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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

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

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

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

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

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.

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

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

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

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

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

Spherical surfaces with conical points: systole inequality and moduli spaces with many connected componentsJul 11 2018Jul 25 2019In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider some features ... More

Moment-angle manifolds and complexes. Lecture notes KAIST'2010Aug 30 2010Oct 15 2010These are notes of the lectures given during the Toric Topology Workshop at the Korea Advanced Institute of Science and Technology in February 2010. We describe several approaches to moment-angle manifolds and complexes, including the intersections 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

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

Hirzebruch genera of manifolds with torus actionOct 17 1999A quasitoric manifold is a smooth 2n-manifold M^{2n} with an action of the compact torus T^n such that the action is locally isomorphic to the standard action of T^n on C^n and the orbit space is diffeomorphic, as manifold with corners, to a simple polytope ... More

Semifree circle actions, Bott towers, and quasitoric manifoldsJul 04 2006Apr 04 2007A Bott tower is the total space of a tower of fibre bundles with base CP^1 and fibres CP^1. Every Bott tower of height n is a smooth projective toric variety whose moment polytope is combinatorially equivalent to an n-cube. A circle action is semifree ... More

On manifolds defined by 4-colourings of simple 3-polytopesMar 20 2017Let $\mathcal{P}$ be the class of combinatorial 3-dimensional simple polytopes $P$, different from a tetrahedron, without 3- and 4-belts of facets. By the results of Pogorelov and Andreev, a polytope $P$ admits a realisation in Lobachevsky space $\mathbb{L}^3$ ... More

Quantum algebraic toriApr 20 1998The author introduces the notion of a quantum form of an algebraic torus. In the case of diagonal algebraic torus we get the algebra of Laurent twisted polynomials. Quantum algebraic torus can be characterized in terms of exact sequences. The author study ... 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

On one criterion of the uniqueness of generalized solutions for linear transport equations with discontinuous coefficientsApr 03 2015We study generalized solutions of multidimensional transport equation with bounded measurable solenoidal field of coefficients $a(x)$. It is shown that any generalized solution satisfies the renormalization property if and only if the operator $a\cdot\nabla ... More

On the Cauchy problem for scalar conservation laws on the Bohr compactification of $\R^n$Aug 04 2014We study the Cauchy problem for a multidimensional scalar conservation law on the Bohr compactification of $\R^n$. The existence and uniqueness of entropy solutions are established in the general case of merely continuous flux vector. We propose also ... More

Decay of periodic entropy solutions to degenerate nonlinear parabolic equationsJan 15 2019Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddingsMar 25 2011May 18 2013We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the well-known Delzant construction ... More

Toric Topology. Chapter 2: Combinatorial structuresFeb 05 2011Oct 09 2012This is the second chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.

Toric TopologyOct 08 2012Jul 04 2014Toric topology emerged in the end of the 1990s on the borders of equivariant topology, algebraic and symplectic geometry, combinatorics and commutative algebra. It has quickly grown up into a very active area with many interdisciplinary links and applications, ... 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 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

On decay of almost periodic viscosity solutions to Hamilton-Jacobi equationsNov 08 2017We establish that a viscosity solution to a multidimensional Hamilton-Jacobi equation with a convex non-degenerate hamiltonian and Bohr almost periodic initial data decays to its infimum as time $t\to+\infty$.

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

On toric generators in the unitary and special unitary bordism ringsDec 16 2014Nov 18 2016We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also construct a family ... More

Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groupsMar 22 2016Sep 01 2016We construct and study polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, general graph product groups and their commutator subgroups. By way of application, we give a criterion of freeness for the commutator subgroup ... More

Representations of quantum ordersOct 06 2010We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted polynomials, the ... More

Dolbeault cohomology of complex manifolds with torus actionAug 18 2019We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM and LVMB-manifolds and, in most generality, complex manifolds ... More

Supercharacters of unipotent and solvable groupsNov 27 2016The notion of the supercharacter theory was introduced by P.Diaconis and I.M.Isaaks in 2008. In this paper we review the main statements of the general theory, we observe the construction of supercharacter theory for algebra groups and the theory of basic ... More

Supercharacter theory for groups of invertible elements of reduced algebrasSep 19 2014Jun 09 2015We construct a supercharacter theory for the group of invertible elements of a reduced algebra. For the case of the triangular group, we obtain the formula for values of supercharacters on superclasses.

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

Moment-angle complexes from simplicial posetsDec 11 2009Apr 28 2011We extend the construction of moment-angle complexes to simplicial posets by associating a certain T^m-space Z_S to an arbitrary simplicial poset S on m vertices. Face rings Z[S] of simplicial posets generalise those of simplicial complexes, and give ... More

Calculation of Hirzebruch genera for manifolds acted on by the group Z/p via invariants of the actionSep 15 1999Dec 29 2005We obtain general formulae expressing Hirzebruch genera of a manifold with Z/p-action in terms of invariants of this action (the sets of weights of fixed points). As an illustration, we consider numerous particular cases of well-known genera, in particular, ... More

On the commutator subgroup of a right-angled Artin groupFeb 01 2017Dec 19 2018We use polyhedral product models to analyse the structure of the commutator subgroup of a right-angled Artin group. In particular, we provide a minimal set of generators for the commutator subgroup, consisting of special iterated commutators of canonical ... More

Sweeping out sectional curvatureJun 19 2011Nov 27 2013We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements ... More

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

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.

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.

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

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

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

Conformal anomalies of CFT's with boundariesOct 06 2015Oct 11 2015The trace anomaly of conformal field theories in four dimensions is characterized by '$a$' and '$c$'-functions. The scaling properties of the effective action of a CFT in the presence of boundaries is shown to be determined by $a$, $c$ and two new functions ... More

Upper Bounds For Hitting Times Of Random Walks On Sparse GraphsFeb 13 2017We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random walk on a connected ... 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

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

Stein manifolds and multiplicity-free representations of compact Lie groupsApr 25 2010The paper is a survey of recent results in geometric representation theory describing group actions which induce multiplicity-free representations in the spaces of holomorphic functions. For connected compact Lie groups of automorphisms of Stein manifolds ... 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.

The Proof of InnocenceApr 01 2012Apr 20 2012A way to fight your traffic tickets. The paper was awarded a special prize of $400 that the author did not have to pay to the state of California. In view of enormous, extremely surprising and completely unexpected public interest to this work, we have ... More

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

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

Germs of local automorphisms of real-analytic CR structures and analytic dependence on $k$-jetsJan 09 1998The topic of the paper is the study of germs of local holomorphisms $f$ between $C^n$ and $C^{n'}$ such that $f(M)\subset M'$ and $df(T^cM)=T^cM'$ for $M\subset C^n$ and $M'\subset C^{n'}$ generic real-analytic CR submanifolds of arbitrary codimensions. ... 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.

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

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

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.

Introduction to the Classical Theory of Higher SpinsMay 08 2004Jun 20 2005We review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.

Introduction to the Superembedding Description of SuperbranesMay 11 2001Basics of the geometrical formulation of the dynamics of supersymmetric objects are considered and its relation to conventional formulations of superbranes is discussed. In particular, we demonstrate how the kappa-symmetry of the Green-Schwarz formulation ... More

Real group orbits on flag manifoldsFeb 10 2011In this survey, we gather together various results on the action of a real form of a complex semisimple Lie group on its flag manifolds. We start with the finiteness theorem of J.Wolf implying that at least one of the orbits is open. We give a new proof ... 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

Sets of Hilbert series and their applicationsFeb 08 2005There are several remarks on Hilbert series of finitely presented (f. p.) associative algebras over a field and their modules. First, given an integer $D$, the set of Hilbert series of right-sided ideals with generators and relations of degrees at most ... 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

Notes on Derivation of 'Generalized Gravitational Entropy'Jun 21 2014Jul 05 2014An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on manifolds with ... More

On different notions of homogeneity for CR-manifoldsAug 12 2006We show that various notions of local homogeneity for CR-manifolds are equivalent. In particular, if germs at any two points of a CR-manifold are CR-equivalent, there exists a transitive local Lie group action by CR-automorphisms near every point.

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

Finite-dimensional differential graded algebras and their geometric realizationsJul 16 2019Jul 20 2019We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with a full separable ... More

Is covariant star product unique?Jan 24 2011We give a nontechnical introduction to the problem of non-uniqueness of star products and describe a covariant resolution of this problem. Some implications (e.g., for noncommutative gravity) and further prospects are discussed.

Real-time dynamics of proton decaySep 28 2005Substituting Skyrmion for nucleon, one can potentially see -- in real time -- how the monopole is catalysing the proton (or neutron) decay, and even obtain a plausible estimate for catalysis cross-section. Here we discuss the key aspects of a practical ... More

Topological transitions at the resonance in gauge sectorDec 04 2001We discuss topological transitions during parametric resonance in the gauge sector of electroweak theory. It is shown that the resonance leads to separation of topological indices of the gauge and Higgs fields, resulting in topological transitions of ... More

On the commutator map for real semisimple Lie algebrasJan 13 2015We find new sufficient conditions for the commutator map of a real semisimple Lie algebra to be surjective. As an application we prove the surjectivity of the commutator map for all simple algebras except $\mathfrak su_{p,q}$ ($p$ or $q$ >1), $\mathfrak ... More

Triviality of the Aharonov-Bohm interaction in a spatially confining vacuumFeb 09 2012May 10 2012This paper explores long-range interactions between magnetically-charged excitations of the vacuum of the dual Landau-Ginzburg theory (DLGT) and the dual Abrikosov vortices present in the same vacuum. We show that, in the London limit of DLGT, the corresponding ... More

Influence of matter fields on the (de-)confining properties of the 3d Georgi-Glashow modelMay 04 2005The influence of various matter fields on the confining and finite-temperature properties of the (2+1)d Georgi-Glashow model is explored. At zero temperature, these fields are W-bosons, which play the role of heavy nodes, through which the quark-antiquark ... More

Shear viscosity of the gluon plasma in the stochastic-vacuum approachMay 20 2009Shear viscosity of the gluon plasma in SU(3) YM theory is calculated nonperturbatively, within the stochastic vacuum model. The result for the ratio of the shear viscosity to the entropy density, proportional to the squared chromo-magnetic gluon condensate ... More

Calculating the gauge-invariant two-point correlation function of gluonic field strengthsOct 26 2005The two-point gauge-invariant correlation function of gluonic field strengths, which is the main input in the stochastic vacuum model, is derived by using its relation to the Green functions of one- and two-gluon gluelumps. These Green functions are found ... More

Exploring quark-gluon plasma on the loop spaceJul 27 2002Langevin equation describing soft modes in the quark-gluon plasma is reformulated on the loop space. The Cauchy problem for the resulting loop equation is solved for the case when the nonvanishing components of the gauge potential correspond to the Cartan ... More

Evaluation of Self-Intersecting Wilson Loop in the Stochastic Vacuum ModelDec 27 2000Dec 28 2000A Wilson loop is evaluated within the stochastic vacuum model for the case when the respective contour is self-intersecting and its size does not exceed the correlation length of the vacuum. The result has the form of a certain functional of the tensor ... More