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The diversity of symplectic Calabi-Yau six-manifoldsAug 30 2011Oct 14 2011Given an integer b and a finitely presented group G we produce a compact symplectic six-manifold with c_1 = 0, b_2 > b, b_3 > b and fundamental group G. In the simply-connected case we can also arrange for b_3 = 0; in particular these examples are not ... More

Complex surfaces with CAT(0) metricsOct 07 2010Jul 11 2011We study complex surfaces with locally CAT(0) polyhedral Kahler metrics and construct such metrics on CP^2 with various orbifold structures. In particular, in relation to questions of Gromov and Davis-Moussong we construct such metrics on a compact quotient ... More

Real line arrangements with Hirzebruch propertyJul 26 2016Aug 04 2016A line arrangement of $3n$ lines in $\mathbb CP^2$ satisfies Hirzebruch property if each line intersect others in $n+1$ points. Hirzebruch asked if all such arrangements are related to finite complex reflection groups. We give a positive answer to this ... More

Polyhedral Kahler ManifoldsJan 13 2009In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and classify the singularities ... More

Foliations with unbounded deviation on the two-dimensional torusDec 19 2002There exists a smooth foliation with 3 singular points on the two-dimensional torus such that any lifting of a leaf of this foliation on the universal covering of the torus is a dense subset of the covering.

Spherical metrics with conical singularities on a 2-sphere: angle constraintsMay 08 2015In this article we give a criterion for the existence of a metric of curvature $1$ on a $2$-sphere with $n$ conical singularities of prescribed angles $2\pi\vartheta_1,\dots,2\pi\vartheta_n$ and non-coaxial holonomy. Such a necessary and sufficient condition ... More

Symplectic generic complex structures on 4-manifolds with b_+ = 1Dec 16 2010We study symplectic structures on K\"ahler surfaces with p_g = 0. We give an example of a projective surface which admits a symplectic structure which is not compatible with any K\"ahler metric.

Enumeration of almost polynomial rational functions with given critical valuesApr 29 2005Enumerating ramified coverings of the sphere with fixed ramification types is a well-known problem first considered by A. Hurwitz. Up to now, explicit solutions have been obtained only for some families of ramified coverings, for instant, those realized ... More

Slope Stability and Exceptional Divisors of High GenusOct 22 2007Aug 06 2008We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse direction we ... More

Symplectic dominationMay 14 2019Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is a theorem ... More

Symplectic Calabi-Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifoldFeb 25 2008Mar 05 2008Given an SO(3)-bundle with connection, the associated two-sphere bundle carries a natural closed 2-form. Asking that this be symplectic gives a curvature inequality first considered by Reznikov. We study this inequality in the case when the base has dimension ... More

Counting Meromorphic Functions with Critical Points of Large MultiplicitiesSep 02 2002We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is $\CP^1$ and the function is a polynomial, we give an elementary way of ... More

Circle-invariant fat bundles and symplectic Fano 6-manifoldsJul 03 2014We prove that a compact 4-manifold which supports a circle-invariant fat SO(3)-bundle is diffeomorphic to either S^4 or CP^2-bar. The proof involves studying the resulting Hamiltonian circle action on an associated symplectic 6-manifold. Applying our ... More

Hyperbolic geometry and non-Kahler manifolds with trivial canonical bundleMay 20 2009Dec 22 2009We use hyperbolic geometry to construct simply-connected symplectic or complex manifolds with trivial canonical bundle and with no compatible Kahler structure. We start with the desingularisations of the quadric cone in C^4: the smoothing is a natural ... More

The telescopic construction; a microsurveyFeb 18 2014We overview few results which use the construction described in our paper "Telescopic actions".

Manin triples of real simple Lie algebras. Part 1Apr 28 1999The article is devoted to the problem of classification of Manin triples up to weak and gauge equivalence. The case of complex simple Lie algebras can be obtained by the papers of A.Belavin, V.Drinfel'd, M.Semenov-Tian-Shanskii. Studing the action of ... More

A gauge theoretic approach to Einstein 4-manifoldsDec 10 2013Aug 07 2016This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent ... More

Higher Whitehead products in moment-angle complexes and substitution of simplicial complexesJan 23 2019We study the question of realisability of iterated higher Whitehead products with a given form of nested brackets by simplicial complexes, using the notion of the moment-complex $Z_K$. Namely, we say that a simplicial complex $K$ realises an iterated ... More

Restriction and induction for supercharacters of finite groups of triangular typeOct 16 2016It is proved the the restriction of any supercharacter of a finite group of triangular type on its subgroup is a sum of supercharacters with nonnegative integer coefficients. We define superinduction and prove the analog of the Frobenius formula for supercharacters. ... More

Statistical inference for exponential functionals of Lévy processesDec 17 2013In this paper, we consider the exponential functional \(A_{\infty}=\int_0^\infty e^{-\xi_s}ds\) of a L{\'e}vy process \(\xi_s\) and aim to estimate the characteristics of \(\xi_{s}\) from the distribution of \(A_{\infty}\). We present a new approach, ... More

On the geometric median of triangular domains and other median type pointsNov 18 2018The geometric median of a domain is the point that minimises the average distance from itself to the points of the domain. We will give a gradient system of equations that defines the geometric median of a triangular domain and will prove a simple geometric ... More

On almost periodic viscosity solutions to Hamilton-Jacobi equationsJul 01 2017We establish that a viscosity solution to a multidimensional Hamilton-Jacobi equation with Bohr almost periodic initial data remains to be spatially almost periodic and the additive subgroup generated by its spectrum does not increase in time. In the ... More

Retrieving nonlinear refractive index of nanocomposites using finite-difference time-domain simulationsFeb 07 2018In recent decades, considerable attention has been given to the study of the composite materials with nonlinear optical properties. Particularly, metamaterials with the tailored nonlinear optical response are promising materials for a plethora of applications, ... More

Involutions in $S_n$ and associated coadjoint orbitsJan 19 2008In the paper we study the coadjoint orbits of the group $\mathrm{UT}(n,K)$ associated with involutions. We obtain a formula for dimension of the orbit. We construct a polarization for the canonical element of orbit. We find a system of generators in the ... More

New supercharacter theory for Sylow subgroups in orthogonal and symplectic groupsAug 26 2018Applying the embedding of $A_{n-1}$ in $B_n$, $C_n$ and $D_n$ we construct a new supercharacter theory for the Sylow subgroups in orthogonal and symplectic groups over a finite field. The constructed supercharacter appears to be a little bit more precise ... More

Finite Sample Bernstein -- von Mises Theorem for Semiparametric ProblemsOct 29 2013Jun 15 2014The classical parametric and semiparametric Bernstein -- von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain an upper bound ... More

On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions: global well-posedness and decay propertyJun 18 2014Jun 19 2014We study the Cauchy problem for a multidimensional scalar conservation law with merely continuous flux vector in the class of Besicovitch almost periodic functions. The existence and uniqueness of entropy solutions are established. We propose also the ... More

On the long time behavior of almost periodic entropy solutions to scalar conservation lawsJan 07 2017We found the precise condition for the decay as $t\to\infty$ of Besicovitch almost periodic entropy solutions of multidimensional scalar conservation laws. Moreover, in the case of one space variable we establish asymptotic convergence of the entropy ... More

Ramification conjecture and Hirzebruch's property of line arrangementsDec 24 2013Jun 24 2016The ramification of a polyhedral space is defined as the metric completion of the universal cover of its regular locus. We consider mainly polyhedral spaces of two origins: quotients of Euclidean space by a discrete group of isometries and polyhedral ... More

Reconstructing signal from fiber-optic measuring system with non-linear perceptronMar 05 2001A computer model of the feed-forward neural network with the hidden layer is developed to reconstruct physical field investigated by the fiber-optic measuring system. The Gaussian distributions of some physical quantity are selected as learning patterns. ... More

Quantum Zeno-like effect and spectra of particles in cascade transitionSep 16 2000Shr\"odinger equation for two-step spontaneous cascade transition in a three-level quantum system is solved by means of Markovian approximation for non-Markovian integro-differential evolution equations for amplitudes of states. It is shown that both ... More

Fields of fractions of quantum solvable algebrasJun 10 1999Nov 09 1999We introduce the notion of pure Q-solvable algebra. The quantum matrices, quantum Weyl algebra, U_q(n) are the examples. It is proved that the skew field of fractions of pure Q-solvable algebra is isomorphic to the skew field of twisted rational functions. ... More

On index of certain nilpotent Lie algebrasJan 19 2008We introduce the method of calculation of index of Lie algebras that are factors of the unitriangular Lie algebra with respect to ideals spanned by subsets of root vectors.

On decay of entropy solutions to multidimensional conservation lawsApr 02 2019Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.

On long time behavior of periodic entropy solutions of a degenerate non-linear parabolic equationFeb 12 2018We prove the asymptotic convergence of a space-periodic entropy solution of a one-dimensional degenerate parabolic equation to a traveling wave. It is also shown that on a segment containing the essential range of the limit profile the flux function is ... More

Supercharacters for the finite groups of triangular typeAug 24 2015We construct the supercharacter theory for the finite groups of triangular type. Its special case is the supercharacter theory for algebra groups of P.Diaconis and I.M.Isaacs. The supercharacter analog of the A.A. Kirillov formula for irreducible characters ... More

On variants of $H$-measures and compensated compactnessMar 25 2014We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we present new compensated ... More

Weighted graphs and complex Gaussian free fieldsMar 30 2018Apr 03 2018We prove a combinatorial lemma about the distribution of directed currents in a complex "loop soup" and use it to give a new proof of the isomorphism relating loop measures and complex Gaussian fields.

Deconfining phase transition in the 3D Georgi-Glashow model with finite Higgs-boson massApr 14 2002The (2+1)D Georgi-Glashow model is explored at finite temperature in the regime when the Higgs boson is not infinitely heavy. The resulting Higgs-mediated interaction of monopoles leads to the appearance of a certain upper bound for the parameter of the ... More

Confining strings in the Abelian-projected SU(3)-gluodynamics II. 4D-case with $θ$-termDec 01 2000Apr 11 2001The generalization of 4D confining string theory to the SU(3)-inspired case is derived. It describes string representation of the Wilson loop in the SU(3)-analogue of compact QED extended by the $\theta$-term. It is shown that although the obtained theory ... More

Aharonov-Bohm Effect in the Abelian-Projected SU(3)-QCD with $Θ$-termNov 29 1999By making use of the path-integral duality transformation, string representation of the Abelian-projected SU(3)-QCD with the $\Theta$-term is derived. Besides the short-range (self-)interactions of quarks (which due to the $\Theta$-term acquire a nonvanishing ... More

String Nature of Confinement in (Non-)Abelian Gauge TheoriesSep 29 1999May 09 2000Recent progress achieved in the solution of the problem of confinement in various (non-)Abelian gauge theories by virtue of a derivation of their string representation is reviewed. The theories under study include QCD within the so-called Method of Field ... More

Ensemble of Vortex Loops in the Abelian-Projected SU(3)-GluodynamicsAug 04 1999Sep 01 1999Grand canonical ensemble of small vortex loops emerging in the London limit of the effective Abelian-projected theory of the SU(3)-gluodynamics is investigated in the dilute gas approximation. An essential difference of this system from the SU(2)-case ... More

A Possible Universal Treatment of the Field Strength Correlator in the Abelian-Projected SU(2)-TheoryNov 05 2000Feb 12 2001An integral relation between two functions parametrizing the bilocal field strength correlator within the Stochastic Vacuum Model is obtained in the effective Abelian-projected SU(2)-theory. This relation is independent of the concrete properties of the ... More

On origami ringsFeb 27 2015In the paper "origami rings" by Joe Buhler et al. the authors investigate the so called origami rings. Taking this paper as a starting point we find some further properties of these rings.

Comment on gauge choices and physical variables in QEDMay 17 1994We consider possible definitions of physical variables in QED. We demonstrate that the condition $\partial_i A_i$$=0$ is the most convenient one because it leads to path integral over physical components with local action. However, other choices, as $A_3=0$, ... More

On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimizationAug 13 2015Jan 05 2016Various implementations of the Toffoli gate up to a relative phase have been known for years. The advantage over regular Toffoli gate is their smaller circuit size. However, their use has been often limited to a demonstration of quantum control in designs ... More

Yuri Safarov (1958-2015)Aug 22 2016This is the editor's preface to the special issue of Journal of Spectral Theory, in memory of Yuri Safarov.

The Kähler metric of a blow-upJul 10 2013After a review of the general properties of holomorphic spheres in complex surfaces we describe the local geometry in the vicinity of a CP^1 embedded with a negative normal bundle. As a by-product, we build (asymptotically locally hyperbolic) Kahler-Einstein ... More

The geometry of antiferromagnetic spin chainsJun 13 2012We construct spin chains that describe relativistic sigma-models in the continuum limit, using symplectic geometry as a main tool. The target space can be an arbitrary complex flag manifold, and we find universal expressions for the metric and theta-term. ... More

Comments on the del Pezzo coneMay 09 2014We describe a framework for constructing the general Ricci-flat metric on the anticanonical cone over the del Pezzo surface of rank one.

Asymptotic conformal welding via Loewner-Kufarev evolutionOct 28 2012The Loewner-Kufarev evolution produces asymptotics for mappings onto domains close to the unit disk or the exterior of the unit disk. We deduce variational formulae which lead to the asymptotic conformal welding for such domains. The comparison of mappings ... More

Koszul algebras associated to graphsFeb 15 2006Quadratic algebras associated to graphs have been introduced by I. Gelfand, S. Gelfand, and Retakh in connection with decompositions of noncommutative polynomials. Here we show that, for each graph with rare triangular subgraphs, the corresponding quadratic ... More

Upper bound on the number of edges of an almost planar bipartite graphJul 03 2013Let $G$ be a bipartite graph without loops and multiple edges on $v\ge 4$ vertices, which can be drawn on the plane such that any edge intersects at most one other edge. We prove that such graph has at most $3v-8$ edges for even $v\ne 6$ and at most $3v-9$ ... More

Lectures on scattering theoryMar 12 2004The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}. The last two ... More

Linear equations over noncommutative graded ringsApr 22 2004Jan 14 2005We call a graded connected algebra $R$ effectively coherent, if for every linear equation over $R$ with homogeneous coefficients of degrees at most $d$, the degrees of generators of its module of solutions are bounded by some function $D(d)$. For commutative ... More

The tree of decomposition of a biconnected graphMay 28 2014The tree of decomposition of a $k$-connected graph by a set $\mathfrak S$ of pairwise independent $k$-vertex cutsets is defined as follows. The vertices of this tree are cutsets of $\mathfrak S$ and parts of decomposition of the graph by the set $\mathfrak ... More

Towards on convolutions on configuration spaces. II. Spaces of locally finite configurationsOct 18 2012In the second part of the paper we consider a convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation measures and functionals. ... More

Around Ovsyannikov's methodDec 30 2014We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical assumptions of Ovsyannikov's ... More

Functional evolutions for homogeneous stationary death-immigration spatial dynamicsJul 19 2011We discover death-immigration non-equilibrium stochastic dynamics in the continuum also known as the Surgailis process. Explicit expression for the correlation functions is presented. Dynamics of states and their generating functionals are studied. Ergodic ... More

Metcalfe's Law RevisitedApr 18 2016Rudimentary mathematical analysis of simple network models suggests bandwidth-independent saturation of network growth dynamics and hints at linear decrease in information density of the data. However it strongly confirms Metcalfe's law as a measure of ... More

Clustering implies geometry in networksApr 06 2016May 19 2016Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble ... More

Can Spectral Action be a Window to Very High Energies?Oct 14 2015The principles of noncommutative geometry impose severe restrictions on the structure of (almost) commutative field theories. The Standard Model fits surprisingly well into the noncommutative framework. Here we overview some universal predictions of the ... More

Optimal and asymptotically optimal NCT reversible circuits by the gate typesFeb 08 2016Aug 22 2016We report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the realization of reversible ... More

Shear viscosity of a nonperturbative gluon plasmaFeb 10 2012Shear viscosity is evaluated within a model of the gluon plasma, which is based entirely on the stochastic nonperturbative fields. We consider two types of excitations of such fields, which are characterized by the thermal correlation lengths ~ 1/(g^2 ... More

Heavy-quark condensate at zero and finite temperatures for various forms of the short-distance potentialNov 04 2004With the use of the world-line formalism, the heavy-quark condensate in the SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the quark-antiquark potential at short distances is either quadratic, or linear. In the former case, which takes ... More

Topological and confining properties of Abelian-projected SU(3)-QCDAug 11 2000Sep 25 2000In this talk, we discuss several topics related to the Abelian-projected SU(3)-QCD. First of them is the Aharonov-Bohm effect emerging during the extension of this theory by the introduction of the $\Theta$-term. Another topic is devoted to various consequences ... More

The Abelian Higgs Model as an Ensemble of Vortex LoopsJun 04 1999Dec 30 1999In the London limit of the Ginzburg-Landau theory (Abelian Higgs model), vortex dipoles (small vortex loops) are treated as a grand canonical ensemble in the dilute gas approximation. The summation over these objects with the most general rotation- and ... More

Monopole potential and confining strings in the (2+1)-dimensional Georgi-Glashow modelSep 08 2001Confining strings are investigated in the (2+1)D Georgi-Glashow model. This is done in the limit when the electric coupling constant is much larger than the square root of the mass of the Higgs field, but much smaller than the vacuum expectation value ... More

Complex structures and zero-curvature equations for sigma-modelsMay 03 2016We construct zero-curvature representations for the equations of motion of a class of sigma-models with complex homogeneous target spaces, not necessarily symmetric. We show that in the symmetric case the proposed flat connection is gauge-equivalent to ... More

Integrable properties of sigma-models with non-symmetric target spacesDec 11 2014It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast ... More

Spanning trees with many leaves: lower bounds in terms of number of vertices of degree 1, 3 and at least~4May 23 2012We prove that every connected graph with $s$ vertices of degree~1 and 3 and $t$ vertices of degree at least~4 has a spanning tree with at least ${1\over 3}t +{1\over 4}s+{3\over 2}$ leaves. We present infinite series of graphs showing that our bound is ... More

Adjoint cohomology of graded Lie algebras of maximal classSep 16 2007We compute explicitly the adjoint cohomology of two N-graded Lie algebras of maximal class (infinite dimensional filiform Lie algebras) m_0 and m_2. It is known that up to an isomorphism there are only three N-graded Lie algebras of the maximal class. ... More

Exponential driving function for the Löwner equationJan 04 2012We consider the chordal L\"owner differential equation with the model driving function $\root3\of t$. Holomorphic and singular solutions are represented by their series. It is shown that a disposition of values of different singular and branching solutions ... More

Comformal mapping asymptotics at a cuspNov 02 2015We describe the asymptotic behavior of the mapping function at an analytic cusp compared with Kaiser's results for cusps with small perturbation of angles and the known explicit formulae for cusps with circular boundary curves. We propose a boundary curve ... More

Smooth and proper noncommutative schemes and gluing of DG categoriesFeb 28 2014Nov 17 2015In this paper we discuss different properties of noncommutative schemes over a field. We define a noncommutative scheme as a differential graded category of a special type. We study regularity, smoothness and properness for noncommutative schemes. Admissible ... More

Bilinear gauge operatorsAug 03 2016We construct a family of bilinear differential operators which satisfy certain gauge properties. These operators can be naturally associated with $q$-deformations of classical integrable hierarchies. In particular, we consider the case when gauge function ... More

Spectral geometry of symplectic spinorsAug 15 2015Oct 26 2015Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by K.~Habermann. Here we study the spectral geometry aspects of these operators. In particular, we define the associated distance function ... More

Landau-Ginzburg Models, D-branes, and Mirror SymmetryNov 12 2011This paper is an introduction to D-branes in Landau-Ginzburg models and Homological Mirror Symmetry. The paper is based on a series of lectures which were given on Second Latin Congress on Symmetries in Geometry and Physics that took place at the University ... More

Remarks on generators and dimensions of triangulated categoriesApr 07 2008Apr 16 2008In this paper we prove that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is equal to one. We also discuss dimension spectrums of these categories.

Mixed heavy-quark-gluon condensate in the stochastic vacuum model and dual superconductorJul 15 2005Sep 30 2005The world-line formalism is used for the evaluation of the mixed heavy-quark-gluon condensate in two models of QCD - the stochastic vacuum model and the dual superconductor one. Calculations are performed for an arbitrary dimensionality of space-time ... More

Heavy-quark condensate at zero- and nonzero temperatures for various forms of the short-distance potentialAug 04 2003With the use of the world-line formalism, the heavy-quark condensate in the SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the quark-antiquark potential at short distances is either quadratic, or linear. In the former case, the standard ... More

SU(N) fundamental and adjoint confining stringsApr 10 2003Sep 02 2003String representations of the Wilson loop are constructed in the SU(N)-version of compact QED in three and four dimensions. This is done exactly in the case of the fundamental Wilson loop and in the large-N limit in the case of the adjoint Wilson loop. ... More

String representation of the SU(N)-inspired dual Abelian-Higgs-type theory with the $Θ$-termJul 10 2002String representation of the $[U(1)]^{N-1}$ gauge-invariant dual Abelian-Higgs-type theory, which is relevant to the SU(N)-QCD with the $\Theta$-term and provides confinement of quarks, is derived. The N-dependence of the Higgs vacuum expectation value ... More

Confining Strings in the Abelian-Projected SU(3)-GluodynamicsMar 06 2000May 30 2000String representation of the Wilson loop in 3D Abelian-projected SU(3)-gluodynamics is constructed in the approximation that Abelian-projected monopoles form a gas. Such an assumption is much weaker than the standard one, demanding the monopole condensation. ... More

Accounting for the finiteness of the Higgs-boson mass in the 3D Georgi-Glashow modelJan 03 2002(2+1)-dimensional Georgi-Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W boson. In the weak-coupling limit, the Debye mass of the dual photon ... More

Field Correlators in Abelian-Projected Theories and Stochastic Vacuum ModelJun 14 2000The bilocal electric field strength correlators in Abelian-projected SU(2)- and SU(3)-theories are derived with accounting for the contributions to these quantities brought about by the virtual vortex loops, built out of the dual Nielsen-Olesen strings. ... More

Hadron Colliders and Hadron Collider Physics SymposiumJun 28 2013This article summarizes main developments of the hadron colliders and physics results obtained since their inception around forty years ago. The increase in the collision energy of over two orders of magnitude and even larger increases in luminosity provided ... More

Haldane limits via Lagrangian embeddingsApr 07 2011In the present paper we revisit the so-called Haldane limit, i.e. a particular continuum limit, which leads from a spin chain to a sigma model. We use the coherent state formulation of the path integral to reduce the problem to a semiclassical one, which ... More

Off-shell symmetry algebra of the AdS_4 x CP^3 superstringApr 01 2009By direct calculation in classical theory we derive the central extension of the off-shell symmetry algebra for the string propagating in AdS_4 x CP^3. It turns out to be the same as in the case of the AdS_5 x S^5 string. We also elaborate on the kappa-symmetry ... More

Study of Cronin effect and nuclear modification of strange particles in d-Au and Au-Au collisions at 200 GeV in PHENIXMay 31 2004Effects of strangeness on nuclear modification in d-Au and Au-Au collisions at 200 GeV are studied, in order to quantify the effects of quark content and mass. Measurements of ratios of the yields in central collisions to the yields in peripheral collisions ... More

Normal forms for almost non-integrable CR structuresDec 05 2008Oct 12 2017We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the Chern-Moser normalization into pure intrinsic setting, whereas the other directly ... More

A tensor interpretation of the 2D Dirac equationJun 17 2000We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron ... More

Flag manifold sigma-models: the 1/N-expansion and the anomaly two-formJan 09 2019We construct a gauged linear sigma-model representation and develop a 1/N-expansion for flag manifold sigma-models previously proposed by the author. Classically there exists a zero-curvature representation for the equations of motion of these models, ... More

A remark on Golod--Shafarevich algebrasDec 30 2014We show that a direct limit of surjections of (weak) Golod--Shafarevich algebras is a weak Golod--Shafarevich algebra as well. This holds both for graded and for filtered algebras provided that the filtrations are induced by the filtration of the first ... More

Algebras associated to pseudo-roots of noncommutative polynomials are KoszulMay 19 2004Quadratic algebras associated to pseudo-roots of noncommutative polynomials have been introduced by I. Gelfand, Retakh, and Wilson in connection with studying the decompositions of noncommutative polynomials. Later they (with S. Gelfand and Serconek) ... More

Spectral and scattering theory for differential and Hankel operatorsNov 15 2015We consider a class of Hankel operators $H$ realized in the space $L^2 ({\Bbb R}_{+}) $ as integral operators with kernels $h(t+s)$ where $h(t)=P (\ln t) t ^{-1}$ and $P(X)= X^n+p_{n-1} X^{n-1}+\cdots$ is an arbitrary real polynomial of degree $n$. This ... More

Obstructions to embeddability into hyperquadrics and explicit examplesDec 11 2006Oct 16 2007We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface ... More

A Duality Theorem for Quantum GroupoidsDec 29 1999We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras.

Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spacesJan 09 1998Jan 30 1998We prove that a germ of a holomorphic map $f$ between $C^n$ and $C^{n'}$ sending one real-algebraic submanifold $M\subset C^n$ into another $M'\subset C^{n'}$ is algebraic provided $M'$ contains no complex-analytic discs and $M$ is generic and minimal. ... More