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Apparent contours of nonsingular real cubic surfacesJun 09 2013Feb 09 2015We give a complete deformation classification of real Zariski sextics, that is of generic apparent contours of nonsingular real cubic surfaces. As a by-product, we observe a certain "reversion" duality in the set of deformation classes of these sextics. ... More

Rokhlin Conjecture and Topology of Quotients of Complex Surfaces by Complex ConjugationJun 14 1995Jul 29 1996Quotients $Y=X/conj$ of complex surfaces by anti-holomorphic involutions $conj\: X\to X$ tend to be completely decomposable when they are simply connected, i.e., split into connected sums, $n CP^2\#m\barCP2$, if $w_2(Y)\ne0$, or into $n(S^2\times S^2)$ ... More

Exotic embeddings of $#6\Bbb R\roman{P}^2$ in the 4-sphereMar 10 2007We present an infinite sequence of smooth embeddings of a connected sum of 6 projective planes in the 4-sphere, which are all ambient homeomorphic, but pairwise ambient non-diffeomorphic. The double covers of the 4-sphere ramified along these surfaces ... More

Knotting of algebraic curves in complex surfacesNov 27 2000A non-singular connected algebraic curve $A$ in a simply connected algebraic surface $X$ can be knotted so that its homology class and the fundamental group of its complement in $X$ is preserved, provided $A$ is sufficiently complex (not too ``rigid''). ... More

Generalization of Arnold-Viro inequalities for real singular algebraic curvesJun 03 1997The Arnold inequalities characterizing the topology of non-singular plane real algebraic curves and the generalization of these inequalities for nodal curves by Viro are extended in this paper for the curves whose singularities have non-degenerated Milnor ... More

Relative Seiberg-Witten and Ozsvath-Szabo 4-dimensional invariants with respect to embedded surfacesJan 26 2004Jul 14 2005We study the invariants of surfaces in 4-manifolds extracted from the Seiberg-Witten and the Ozsvath-Szabo invariants of their fiber sums with auxiliary Lefschetz fibrations. Such invariants involve relative Spin_c structures and can be treated as refinements ... More

Knotting of Algebraic Curves in CP2Jul 16 1999Jul 27 1999I construct "fake algebraic curves" in $Cp^2$. More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces $F\subset Cp^2$ homeomorphic to a non-singular algebraic curve ... More

A Rokhlin Conjecture and Smooth Quotients by the Complex Conjugation of Singular Real Algebraic SurfacesMar 18 1999The topology of the orbit space, $Y$, for the action of the complex conjugation on a complex surface, $X$, defined over reals, is studied. I give a criterion for blow-up stable triviality of $Y$ (which implies vanishing of its Seiberg-Witten invariants). ... More

Deformation classes of real Cayley M-octadsJul 10 2019We study 8-point configurations in the real projective space forming an intersection locus of three quadrics and containing no coplanar quadruples. We found that there exists precisely 8 mirror-pairs of deformation classes of such configurations. We describe ... More

Abundance of 3-planes on real projective hypersurfacesOct 14 2014Jul 29 2015We show that a generic real projective $n$-dimensional hypersurface of odd degree $d$, such that $4(n-2)=\binom{d+3}3$, contains "many" real 3-planes, namely, in the logarithmic scale their number has the same rate of growth, $d^3\log d$, as the number ... More

Segre indices and Welschinger weights as options for invariant count of real linesJan 19 2019In our previous paper we have elaborated a certain signed count of real lines on real projective n-dimensional hypersurfaces of degree 2n-1. Contrary to the honest "cardinal" count, it is independent of the choice of a hypersurface, and by this reason ... More

On imaginary plane curves and Spin quotients of complex surfaces by complex conjugationJul 18 1996It is proven that for any topological or analytical types of isolated singular points of plane curves, there exists a non-real irreducible plane algebraic curve of degree $d$ which goes through $d^2$ real distinct points and has imaginary singular points ... More

Chirality of Real Non-singular Cubic Fourfolds and Their Pure Deformation ClassificationMay 22 2019In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface ... More

Deformation classification of real non-singular cubic threefolds with a marked lineMar 01 2018Mar 01 2019We prove that the space of pairs $(X,l)$ formed by a real non-singular cubic hypersurface $X\subset P^4$ with a real line $l\subset X$ has 18 connected components and give for them several quite explicit interpretations. The first one relates these components ... More

Deformation classification of real non-singular cubic threefolds with a marked lineMar 01 2018We prove that the space of pairs $(X,l)$ formed by a real non-singular cubic hypersurface $X\subset P^4$ with a real line $l\subset X$ has 18 connected components and give for them several quite explicit interpretations. The first one relates these components ... More

Deformation Classification of Typical Configurations of 7 Points in the Real Projective PlaneFeb 03 2015Jul 28 2015A configuration of 7 points in RP2 is called typical if it has no collinear triples and no coconic sextuples of points. We show that there exist 14 deformation classes of such configurations. This yields classification of real Aronhold sets.

Deformation Classes of Real Four-dimensional Cubic HypersurfacesJul 05 2006We study real nonsingular projective cubic fourfolds up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in the middle homology. ... More

Quotients by complex conjugation for real complete intersection surfacesDec 11 1995Quotients $Y=X/conj$ by the complex conjugation $conj\: X\to X$ for complex surfaces $X$ defined over $\R$ tend to be completely decomposable when they are simply connected, i.e., split into connected sums $\#_n CP^2\#_m\barCP^2$ if $w_2(Y)\ne0$, or into ... More

Complex Intersections of Real Cycles in Real Algebraic Varieties and Generalized Arnold-Viro InequalitiesFeb 03 1999Consider a real algebraic variety, $\R X$, of dimension $d$. If its complexification, $\C X$, is a rational homology manifold (at least in a neighborhood of $\R X$), then the intersection form in $\C X$ defines a bilinear form in $d$-homologies of $\R ... More

Decomposability of quotients by complex conjugation for rational and Enriques surfacesMar 08 1996The quotients $Y=X/conj$ by the complex conjugation $conj\: X\to X$ for complex rational and Enriques surfaces $X$ defined over $\R$ are shown to be diffeomorphic to connected sums of $\barCP2$, whenever $Y$ are simply connected.

$Pin$-structures on surfaces and quadratic formsJul 10 1995A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.

Abundance of real lines on real projective hypersurfacesJan 13 2012We show that a generic real projective n-dimensional hypersurface of degree 2n-1 contains "many" real lines, namely, not less than (2n-1)!!, which is approximately the square root of the number of complex lines. This estimate is based on the interpretation ... More

On the deformation chirality of real cubic fourfoldsApr 30 2008According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold up to projective equivalence and deformation. Here, we show how to ... More

Topology of real cubic fourfoldsJun 08 2009A solution to the problem of topological classification of real cubic fourfolds is presented. It is shown that the real locus of a real non-singular cubic fourfold is obtained from a projective 4-space either by adding several trivial one- and two-handles, ... More

Generalized Zero Range Potentials and Multi-Channel Electron-Molecule ScatteringSep 09 2002A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges is considered. ... More

Approximate Differentiability of Mappings of Carnot-Carathéodory SpacesJun 22 2012Feb 05 2013We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory spaces. We show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic horizontal vector fields ... More

Inverse shadowing and related measuresJul 15 2019We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along the exact trajectory ... More

On uniquely k-determined permutationsOct 10 2006There are several approaches to study occurrences of consecutive patterns in permutations such as the inclusion-exclusion method, the tree representations of permutations, the spectral approach and others. We propose yet another approach to study occurrences ... More

Physical conditions in nearby active galaxies correlated with ultra-high-energy cosmic rays detected by the Pierre Auger ObservatoryAug 04 2008Mar 29 2010We analyze the active-galaxy correlation reported in 2007 by the Pierre Auger Collaboration. The signal diminishes if the correlation-function approach (counting all "source-event" pairs and not only "nearest neighbours") is used, suggesting that the ... More

Zeroes of the spectral density of the periodic Schroedinger operator with Wigner-von Neumann potentialFeb 25 2011We consider the Schroedinger operator L_{\alpha} on the half-line with a periodic background potential and the Wigner-von Neumann potential of Coulomb type: csin(2\omega x+d)/(x+1). It is known that the continuous spectrum of the operator L_{\alpha} has ... More

Partial hyperbolicity and central shadowingDec 19 2011Feb 11 2012We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof is based on ... More

Study of internal wave breaking dependence on stratificationJun 26 2012Mixing effect in a stratified fluid is considered and examined. Euler equations for incompressible fluid stratified by a gravity field are applied to state a mathematical problem and describe the effect. It is found out that a system of Euler equations ... More

Motion of a rough disc in Newtonian aerodynamicsNov 25 2013Nov 30 2014Dynamics of rough discs in a rarified media is considered. We study possible trajectories of centers of discs. The main result of the paper is the following: any finite rectifiable curve can be approximated by trajectories of centers of rough discs, provided ... More

Finite group subschemes of abelian varieties over finite fieldsJun 30 2010Nov 29 2013Let $A$ be an abelian variety over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by the Weil polynomial $f_A$. We assume that $f_A$ is separable. For a given prime number $\ell\neq\mathrm{char}\, k$ we give a classification of ... More

Duality theory for nonergodic actionsMar 25 2013Apr 03 2013Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of our construction ... More

Von Neumann algebras arising from Bost-Connes type systemsJul 09 2009We show that the KMS_beta-states of Bost-Connes type systems for number fields in the region 0<beta\le 1, as well as of the Connes-Marcolli GL_2-system for 1<beta\le 2, have type III_1. This is equivalent to ergodicity of various actions on adelic spaces. ... More

Fixed Interfaces, Adaptive Interfaces... What is next? Total movability - a new paradigm for the user interfaceAug 02 2012Users can't talk with computers in their natural language (machine codes), so there are interfaces that allow such communication. 40 years ago the outcome of computer programs was in the form of long listings covered by numbers and even the format of ... More

A Door into Another WorldDec 10 2011Is it possible to design programs which each user can change according to his preferences? Not an illusion of such a thing that adaptive interface provides but really an interface ruled by users. What is the main problem of such design and what is the ... More

World of Movable Objects. Part 2Nov 24 2010This book is about the transformation of screen objects into movable and resizable and about the design of applications entirely on the basis of such elements. The screen objects have a wide variety of shapes; they can be either graphical objects or controls; ... More

On the theory of moveable objectsDec 14 2009Jan 21 2010User-driven applications belong to the new type of programs, in which users get the full control of WHAT, WHEN, and HOW must appear on the screen. Such programs can exist only if the screen view is organized not according with the predetermined scenario, ... More

Discharge convective instability as modifier of nonlinear hydrodynamic spectrumApr 26 2012Jan 24 2014Discharge source is considered as modifier of flow hydrodynamic spectrum. Characteristic frequency of nonlinear spectrum and spectrum power were determined under conditions of arc sliding discharge in supersonic flow. Two stages of discharge were defined: ... More

The Inverse Task of the Reflexive Game Theory: Theoretical Matters, Practical Applications and Relationship with Other IssuesNov 15 2010The Reflexive Game Theory (RGT) has been recently proposed by Vladimir Lefebvre to model behavior of individuals in groups. The goal of this study is to introduce the Inverse task. We consider methods of solution together with practical applications. ... More

Emotionally Colorful Reflexive GamesDec 27 2010This study addresses the matter of reflexive control of the emotional states by means of Reflexive Game Theory (RGT). It is shown how to build a bridge between RGT and emotions. For this purpose the Pleasure-Arousal-Dominance (PAD) model is adopted. The ... More

Finite Bases with Respect to the Superposition in Classes of Elementary Recursive Functions, dissertationNov 14 2016Nov 16 2016This is a thesis that was defended in 2009 at Lomonosov Moscow State University. In Chapter 1: 1. It is proved that that the class of lower (Skolem) elementary functions is the set of all functions that can be obtained by a composition of $x+1$, $xy$, ... More

BABAR status and prospects for CP asymmetry measurements: sin(2beta+gamma)Mar 21 2007The recent experimental results on CP violation related to the angles of the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle 2beta+gamma are summarized in these proceedings. These results are obtained with approximately 232 million Y4S->BBbar events ... More

Semiinfinite cohomology of quantum groups IIOct 15 1996It is known that the semi-infinite cohomology spaces of the infinitely twisted nilpotent subalgebra in an affine Lie algebra $g$ with coefficients in an integrable simple module over the affine Lie algebra have a base enumerated by elements of the corresponding ... More

Kelvin-wave turbulence generated by vortex reconnectionsOct 16 2006Reconnections of quantum vortex filaments create sharp bends which degenerate into propagating Kelvin waves. These waves cascade their energy down-scale and their waveaction up-scale via weakly nonlinear interactions, and this is the main mechanism of ... More

Market shape formation, statistical equilibrium and neutral evolution theoryJun 23 2015Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium ... More

Nonequilibrium Majorana fluctuationsJun 06 2016Nonequilibrium physics of rare events, or fluctuations, is an unique fingerprint of a given system. By virtue of its very nature, it differs from the nonequilibrium physics enclosed in the system's mean quantities and provides an experimental alternative ... More

On partial traces and compactification of $*$-autonomous Mix-categoriesAug 04 2016We study the question when a $*$-autonomous Mix-category has a representation as a $*$-autonomous Mix-subcategory of a compact one. We define certain partial trace-like operation on morphisms of a Mix-category, which we call a mixed trace, and show that ... More

Bs Mixing, Lifetime Difference and Rare Decays at the TevatronMay 16 2005Recent results on Bs mixing, lifetime difference and rare decays obtained by the CDF and DO collaborations using the data samples collected at the Tevatron Collider in the period 2002 - 2005 are presented.

Role of pion pole in hard exlusive meson leptoproductionDec 03 2015We consider the pion pole contribution and transversity effects determined by the $H_T$ and $\bar E_T$ Generalized Parton Distributions (GPDs) which are essential in hard pseudoscalar and vector meson leptoproduction. We investigate spin effects in the ... More

Simple Fuzzy Score for Russian Public Companies Risk of DefaultApr 05 2010Apr 12 2010The model is aimed to discriminate the 'good' and the 'bad' companies in Russian corporate sector based on their financial statements data based on Russian Accounting Standards. The data sample consists of 126 Russian public companies- issuers of Ruble ... More

Pseudo-conformal Universe: late-time contraction and generation of tensor modesNov 01 2012Dec 11 2012We consider a bouncing Universe model which explains the flatness of the primordial scalar spectrum via complex scalar field that rolls down its negative quartic potential and dominates in the Universe. We show that in this model, there exists a rapid ... More

Search for Galactic disk and halo components in the arrival directions of high-energy astrophysical neutrinosNov 05 2015Feb 13 2016Arrival directions of 40 neutrino events with energies >~100 TeV, observed by the IceCube experiment, are studied. Their distribution in the Galactic latitude and in the angular distance to the Galactic Center allow to search for the Milky-Way disk and ... More

Scaling dimensions from the mirror TBAJan 11 2012The mirror TBA equations proposed by Arutyunov, Suzuki and the author are solved numerically up to 't Hooft's coupling $\lambda\approx 2340$ for several two-particle states dual to ${\cal N}=4$ SYM operators from the $\sl(2)$ sector. The data obtained ... More

Konishi operator at intermediate couplingJun 25 2010Jul 27 2010TBA equations for two-particle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained is used to analyze the properties ... More

The growth of polynomials orthogonal on the unit circle with respect to a weight w that satisfies w,1/w \in L^\infty(T)Nov 01 2016We consider the weight w: 1<w<T on the unit circle and prove that the corresponding orthonormal polynomials can grow.

Regge Field Theory in zero transverse dimensions: loops versus "net" diagramsNov 17 2010Nov 22 2010Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum ... More

Conformal intercept of BFKL pomeron with NLO running coupling constant correctionsAug 23 2008In the present note we propose a shift of the anomalous dimension function of the eigenfunctions of the BFKL equation with the NLO running coupling corrections. The calculated eigenvalue of the modified equation turns out to be conformal invariant and ... More

Higgs bundles over P^1 and quiver representationsNov 25 2016In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The formula can ... More

Metrizable DH-spaces of the first categoryJan 30 2014Feb 01 2014We show that if a separable space X has a meager open subset containing a copy of the Cantor set 2^\omega, then X has $\frak{c}$ types of countable dense subsets. We suggest a generalization of the \lambda-set for non-separable spaces. Let X be an h-homogeneous ... More

Small rational model of subspace complementJun 26 1998Jan 21 1999In the paper we compute the ring strucure on the rational cohomology of a complex subspace complement. For that we construct a small differential graded subalgebra of the De Concini-Procesi wonderful model that is quasi isomorphic to this model. For two ... More

Approximations of theoriesJan 24 2019We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of theories as ... More

TTbar deformation and the light-cone gaugeMay 20 2019The homogeneous inviscid Burgers equation which determines the spectrum of a TTbar deformed model has a natural interpretation as the condition of the gauge invariance of the target space-time energy and momentum of a (non-critical) string theory quantised ... More

Bochner-Hartogs type extension theorem for roots and logarithms of holomorphic line bundlesApr 17 2011We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when dimension and Morse index of a critical point is two. In that case we give an explicit ... More

Density and metallicity of the Milky-Way circumgalactic gasJul 19 2016Feb 03 2017The halo of the Milky-Way circumgalactic gas extends up to the virial radius of the Galaxy, ~250 kpc. The halo properties may be deduced from X-ray spectroscopic observations and from studies of the ram-pressure stripping of satellite dwarf galaxies. ... More

Twisted geometric Satake equivalence: reductive caseNov 25 2014Jan 21 2016In this paper we extend the twisted Satake equivalence established in arXiv:0809.3738 for almost simple groups to the case of split reductive groups.

Whittaker and Bessel functors for GSp_4Oct 22 2003May 20 2005One of the important technical tools in Gaitsgory's proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([3]) is the theory of Whittaker functors for GL_n. We define Whittaker functors for GSp_4 and study their properties. ... More

Stabilizers and orbits of circle-valued smooth functionsMar 31 2005Let $M$ be a smooth compact manifold and $P$ be either $R^1$ or $S^1$. There is a natural action of the groups $Diff(M)$ and $Diff(M) \times Diff(P)$ on the space of smooth mappings $C^{\infty}(M,P)$. For $f\in C^{\infty}(M,P)$ let $S_f$, $S_{MP}$, $O_f$, ... More

Quantum corrections to static solutions of Nahm equation and Sin-Gordon models via generalized zeta-functionJun 16 2008Jan 12 2009One-dimensional Yang-Mills Equations are considered from a point of view of a class of nonlinear Klein-Gordon-Fock models. The case of self-dual Nahm equations and non-self-dual models are discussed. A quasiclassical quantization of the models is performed ... More

Towards discrimination between galactic and intergalactic axion-photon mixingJul 30 2015Feb 12 2016There exists a growing evidence for the anomalous transparency of the Universe for energetic gamma rays. Popular explanations include conversion of photons into hypothetical axion-like particles (ALPs) and back in astrophysical magnetic fields. Two distinctive ... More

Restart could optimize the probability of success in a Bernoulli trialMar 04 2017Jul 29 2017Recently noticed ability of restart to reduce the expected completion time of first-passage processes allows appealing opportunities for performance improvement in a variety of settings. However, complex stochastic processes often exhibit several possible ... More

Synchronization transition in ensemble of coupled phase oscillators with coherence-induced phase correctionMar 08 2015May 27 2015We study synchronization phenomenon in a self-correcting population of noisy phase oscillators with randomly distributed natural frequencies. In our model each oscillator stochastically switches its phase to the ensemble-averaged value $\psi$ at a typical ... More

The wave model of the Sturm-Liouville operator on an intervalJun 19 2019In the paper we construct the wave functional model of a symmetric restriction of the regular Sturm-Liouville operator on an interval. The model is based upon the notion of the wave spectrum and is constructed according to an abstract scheme which was ... More

Twisted geometric Langlands correspondence for a torusDec 16 2013Oct 20 2014Let T be a split torus over local or global function field. The theory of Brylinski-Deligne gives rise to the metaplectic central extensions of T by a finite cyclic group. The representation theory of these metaplectic tori has been developped to some ... More

On the automorphic sheaves for GSp_4Jan 14 2019Jan 21 2019For G=GSp_4 we construct an automorphic sheaf correspinding to a G^L-local system on a curve X such that its standard representation is an irreducible local system of rank 4 on X. This is obtained an an application of some more general results related ... More

On a Certain Integral Over a TriangleNov 09 2005Dec 13 2005We study integrals over the triangle with vertices (1,0), (0,1), (1,1) that give linear combinations of multiple zeta values.

Classical theory of the hydrogen atomFeb 04 2016It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field, an "electron ... More

Proof of the Poincare' conjectureOct 22 2002Dec 10 2002This paper proves that any compact, closed, simply connected and connected three dimensional stellar manifold is stellar equivalent to the three dimensional sphere.

On 3-manifoldsNov 18 2005Feb 06 2006It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in pairs leads us ... More

$L^p$ estimates for angular maximal functions associated with Stieltjes and Laplace transformsMay 24 2009Oct 12 2011Maximal angular operator sends a function defined in a sector of the complex plane to a Maximal angular operator sends a function defined in a sector of the complex plane with vertex at 0 to the function of modulus obtained by maximizing over argument. ... More

On rigidity of trinomial hypersurfaces and factorial trinomial varietiesFeb 16 2019Trinomial varieties are affine varieties given by some special system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal rational varieties with torus action of complexity one. For an affine variety ... More

Some Open Problems Related to StabilitySep 02 2009The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on open problems, ... More

Flows of co-closed $G_{2}$-structuresNov 26 2018We survey recent progress in the study of $G_{2}$-structure Laplacian coflows, that is, heat flows of co-closed $G_{2}$-structures. We introduce the properties of the original Laplacian coflow of $G_{2}$-structures as well as the modified coflow, reviewing ... More

Homotopy types of stabilizers and orbits of Morse functions on surfacesOct 06 2003Aug 14 2006Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ ... More

G2-structures and octonion bundlesOct 14 2015Jan 12 2017We use a G2-structure on a 7-dimensional Riemannian manifold with a fixed metric to define an octonion bundle with a fiberwise non-associative product. We then define a metric-compatible octonion covariant derivative on this bundle that is compatible ... More

Estimates and monotonicity for a heat flow of isometric G2-structuresApr 18 2019Apr 24 2019Given a $7$-dimensional compact Riemannian manifold $\left( M,g\right) $ that admits $G_{2}$-structure, all the $G_{2}$-structures that are compatible with the metric $g$ are parametrized by unit sections of an octonion bundle over $M$. We define a natural ... More

On the K-property of quantized Arnold cat mapsFeb 10 2000We prove that some quantized Arnold cat maps are entropic K-systems. This result was formulated by H. Narnhofer[1], but the fact that the optimal decomposition for the multi-channel entropy constructed there is not strictly local was not appropriately ... More

On rigidity of trinomial hypersurfaces and factorial trinomial varietiesFeb 16 2019Jul 12 2019Trinomial varieties are affine varieties given by some special system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal rational varieties with torus action of complexity one. For an affine variety ... More

Leap Gradient AlgorithmMay 21 2014Jan 25 2016The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several evolutionary leaps ... More

Quantum corrections to finite-gap solutions for Yang-Mills-Nahm equations via zeta-function techniqueApr 19 2011One-dimensional Yang-Mills-Nahm models are considered from algebrogeometric points of view. A quasiclassical quantization of the models based on path integral and its zeta function representation in terms of a Green function diagonal for a heat equation ... More

Properties of Coefficients of Certain Linear Forms in Generalized PolylogarithmsNov 09 2005We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.

Degenerations, transitions and quantum cohomologySep 08 2018Sep 11 2018Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations helps with computing Gromov--Witten invariants, and the role of this story in Fanosearch programme. ... More

Essential Spectrum of Multiparticle Brown-Ravenhall Operators in External FieldFeb 04 2008The essential spectrum of multiparticle Brown-Ravenhall operators is characterized in terms of two--cluster decompositions for a wide class of external fields and interparticle interactions and for the systems with prescribed symmetries.

Non-separable h-homogeneous absolute F_{σδ}-spaces and G_{δσ}-spacesOct 05 2011Denote by Q(k) a \sigma-discrete metric weight-homogeneous space of weight k. We give an internal description of the space Q(k)^\omega. We prove that the Baire space B(k) is densely homogeneous with respect to Q(k)^\omega if k > \omega. Properties of ... More

Zeroes of the spectral density of the Schroedinger operator with the slowly decaying Wigner-von Neumann potentialMar 17 2016We consider the Schr\"odinger operator $\mathcal L_{\alpha}$ on the half-line with a periodic background potential and a perturbation which consists of two parts: a summable potential and the slowly decaying Wigner--von Neumann potential $\frac{c\sin(2\omega ... More

Shadowing in linear skew productsNov 06 2014We consider a linear skew product with the full shift in the base and nonzero Lyapunov exponent in the fiber. We provide a sharp estimate for the precision of shadowing for a typical pseudotrajectory of finite length. This result indicates that the high-dimensional ... More

Introduction to Partially Ordered PatternsMar 05 2006Sep 28 2006We review selected known results on partially ordered patterns (POPs) that include co-unimodal, multi- and shuffle patterns, peaks and valleys ((modified) maxima and minima) in permutations, the Horse permutations and others. We provide several (new) ... More

An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weightsMar 18 2010We consider self-adjoint unbounded Jacobi matrices with diagonal q_n=n and weights \lambda_n=c_n n, where c_n is a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum is either purely ... More