is Proposition 1.8, giving additional information on the constructible sheaf $\F=R^0f_*(\LL)$, ... More

All Siegel Hecke eigensystems (mod p) are cuspidalNov 30 2005May 23 2006We show that the systems of Hecke eigenvalues occurring in the spaces of Siegel modular forms (mod p) of fixed dimension g, fixed level N, and varying weight, are the same as the systems occurring in the spaces of Siegel cusp forms with the same parameters ... More

The Kunneth formula in Floer homology for manifolds with restricted contact type boundaryMar 22 2004Aug 26 2005We prove the Kunneth formula in Floer (co)homology for manifolds with restricted contact type boundary. We use Viterbo's definition of Floer homology, involving the symplectic completion by adding a positive cone over the boundary. The Kunneth formula ... More

Versality, bounds of global Tjurina numbers and logarithmic vector fields along hypersurfaces with isolated singularitiesApr 01 2019We recall first the relations between the syzygies of the Jacobian ideal of the defining equation for a projective hypersurface $V$ with isolated singularities and the versality properties of $V$, as studied by du Plessis and Wall. Then we show how the ... More

Distinguishing Hecke eigenformsApr 27 2010We revisit a theorem of Ram Murty about the number of initial Fourier coefficients that two cuspidal eigenforms of different weights can have in common. We prove an explicit upper bound on this number, and give better conditional and unconditional asymptotic ... More

Parametrizations of Ideals in K[x,y] and K[x,y,z]Jan 13 2012We parametrize the affine space of Artinian affine ideals of K[x,y] which have a given initial ideal with respect to the degree reverse lexicographic term order. The fact that the term order is degree compatible allows us to extend the parametrization ... More

About intrinsic Finsler connections for the homogeneous lift to the Osculator Bundle of a Finsler metricFeb 08 2013In this article we present a study of the subspaces of the manifold OscM, the total space of the osculator bundle of a real manifold M. We obtain the induced connections of the canonical metrical N-linear connection determined by the homogeneous prolongation ... More

New features of the first eigenvalue on negatively curved spacesOct 15 2018The paper is devoted to the study of fine properties of the first eigenvalue on negatively curved spaces. First, depending on the parity of the space dimension, we provide asymptotically sharp harmonic-type expansions of the first eigenvalue for large ... More

Approximation for the distribution of extremes of one dependent stationary sequences of random variablesNov 23 2012In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation error. An application ... More

Relative Fourier transforms and expectations on coideal subalgebrasFeb 09 2018Jul 13 2018For an algebraic compact quantum group $H$ we establish a bijection between the set of right coideal $*$-subalgebras $A\to H$ and that of left module quotient $*$-coalgebras $H\to C$. It turns out that the inclusion $A\to H$ always splits as a map of ... More

On the Influence of Initial Qubit Placement During NISQ Circuit CompilationNov 22 2018Jan 30 2019Noisy Intermediate-Scale Quantum (NISQ) machines are not fault-tolerant, operate few qubits (currently, less than hundred), but are capable of executing interesting computations. Above the quantum supremacy threshold (approx. 60 qubits), NISQ machines ... More

Freeness versus maximal degree of the singular subscheme for surfaces in $P^3$Sep 07 2015Sep 11 2015We show that a free surface in $P^3$ is characterized by the maximality of the degree of its singular subscheme, in the presence of an additional tameness condition. This is similar to the characterization of free plane curves by the maximality of their ... More

Transcendental numbers as solutions to arithmetic differential equationsAug 26 2014Arithmetic differential equations are analogues of algebraic differential equations in which derivative operators acting on functions are replaced by Fermat quotient operators acting on numbers. Now, various remarkable transcendental functions are solutions ... More

New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact caseFeb 05 2015Feb 07 2019In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform estimates via Gromov's ... More

Parkable convex sets and finite-dimensional Hilbert spacesMar 29 2016A subset of a convex body $B$ containing the origin in a Euclidean space is {\it parkable in $B$} if it can be translated inside $B$ in such a manner that the translate the origin. We provide characterizations of ellipsoids and of centrally symmetric ... More

Characteristic varieties and constructible sheavesFeb 28 2007May 18 2007We explore the relation between the positive dimensional irreducible components of the characteristic varieties of rank one local systems on a smooth surface and the associated (rational or irrational) pencils. Our study, which may viewed as a continuation ... More

Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular formsAug 31 2003In a letter to Tate (published in Israel J. Math. in 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions on an adelic double coset space constructed ... More

Syzygies of Jacobian ideals and defects of linear systemsOct 05 2012Dec 24 2012Our main result describes the relation between the syzygies involving the first order partial derivatives $f_0,...,f_n$ of a homogeneous polynomial $f\in \C[x_0,...x_n]$ and the defect of the linear systems vanishing on the singular locus subscheme $\Sigma_f=V(f_0,...,f_n)$ ... More

On the connectivity of some complete intersectionsJul 25 2005We show that the complement of a degree $d$ hypersurface in a projective complete intersection, whose defining equations have degrees strictly larger than $d$, has a rational connectivity higher than expected. The key new feature is that a positivity ... More

Sharp uncertainty principles on Riemannian manifolds: the influence of curvatureNov 25 2013Jun 20 2017We present a rigidity scenario for complete Riemannian manifolds supporting the Heisenberg-Pauli-Weyl uncertainty principle with the sharp constant in $\mathbb R^n$ (shortly, sharp HPW principle). Our results deeply depend on the curvature of the Riemannian ... More

Differential modular forms attached to newforms mod pSep 18 2014In a previous paper we attached to classical complex newforms $f$ of weight $2$ certain $\delta_p$-modular forms $f^{\sharp}$ of order $2$ and weight $0$; the forms $f^{\sharp}$ can be viewed as "dual" to $f$ and played a key role in some of the applications ... More

Ricci identities of the Liouville d-vector fields z^(1)alpha and z^(2)alphaJul 27 2012It is the purpose of the present paper to outline an introduction in theory of embeddings in the manifold Osc^{2}M. First, we recall the notion of 2-osculator bundle. The second section is dedicated to the notion of submanifold in the total space of the ... More

Free unitary groups are (almost) simpleOct 17 2012We show that the quotients of Wang and Van Daele's universal quantum groups by their centers are simple in the sense that they have no normal quantum subgroups, thus providing the first examples of simple compact quantum groups with non-commutative fusion ... More

Stable ample 2-vector bundles on Hirzebruch surfacesJul 11 2013We discuss stability conditions for all rank-2 ample vector bundles on Hirzebruch surfaces with the second Chern class less than 7.

Curve arrangements, pencils, and Jacobian syzygiesJan 04 2016Feb 08 2016Let $\mathcal C :f=0$ be a curve arrangement in the complex projective plane. If $\mathcal C$ contains a curve subarrangement consisting of at least three members in a pencil, then one obtains an explicit syzygy among the partial derivatives of the homogeneous ... More

On the topology of some quasi-projective surfacesApr 27 2015May 13 2015Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental groups and the ... More

On the syzygies and Hodge theory of nodal hypersurfacesOct 20 2013Nov 03 2016We give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and the author for ... More

Monodromy of triple point line arrangementsJul 12 2011Dec 11 2012We show that the monodromy operator action on the first cohomology group of the Milnor fiber is combinatorially determined for line arrangements with at most triple points and containing at most 18 lines, with one possible exception.

p-jets Of p-isogeniesApr 01 2011p-jets of finite flat maps of schemes are generally neither finite nor flat. This phenomenon can be seen already in the case of p-isogenies of group schemes. However, for p-divisible groups, this pathology tends to disappear mod p "in the limit". We illustrate ... More

Fibered Symplectic Cohomology and the Leray-Serre Spectral SequenceMar 10 2005Jul 24 2007We define Symplectic cohomology groups for a class of symplectic fibrations with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex ... More

Complex dynamics and invariant forms mod pMay 02 2005May 31 2005Complex dynamical systems on the Riemann sphere do not possess ``invariant forms''. However there exist non-trivial examples of dynamical systems, defined over number fields, satisfying the property that their reduction modulo $\wp$ possesses ``invariant ... More

Upper bound on the number of systems of Hecke eigenvalues for Siegel modular forms (mod p)Dec 22 2003May 23 2006We derive an explicit upper bound for the number of systems of Hecke eigenvalues coming from Siegel modular forms (mod p) of dimension g and level N relatively prime to p. In the special case of elliptic modular forms (g=1), our result agrees with recent ... More

Multi-variable subordination distributions for free additive convolutionOct 14 2008Oct 30 2008Let k be a positive integer and let D_k denote the space of joint distributions for k-tuples of selfadjoint elements in C*-probability space. The paper studies the concept of "subordination distribution of \mu \boxplus \nu with respect to \nu" for \mu, ... More

Subcoalgebras and endomorphisms of free Hopf algebrasFeb 17 2010Jun 17 2010For a matrix coalgebra $C$ over some field, we determine all small subcoalgebras of the free Hopf algebra on $C$, the free Hopf algebra with a bjective antipode on $C$, and the free Hopf algebra with antipode $S$ satisfying $S^{2d}={\rm id}$ on $C$ for ... More

Metric measure spaces supporting Gagliardo-Nirenberg inequalities: volume non-collapsing and rigiditiesDec 23 2013Aug 25 2016Let $({M},\textsf{d},\textsf{m})$ be a metric measure space which satisfies the Lott-Sturm-Villani curvature-dimension condition $\textsf{CD}(K,n)$ for some $K\geq 0$ and $n\geq 2$, and a lower $n-$density assumption at some point of $M$. We prove that ... More

Nowhere-zero harmonic spinors and their associated self-dual 2-formsOct 31 2001Apr 11 2003Let M be a closed oriented 4-manifold, with Riemannian metric g, and a spin^C structure induced by an almost-complex structure \omega. Each connection A on the determinant line bundle induces a unique connection \nabla^A, and Dirac operator \D^A on spinor ... More

Residually finite quantum group algebrasOct 05 2014We show that provided $n\ne 3$, the involutive Hopf *-algebra $A_u(n)$ coacting universally on an $n$-dimensional Hilbert space has enough finite-dimensional representations in the sense that every non-zero element acts non-trivially in some finite-dimensional ... More

Differential eigenformsJun 28 2006The aim of this paper is to show how differential characters of Abelian varieties can be used to construct differential modular forms of weight 0 and order 2 which are eigenvectors of Hecke operators. These differential modular forms have "essentially ... More

Dedekind complete posets from sheaves on von Neumann algebrasJul 31 2013We show that for any two von Neumann algebras $M$ and $N$, the space of non-unital normal homomorphisms $N\to M$ with finite support, modulo conjugation by unitaries in $M$, is Dedekind complete with respect to the partial order coming from the addition ... More

On epimorphisms and monomorphisms of Hopf algebrasJul 16 2009Dec 29 2009We provide examples of non-surjective epimorphisms $H\to K$ in the category of Hopf algebras over a field, even with the additional requirement that $K$ have bijective antipode, by showing that the universal map from a Hopf algebra to its enveloping Hopf ... More

Laplace operators on holomorphic Lie algebroidsSep 07 2017The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined ... More

Hilbert Function and Betti Numbers of Algebras with Lefschetz Property of Order mJul 16 2007Jul 19 2007The authors T.Harima, J.C.Migliore, U.Nagel and J.Watanabe characterized the Hilbert function of algbebras with the Lefschetz property. We extend this characterization to algebras with the Lefschetz property m times. We also give upper bounds for the ... More

Translations in quantum groupsSep 30 2018Nov 30 2018Let $H$ be the Hopf $C^*$-algebra of continuous functions on a (locally) compact quantum group of either reduced or full type. We show that endomorphisms of $H$ that respect its right regular comodule structure are translations by elements of largest ... More

Generic quantum metric rigidityAug 15 2018Nov 30 2018We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric measure spaces appropriately, ... More

Topological generation results for free unitary and orthogonal groupsApr 08 2019We show that for every $N\ge 3$ the free unitary group $U^+_N$ is topologically generated by its classical counterpart $U_N$ and the lower-rank $U^+_{N-1}$. This allows for a uniform inductive proof that a number of finiteness properties, known to hold ... More

When is the diagonal functor Frobenius?Feb 23 2009Jun 04 2009Given a complete, cocomplete category $\mathcal C$, we investigate the problem of describing those small categories $I$ such that the diagonal functor $\Delta:\mathcal C\to {\rm Functors}(I,\mathcal C)$ is a Frobenius functor. This condition can be rephrased ... More