Results for "Adrian Hagerty"

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Relaxation of Functionals in the Space of Vector-Valued Functions of Bounded HessianFeb 08 2018In this paper it is shown that if $\Omega \subset \mathbb{R}^N$ is an open, bounded Lipschitz set, and if $f: \Omega \times \mathbb{R}^{d \times N \times N} \rightarrow [0, \infty)$ is a continuous function with $f(x, \cdot)$ of linear growth for all ... More
Synchronicity, Instant Messaging and Performance among Financial TradersOct 03 2011Successful animal systems often manage risk through synchronous behavior that spontaneously arises without leadership. In critical human systems facing risk, such as financial markets or military operations, our understanding of the benefits associated ... More
Charged and Neutral Currents in a 3-3-1 Model with Right-Handed NeutrinosDec 29 2007The charged and the neutral currents are obtained by using a formal algebraical approach (developed and applied by the author) within the exact solution of a 3-3-1 gauge model with right-handed neutrinos. The entire Standard Model phenomenology is recovered ... More
Book review of SUPERSTITION by Robert ParkJan 13 2009The 2008 book Superstition: Belief in the age of science, by Robert Park, published by Princeton University Press is briefly reviewed.
Metric inequalities for polygonsDec 19 2009Jun 21 2012Let $A_1,A_2,...,A_n$ be the vertices of a polygon with unit perimeter, that is $\sum_{i=1}^n |A_i A_{i+1}|=1$. We derive various tight estimates on the minimum and maximum values of the sum of pairwise distances, and respectively sum of pairwise squared ... More
ECA-RuleML: An Approach combining ECA Rules with temporal interval-based KR Event/Action Logics and Transactional Update LogicsOct 30 2006Nov 10 2006An important problem to be addressed within Event-Driven Architecture (EDA) is how to correctly and efficiently capture and process the event/action-based logic. This paper endeavors to bridge the gap between the Knowledge Representation (KR) approaches ... More
Initial Conditions and Global Event Properties from Color Glass CondensateAug 30 2010Perturbative unitarization from non-linear effects is thought to deplete the gluon density for transverse momenta below the saturation scale. Such effects also modify the distribution of gluons produced in heavy-ion collisions in transverse impact parameter ... More
Relative Property (T) for the Subequivalence Relations Induced by the Action of SL$_2(\Bbb Z)$ on $\Bbb T^2$Jan 13 2009Let $\Cal S$ be the equivalence relation induced by the action SL$_2(\Bbb Z)\curvearrowright (\Bbb T^2,\lambda^2)$, where $\lambda^2$ denotes the Haar measure on the 2-torus, $\Bbb T^2$. We prove that any ergodic subequivalence relation $\Cal R$ of $\Cal ... More
Beable-Guided Quantum Theories: Generalising Quantum Probability LawsApr 26 2012We introduce the idea of a {\it beable-guided quantum theory}. Beable-guided quantum theories (BGQT) are generalisations of quantum theory, inspired by Bell's concept of beables. They modify the quantum probabilities for some specified set of fundamental ... More
Unconditionally Secure Bit Commitment by Transmitting Measurement OutcomesAug 14 2011Apr 02 2012We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen BB84 qubits to the committer at a given point in space-time. The ... More
Unconditionally Secure Bit Commitment with Flying QuditsJan 24 2011Oct 25 2011In the task cryptographers call bit commitment, one party encrypts a prediction in a way that cannot be decrypted until they supply a key, but has only one valid key. Bit commitment has many applications, and has been much studied, but completely and ... More
The Many Worlds of Hugh Everett IIIMar 21 2011Jun 21 2011A review of Peter Byrne's biography of Hugh Everett III, "The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family", (Oxford University Press, 2010).
A No-summoning theorem in Relativistic Quantum TheoryJan 24 2011Jul 08 2012Alice gives Bob an unknown localized physical state at some point P. At some point Q in the causal future of P, Alice will ask Bob for the state back. Bob knows this, but does not know at which point Q until the request is made. Bob can satisfy Alice's ... More
Nonlinearity without SuperluminalityApr 18 2002May 11 2005Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Czachor, Gisin ... More
Quasiclassical Dynamics in a Closed Quantum SystemDec 11 1995Jun 03 1996We consider Gell-Mann and Hartle's consistent histories formulation of quantum cosmology in the interpretation in which one history, chosen randomly according to the decoherence functional probabilities, is realised from each consistent set. We show that ... More
A derivation of Witten's conjecture relating Donaldson and Seiberg-Witten invariantsMar 23 2000May 02 2000We generalize Witten's conjectured formula relating Donaldson and Seiberg-Witten invariants to manifolds of non-simple type, via equivariant localization techniques. This approach does not use the theory of non-abelian monopoles, but works directly on ... More
On the Spectrum of the Generalised Petersen GraphsDec 11 2014Apr 10 2015We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs $P(n,k)$ tends to zero as $n \rightarrow \infty$. Moreover, we provide explicit upper bounds on the size of this gap. It follows that these graphs have poor expansion ... More
A new realization of the Langlands correspondence for PGL(2,F)Oct 11 2012In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters of elliptic ... More
On the Riemann Hypothesis and the Difference Between PrimesFeb 26 2014May 20 2014We prove some results concerning the distribution of primes on the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval $(x-\frac{4}{\pi} \sqrt{x} \log x,x]$ for all $x \geq 2$; this improves a result of Ramar\'{e} ... More
Depth and Stanley Depth of the Canonical Form of a factor of monomial idealsFeb 24 2014Apr 05 2014In this paper we show that the depth and the Stanley depth of the factor of two monomial ideals is invariant under taking a so called canonical form. It follows easily that the Stanley Conjecture holds for the factor if and only if it holds for its canonical ... More
Orbit equivalence and Borel reducibility rigidity for profinite actions with spectral gapSep 12 2013Jul 30 2015We study equivalence relations $\mathcal R(\Gamma\curvearrowright G)$ that arise from left translation actions of countable groups on their profinite completions. Under the assumption that the action $\Gamma\curvearrowright G$ is free and has spectral ... More
On the local constants of simple supercuspidal representations of GL(n,F)Jul 17 2013Apr 29 2014In this paper, we explicitly compute the standard epsilon factors on both sides of the local Langlands correspondence for simple supercuspidal representations of GL(n,F).
On deriving nonreflecting boundary conditions in generalized curvilinear coordinatesJan 20 2015In this work, nonreflecting boundary conditions in generalized three-dimensional curvilinear coordinates are derived, relying on the original analysis that was done in Cartesian two-dimensional coordinates by Giles (AIAA Journal, 28.12, 2050-2058, 1990). ... More
Lorentzian Quantum Reality: Postulates and Toy ModelsNov 11 2014We describe postulates for a novel realist version of relativistic quantum theory or quantum field theory in Minkowski space or other background spacetimes with suitable asymptotic properties. We illustrate their application in toy models.
Scaling Behaviour of the Maximal Growth Rate in the Rosensweig InstabilityJul 16 2001The dependence of the maximal growth rate of the modes of the Rosensweig instability on the properties of the magnetic fluid and the external magnetic induction is studied. An expansion and a fit procedure are applied in the appropriate ranges of the ... More
Dynamic Markov BasesMar 25 2011We present a computational approach for generating Markov bases for multi-way contingency tables whose cells counts might be constrained by fixed marginals and by lower and upper bounds. Our framework includes tables with structural zeros as a particular ... More
Time-dependent CP asymmetries in charm decaysNov 01 2011The CKM paradigm has been tested thoroughly over the last 40 years in both the neutral $K$ and $B$ systems. The recent discovery of neutral charm meson mixing has prompted the search for CP violation in $D$ decays. We discuss the prospects of performing ... More
Nef line bundles over finite fieldsNov 27 2011We use Totaro's examples of non-semiample nef line bundles on smooth projective surfaces over finite fields to construct nef line bundles for which the first cohomology group cannot be killed by any generically finite covers. This is used to show a similar ... More
Moduli spaces of principal bundles on singular varietiesAug 31 2011Mar 21 2015Let k be an algebraically closed field of characteristic zero. Let f:X-->S be a flat, projective morphism of k-schemes of finite type with integral geometric fibers. We prove existence of a projective relative moduli space for semistable singular principal ... More
A note on k-jet ampleness on surfacesFeb 20 1998We prove Reider type criterions for k-jet spannedness and k-jet ampleness of adjoint bundles for surfaces with at most rational singularities. Moreover, we prove that on smooth surfaces [n(n+4)/4]-very ampleness implies n-jet ampleness.
Semistable modules over Lie algebroids in positive characteristicNov 12 2013Mar 26 2014We study Lie algebroids in positive characteristic and moduli spaces of their modules. In particular, we show a Langton's type theorem for the corresponding moduli spaces. We relate Langton's construction to Simpson's construction of gr-semistable Griffiths ... More
A Wiki for Business Rules in Open Vocabulary, Executable EnglishMar 03 2011The problem of business-IT alignment is of widespread economic concern. As one way of addressing the problem, this paper describes an online system that functions as a kind of Wiki -- one that supports the collaborative writing and running of business ... More
$\mathbb{Z}_{2}^{2}$-cordiality of complete and complete bipartite graphsSep 03 2007We prove that $K_{n}$ is $\mathbb{Z}_{2}^{2}$-cordial if and only if $1 \leq n \leq 3$ and that $K_{m,n}$ is $\mathbb{Z}_{2}^{2}$ if and only if it is false that $m=n=2$.
Algebraic structures in quantum gravitySep 30 2009Mar 01 2010Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with quantum field ... More
Generalization of the Bollobás-Riordan polynomial for tensor graphsDec 08 2010Jul 19 2011Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial $\mathcal T$ encoding the supplementary topological information. This polynomial is a natural generalization of the Bollob\'as-Riordan ... More
Extension of the Poincaré Symmetry and Its Field Theoretical ImplementationOct 31 2005May 29 2006We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding degrees of freedom, compatibility with Abelian gauge ... More
Shape universality classes in the random sequential addition of non-spherical particlesNov 09 2016Random sequential addition (RSA) models are used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the algebraic time dependence of the asymptotic jamming coverage as $t\to\infty$. For the RSA of ... More
Deformation subspaces of p-divisible groups as formal Lie groups associated to p-divisible groupsJul 20 2006Jun 15 2010Let $k$ be an algebraically closed field of characteristic $p>0$. Let $D$ be a $p$-divisible group over $k$ which is not isoclinic. Let $\scrD$ (resp. $\scrD_k$) be the formal deformation space of $D$ over $\Spf(W(k))$ (resp. over $\Spf(k)$). We use axioms ... More
On the S-fundamental group schemeMay 28 2009Jul 03 2010We introduce a new fundamental group scheme for varieties defined over an algebraically closed field of positive characteristic and we use it to study generalization of some of C. Simpson's results to positive characteristic. We also study the properties ... More
Two--loop heavy Higgs corrections to the Higgs fermionic widthMay 27 1994We calculate the two--loop electroweak corrections to the fermionic decay width of the Higgs boson at leading order in $m_{H}$. The sum of one--loop and two--loop radiative corrections turns out to be at 6% level over the whole range of $m_{H}$ where ... More
Two-loop virtual QCD correction to the B -> X_s l+l- decayMay 28 2003I discuss an application of numerical techniques for massive two-loop Feynman diagram evaluation to a phenomenologically very important rare decay process, B -> X_s l+l-. This process, currently being measured at B factories, has been calculated at two-loop ... More
Good Reductions of Shimura Varieties of Hodge Type in Arbitrary Unramified Mixed Characteristic, Part IIDec 10 2007Jul 24 2012We prove a conjecture of Milne pertaining to the existence of integral canonical models of Shimura varieties of abelian type in arbitrary unramified mixed characteristic $(0,p)$. As an application we prove for $p=2$ a motivic conjecture of Milne pertaining ... More
Integral models in unramified mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part IJul 15 2003Mar 27 2012Let $(G,X)$ be a Shimura variety of PEL type such that $G_{{\bf Q}_2}$ is a split ${\bf GSO}_{2n}$ group with $n\ge 2$. We prove the existence of the integral canonical models of ${\rm Sh}(G,X)/H_2$ in unramified mixed characteristic $(0,2)$, where $H_2$ ... More
Mod p classification of Shimura F-crystalsApr 02 2003Jan 20 2010Let $k$ be an algebraically closed field of positive characteristic $p$. We first classify the $D$-truncations mod $p$ of Shimura $F$-crystals over $k$ and then we study stratifications defined by inner isomorphism classes of these $D$-truncations. This ... More
On the Tate and Langlands--Rapoport conjectures for special fibres of integral canonical models of Shimura varieties of abelian typeOct 24 2012We prove the isogeny property for special fibres of integral canonical models of compact Shimura varieties of $A_n$, $B_n$, $C_n$, and $D_n^{\dbR}$ type. The approach used also shows that many crystalline cycles on abelian varieties over finite fields ... More
Integral Canonical Models of Shimura Varieties of Preabelian TypeJul 08 2003We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5.
Lifting zero-dimensional schemes and divided powersNov 14 2017Mar 07 2018We study divided power structures on finitely generated $k$-algebras, where $k$ is a field of positive characteristic $p$. As an application we show examples of $0$-dimensional Gorenstein $k$-schemes that do not lift to a fixed noetherian local ring of ... More
The circular $k$-partite crossing number of $K_{m,n}$May 09 2006We define a new kind of crossing number which generalizes both the bipartite crossing number and the outerplanar crossing number. We calculate exact values of this crossing number for many complete bipartite graphs and also give a lower bound.
Electro-weak $SU(4)_L\otimes U(1)_Y$ models without exotic electric chargesFeb 21 2009For the particular class of \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} electro-weak models without exotic electric charges, some plausible phenomenological predictions - such as the boson mass spectrum and charges of all the fermions involved therein - are ... More
Implementing Canonical Seesaw Mechanism in a 3-3-1 Gauge Model without Exotic Electric ChargesMay 13 2006We prove that - even at a low TeV scale - the canonical seesaw mechanism can be naturally implemented in the exact solution of a particular 3-3-1 gauge model, since a very small alteration $\epsilon$ in the parameter matrix of the Higgs sector is taken ... More
A note on heterogeneous decompositions into spanning treesMay 15 2006In answer to a question of Eggleton, we prove that the complete multigraph on 5 vertices with edge multiplicity 6, namely $K_{5}^{(6)}$, has a decomposition into 5 copies of the family of trees of order 5 and that $K_{7}^{(22)}$ has a decomposition into ... More
The traveling salesman problem for lines and rays in the planeApr 26 2012In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of $n$ regions (neighborhoods) and we seek a shortest tour that visits each region. In the path variant, we seek a shortest path that visits each region. We present several linear-time ... More
Quantum Reality via Late Time PhotodetectionAug 16 2016We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local variables that depend ... More
Rule-based Knowledge Representation for Service Level AgreementSep 21 2006Automated management and monitoring of service contracts like Service Level Agreements (SLAs) or higher-level policies is vital for efficient and reliable distributed service-oriented architectures (SOA) with high quality of ser-vice (QoS) levels. IT ... More
Color Glass Condensate at RHIC ?Mar 14 2002Heavy-ion collisions at the BNL-RHIC collider can probe whether gluon saturation effects in nuclei at small x have set in, or whether leading-twist perturbative estimates of particle production are still applicable. I discuss that soon to come data from ... More
Quantum Tagging for Tags Containing Secret Classical DataAug 31 2010Aug 27 2011Various authors have considered schemes for {\it quantum tagging}, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled ... More
Beyond Boundary Conditions: General Cosmological TheoriesMay 05 2009Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more useful possibility ... More
Unconditionally Secure Commitment of a Certified Classical Bit is ImpossibleOct 20 1999Nov 03 1999In a secure bit commitment protocol involving only classical physics, A commits either a 0 or a 1 to B. If quantum information is used in the protocol, A may be able to commit a state of the form $\alpha \ket{0} + \beta \ket{1}$. If so, she can also commit ... More
Coin Tossing is Strictly Weaker Than Bit CommitmentOct 22 1998Oct 29 1999We define cryptographic assumptions applicable to two mistrustful parties who each control two or more separate secure sites between which special relativity guarantees a time lapse in communication. We show that, under these assumptions, unconditionally ... More
Quantum Bit Commitment from a Computation BoundNov 26 1997Aug 20 1999This paper is withdrawn. See quant-ph/9806031 for a discussion.
Comment on "Spacetime Information"Oct 31 1996Mar 21 1997A recent paper by Hartle [Phys. Rev. D 51, 1800 (1995)] proposes a definition of "spacetime information" - the information available about a quantum system's boundary conditions in the various sets of decohering histories it may display - and investigates ... More
Unconditionally Secure Bit CommitmentOct 22 1998Aug 04 1999We describe a new classical bit commitment protocol based on cryptographic constraints imposed by special relativity. The protocol is unconditionally secure against classical or quantum attacks. It evades the no-go results of Mayers, Lo and Chau by requiring ... More
Permanently Secure Quantum Bit Commitment from a Temporary Computation BoundDec 01 1997Aug 20 1999This paper has been withdrawn. See quant-ph/9806031 for a discussion.
Unconditionally Secure Multi-Party ComputationNov 16 1997Feb 28 2005This paper was withdrawn on 20.11.97.
Quantum Histories and Their ImplicationsJul 30 1996May 23 2000Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region $R$ of space, then in these theories we can deduce that it is confined in regions containing $R$. ... More
Abc of SUSYMay 28 2009This article is a very basic introduction to supersymmetry. It introduces the two kinds of superfields needed for supersymmetric extensions of the Standard Model, the chiral superfield and the vector superfield, and discusses in detail how to construct ... More
A theoretical update on t \bar{t} production near thresholdApr 04 2006We present an evaluation of the t\bar{t} cross section near threshold at next-to-next-to-leading logarithmic accuracy, using a two-step matching procedure. QED corrections are taken into account as well and are shown to be numerically important. Finally ... More
The Physics Programme at SuperBDec 06 2011SuperB is a next generation high luminosity $e^+e^-$ collider that will be built at the Cabibbo Laboratory, Tor Vergata, in Italy. The physics goals of this experiment are to search for signs of physics beyond the Standard Model through precision studies ... More
Approximation of smooth functions using Bernstein polynomials in multiple variablesSep 07 2016In this survey, we use (more or less) elementary means to establish the well-known result that for any given smooth multivariate function, the respective multivariate Bernstein polynomials converge to that function in all derivatives on each compact set. ... More
On the Ext Ring of Koszul RingsJun 01 2015Sep 04 2015The aim of this article is to study the Ext ring associated to a Koszul $R$-ring and to use it to provide further characterisations of the former. As such, for $R$ being a semisimple ring and $A$ a graded Koszul $R$-ring, we will prove that there is an ... More
Graphical Modeling of Spatial Health DataNov 24 2014The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying graph is unknown ... More
An Explicit Result for $|L(1+it,χ)|$Sep 08 2014We give an explicit upper bound for non-principal Dirichlet $L$-functions on the line $s=1+it$. This result can be applied to improve the error in the zero-counting formulae for these functions.
Strong ergodicity, property (T), and orbit equivalence rigidity for translation actionsJun 25 2014We study equivalence relations that arise from translation actions $\Gamma\curvearrowright G$ which are associated to dense embeddings $\Gamma<G$ of countable groups into second countable locally compact groups. Assuming that $G$ is simply connected and ... More
Almost-Ramanujan Graphs and Prime GapsFeb 04 2014The method of Murty and Cioab\u{a} shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the search for perfect matchings and thus eliminates ... More
An Explicit Result for Primes Between CubesJan 17 2014We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-function with explicit bounds on the error term. We use this along ... More
Path Integrals and RealityMay 28 2013We define the idea of {\it real path quantum theory}, a realist generalisation of quantum theory in which it is postulated that the configuration space path actually followed by a closed quantum system is probabilistically chosen. This is done a postulate ... More
Parallelisation of PyHEADTAIL, a Collective Beam Dynamics Code for Particle Accelerator PhysicsOct 17 2016The longitudinal tracking engine of the particle accelerator simulation application PyHEADTAIL shows a heavy potential for parallelisation. For basic beam circulation, the tracking functionality with the leap-frog algorithm is extracted and compared between ... More
A remark on the Kottwitz homomorphismAug 11 2016Aug 15 2016We prove that for any split connected reductive group G over a p-adic field F, the Kottwitz homomorphism exhibits a homomorphic section.
Fermions in Rotating Reference FramesDec 02 2015Feb 24 2016Current quantisations of fermions in cylindrical coordinates are shown to be inadequate in calculating some single-particle expectation values. This paper develops an alternate quantisation, applicable to one-particle states, which is generalised to rotating ... More
Data structuring for the ontological modelling of wind energy systemsOct 12 2015Small wind projects encounter difficulties to be efficiently deployed, partly because wrong way data and information are managed. Ontologies can overcome the drawbacks of partially available, noisy, inconsistent, and heterogeneous data sources, by providing ... More
On the relation of three theorems of analysis to the axiom of choiceSep 03 2015Nov 21 2016In what follows, essentially two things will be accomplished: Firstly, it will be proven that a version of the Arzel\`a--Ascoli theorem and the Fr\'echet--Kolmogorov theorem are equivalent to the axiom of countable choice for subsets of real numbers. ... More
On the Langlands parameter of a simple supercuspidal representation: odd orthogonal groupsJan 29 2015In this work, we explicitly compute a certain family of twisted gamma factors of a simple supercuspidal representation $\pi$ of a $p$-adic odd orthogonal group. These computations, together with analogous computations for general linear groups carried ... More
Use of the gravitational-wave interferometers to test Lorentz invariance violationAug 10 2016Currently operating gravitational-wave interferometers are Michelson interferometers with effective arm length L ~ 4x10e5 m. While the interferometer remains in lock, data at the fsr sideband frequency encode information on slow phase changes in the f ... More
Kelvin force in a layer of magnetic fluidApr 09 2002The Kelvin force in a layer of magnetic fluid subjected to a homogeneous magnetic field and local heating is studied. The study is motivated by the question about the corresponding Kelvin force density [M. Liu, Phys. Rev. Lett., 2762 (2000)]. It is shown ... More
The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluidsApr 09 2002The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities ... More
Non-Orbit Equivalent Actions of $\Bbb F_n$Oct 16 2006Apr 07 2009For any $2\leq n\leq \infty$, we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $\Bbb F_n$. These actions arise as diagonal products between a generalized Bernoulli action and the action $\Bbb F_n\curvearrowright ... More
Semistable principal G-bundles in positive characteristicDec 12 2003Sep 27 2004Let $X$ be a normal projective variety defined over an algebraically closed field $k$ of positive characteristic. Let $G$ be a connected reductive group defined over $k$. We prove that some Frobenius pull back of a principal $G$-bundle admits the canonical ... More
The Multi-Orientable Random Tensor Model, a ReviewDec 07 2015Jun 15 2016After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of ... More
Translation-Invariant Noncommutative RenormalizationMar 25 2010Jun 08 2010We review here the construction of a translation-invariant scalar model which was proved to be perturbatively renormalizable on Moyal space. Some general considerations on nonlocal renormalizability are given. Finally, we present perspectives for generalizing ... More
Tensor models, a quantum field theoretical particularizationNov 19 2012Nov 20 2012Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and combinatorics of these ... More
Scalar and gauge translation-invariant noncommutative modelsAug 27 2008We make here a short overview of the recent developments regarding translation-invariant models on the noncommutative Moyal space. A scalar model was first proposed and proved renormalizable. Its one-loop renormalization group flow and parametric representation ... More
Feynman amplitudes in renormalizable non-commutative quantum field theoryNov 21 2007We consider here the Feynman amplitudes of renormalizable non-commutative quantum field theory models. Different representations (the parametric and the Mellin one) are presented. The latter further allows the proof of meromorphy of a amplitude in the ... More
Shimura Varieties and the Mumford-Tate conjecture, part ISep 14 2001We prove the Mumford-Tate conjecture for those abelian varieties over number fields, whose simple factors of their adjoint Mumford-Tate groups have over $\dbR$ certain (products of) non-compact factors. In particular, we prove this conjecture for the ... More
Some cases of the Mumford--Tate conjecture and Shimura varietiesDec 04 2002Dec 18 2007We prove the Mumford--Tate conjecture for those abelian varieties over number fields whose extensions to C have attached adjoint Shimura varieties that are products of simple, adjoint Shimura varieties of certain Shimura types. In particular, we prove ... More
Two-loop effects of enhanced electroweak strength in the Higgs sectorJul 28 1996Aug 11 1996The selfcoupling of the Higgs field grows with the mass of the Higgs particle and induces potentially large radiative corrections in the electroweak model. The technical aspects of performing multiloop calculations in the massive case are discussed briefly. ... More
The rate of convergence of some Riemann-Stieltjes sumsMar 13 2014We give the rate of convergence of some optimal lower Riemann-Stieltjes sums toward the integral.
Projective integral models of Shimura varieties of Hodge type with compact factorsAug 30 2004Mar 27 2007Let $(G,X)$ be a Shimura pair of Hodge type such that $G$ is the Mumford--Tate group of some elements of $X$. We assume that for each simple factor $G_0$ of $G^{\ad}$ there exists a simple factor of $G_{0\dbR}$ which is compact. Let $N\Ge 3$. We show ... More
Points of integral canonical models of Shimura varieties of preabelian type, p-divisible groups, and applications. First PartApr 13 2001Aug 16 2001This work is the first part in a series of three dedicated to the foundations of integral aspects of Shimura varieties and of Fontaine's categories. It deals mostly with the unramified context of (arbitrary) mixed characteristic (0,p). Among the topics ... More
Hypersymplectic four-dimensional Lie algebrasOct 29 2003A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures on four-dimensional ... More
On the outerplanar crossing numbers of complete multipartite graphsMay 10 2006We calculate the outerplanar crossing numbers of complete multipartite graphs which have $n$ partite sets with $m$ vertices and one partite set with $p$ vertices, where either $p|mn$ or $mn|p$.