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Pre-Lie deformation theoryFeb 11 2015Mar 27 2016In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for pre-Lie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide ... More

De Rham cohomology and homotopy Frobenius manifoldsMar 22 2012May 25 2012We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfantsOct 26 2016Nov 17 2016We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessins d'enfants or $r$-hypermaps. These statements answer positively ... More

Half-spin tautological relations and Faber's proportionalities of kappa classesFeb 07 2019Feb 11 2019We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on $\mathcal{M}_g$, $g\geq 2$. We then prove ... More

Blobbed topological recursion: properties and applicationsFeb 03 2015Feb 18 2015We study the set of solutions $(\omega_{g,n})_{g \geq 0,n \geq 1}$ of abstract loop equations. We prove that $\omega_{g,n}$ is determined by its purely holomorphic part: this results in a decomposition that we call "blobbed topological recursion". This ... More

Changes of variables in ELSV-type formulasFeb 21 2006Jun 25 2007In [5] I.P. Goulden, D.M. Jackson, and R. Vakil formulated a conjecture relating certain Hurwitz numbers (enumerating ramified coverings of the sphere) to the intersection theory on a conjectural Picard variety. We are going to use their formula to study ... More

A group action on Losev-Manin cohomological field theoriesSep 04 2009We discuss an analog of the Givental group action for the space of solutions of the commutativity equation. There are equivalent formulations in terms of cohomology classes on the Losev-Manin compactifications of genus 0 moduli spaces; in terms of linear ... More

The spectral curve and the Schroedinger equation of double Hurwitz numbers and higher spin structuresJan 23 2013Jun 04 2013We derive the spectral curves for $q$-part double Hurwitz numbers, $r$-spin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0,1)-geometry. We quantize this family of spectral curves and obtain the ... More

Noncommutative $\overline{M}_{0,n+1}$Oct 12 2015We introduce and study noncommutative analogues of the Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points which exhibit all the remarkable algebraic and geometric features that the Deligne-Mumford compactifications ... More

Toric varieties of Loday's associahedra and noncommutative cohomological field theoriesOct 12 2015Oct 24 2018We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. ... More

Givental Action and Trivialisation of Circle ActionApr 11 2013Jun 09 2014In this paper, we show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in the deformation theory of Batalin--Vilkovisky algebras. We prove ... More

Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfantsOct 26 2016We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessins d'enfants or $r$-hypermaps. These statements answer positively ... More

Bihamiltonian cohomology of KdV bracketsJun 21 2014Mar 13 2015Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular this proves a conjecture of Liu and Zhang about the vanishing of such cohomology groups. ... More

Poisson cohomology of scalar multidimensional Dubrovin-Novikov bracketsDec 17 2015We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with $D$ independent variables. We find that the second and third cohomology groups are generically non-vanishing in $D>1$. Hence, in contrast with the $D=1$ case, ... More

Normal forms of dispersive scalar Poisson brackets with two independent variablesJul 12 2017We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which ... More

Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019Mar 14 2019We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous ... More

Ground states of Nicolai and $\mathbb{Z}_2$ Nicolai modelsAug 08 2018We derive explicit recursions for the ground state generating functions of the one-dimensional Nicolai model and $\mathbb{Z}_2$ Nicolai model. Both are examples of lattice models with $\mathcal{N}=2$ supersymmetry. The relations that we obtain for the ... More

Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebrasDec 06 2011Jan 14 2013In this paper, we initiate the study of the Givental group action on Cohomological Field Theories in terms of homotopical algebra. More precisely, we show that the stabilisers of Topological Field Theories in genus 0 (respectively in genera 0 and 1) are ... More

The bi-Hamiltonian cohomology of a scalar Poisson pencilMay 14 2015Jan 27 2016We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtain that $BH^p_d(\hat{F}, d_1,d_2)$ is isomorphic to $\mathbb{R}$ for $(p,d)=(0,0)$, ... More

The twisting procedureOct 06 2018This paper provides a conceptual study of the twisting procedure, which amounts to create functorially new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer--Cartan element. On the way, ... More

Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous ... More

Hypercommutative operad as a homotopy quotient of BVJun 17 2012Dec 04 2012We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/$\Delta$ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive ... More

Central invariants revisitedNov 28 2016We give a new proof of the statement of Dubrovin-Liu-Zhang that the Miura-equivalence classes of the deformations of semi-simple bi-Hamiltonian structures of hydrodynamic type are parametrized by the so-called central invariants.

Tautological relations and the r-spin Witten conjectureDec 18 2006Jan 21 2009In a series of two preprints, Y.-P. Lee studied relations satisfied by all formal Gromov-Witten potentials, as defined by A. Givental. He called them "universal relations" and studied their connection with tautological relations in the cohomology ring ... More

Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructedJan 18 2015Sep 21 2016We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic ... More

The twisting procedureOct 06 2018Feb 28 2019This paper provides a conceptual study of the twisting procedure, which amounts to create functorially new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer--Cartan element. On the way, ... More

Half-spin tautological relations and Faber's proportionalities of kappa classesFeb 07 2019We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on $\mathcal{M}_g$, $g\geq 2$. We then prove ... More

Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson-Pandharipande-Tseng formulaApr 28 2015In this paper we present an example of a derivation of an ELSV-type formula using the methods of topological recursion. Namely, for orbifold Hurwitz numbers we give a new proof of the spectral curve topological recursion, in the sense of Chekhov, Eynard, ... More

Special cases of the orbifold version of Zvonkine's $r$-ELSV formulaMay 30 2017We prove the orbifold version of Zvonkine's $r$-ELSV formula in two special cases: the case of $r=2$ (complete $3$-cycles) for any genus $g\geq 0$ and the case of any $r\geq 1$ for genus $g=0$.

Givental symmetries of Frobenius manifolds and multi-component KP tau-functionsMay 06 2009We establish a link between two different constructions of the action of the twisted loop group on the space of Frobenius structures. The first construction (due to Givental) describes the action of the twisted loop group on the partition functions of ... More

The tautological ring of $\mathcal{M}_{g,n}$ via Pandharipande-Pixton-Zvonkine $r$-spin relationsMar 02 2017We use relations in the tautological ring of the moduli spaces $\overline{\mathcal{M}}_{g,n}$ derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the $r$-spin Witten class in order to obtain some restrictions on the dimensions ... More

Combinatorial structure of colored HOMFLY-PT polynomials for torus knotsDec 22 2017Mar 05 2018We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz numbers. This ... More

Cut-and-join equation for monotone Hurwitz numbers revisitedJul 11 2018Nov 15 2018We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. Our proof in particular uses a combinatorial technique developed by Han. The main interest in this particular equation ... More

Towards an orbifold generalization of Zvonkine's $r$-ELSV formulaMar 20 2017We perform a key step towards the proof of Zvonkine's conjectural $r$-ELSV formula that relates Hurwitz numbers with completed $(r+1)$-cycles to the geometry of the moduli spaces of the $r$-spin structures on curves: we prove the quasi-polynomiality property ... More

Chiodo formulas for the r-th roots and topological recursionApr 28 2015We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with psi-classes are reproduced via the ... More

Chiodo formulas for the r-th roots and topological recursionApr 28 2015Nov 11 2016We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with psi-classes are reproduced via the ... More

Towards Lax formulation of integrable hierarchies of topological typeJan 18 2012To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable hierarchies. We consider ... More

Givental graphs and inversion symmetryJan 24 2012Dec 17 2012Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental ... More

Bifurcation Diagram of One Generalized Integrable Model of Vortex DynamicsApr 20 2019The article is devoted to the results of a phase topology research on a generalized mathematical model, which covers such two problems as dynamics of two point vortices enclosed in a harmonic trap in a Bose-Einstein condensate and dynamics of two point ... More

Dubrovin's superpotential as a global spectral curveSep 23 2015Dec 25 2016We apply the spectral curve topological recursion to Dubrovin's universal Landau-Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differentials ... More

Dubrovin's superpotential as a global spectral curveSep 23 2015We apply the spectral curve topological recursion to Dubrovin's universal Landau-Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differentials ... More

Primary invariants of Hurwitz Frobenius manifoldsMay 24 2016It is a classical result that flat coordinates for a Hurwitz Frobenius manifold can be obtained as periods of a differential along cycles on the domain curve. We generalise this construction to primary invariants of the Hurwitz Frobenius manifolds. We ... More

Quantum spectral curve for the Gromov-Witten theory of the complex projective lineDec 18 2013Feb 11 2014We construct the quantum curve for the Gromov-Witten theory of the complex projective line.

Primary invariants of Hurwitz Frobenius manifoldsMay 24 2016Dec 25 2016Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds ... More

Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formulaJul 17 2013Dec 31 2013In this paper we give a new proof of the ELSV formula. First, we refine an argument of Okounkov and Pandharipande in order to prove (quasi-)polynomiality of Hurwitz numbers without using the ELSV formula (the only way to do that before used the ELSV formula). ... More

A definition of descendants at one point in graph calculusJul 05 2005Feb 25 2006We study the genus expansion of Barannikov-Kontsevich solutions of the WDVV equation. In terms of the related graph calculus we give a definition of descendants at one point and prove that this definition satisfies the topological recursion relations ... More

BCOV theory via Givental group action on cohomological field theoriesOct 03 2008In a previous paper (arXiv:0704.1001), Losev, me, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of Barannikov and Kontsevich of solution of the WDVV ... More

On the structure of Goulden-Jackson-Vakil formulaOct 03 2008We study the structure of the Goulden-Jackson-Vakil formula that relates Hurwitz numbers to some conjectural "intersection numbers" on a conjectural family of varieties $X_{g,n}$ of dimension $4g-3+n$. We give explicit formulas for the properly arranged ... More

Landau--Kolmogorov inequality revisitedOct 29 2012The Landau-Kolmogorov problem consists of finding the upper bound $M_k$ for the norm of intermediate derivative $|f^{(k)}|$, when the bounds $|f| \le M_0$ and $|f^{(n)}| \le M_n$, for the norms of the function and of its higher derivative, are given. ... More

Geometry of meromorphic functions and intersections on moduli spaces of curvesSep 21 2002Mar 18 2006In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, ... 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

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

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

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

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

A compactification and the Euler characteristic of the spaces of real meromorphic functionsFeb 07 2002For any connected component $H_0$ of the space of real meromorphic functions we build a compactification $N(H_0)$ of the space $H_0$. Then we express the Euler characteristics of the spaces $H_0$ and $N(H_0)$ in terms of topological invariants of functions ... More

A remark on deformations of Hurwitz Frobenius manifoldsDec 27 2009In this note we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux-Egoroff system. As an application, we explain how Shramchenko's deformations of Frobenius manifold ... More

On the Markov inequality in the $L_2$-norm with the Gegenbauer weightJan 26 2017Let $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where $\lambda > -\frac{1}{2}$, be the Gegenbauer weight function, let $\|\cdot\|_{w_{\lambda}}$ be the associated $L_2$-norm, $$ \|f\|_{w_{\lambda}} = \left\{\int_{-1}^1 |f(x)|^2 w_{\lambda}(x)\,dx\right\}^{1/2}\,, ... More

Combinatorics of binomial decompositions of the simplest Hodge integralsOct 31 2003We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of Bernoulli numbers.

Intersections in genus 3 and the Boussinesq hierarchyJul 24 2003In this note we prove that the enlarged Witten's conjecture is true in the case of the Boussinesq hierarchy for correlators in genus 3 with descendants only at one point.

A new proof of Faber's intersection number conjectureDec 27 2009We give a new proof of Faber's intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves $\M_g$. The proof is based on a very straightforward geometric and combinatorial computation with double ... More

Markov $L_2$-inequality with the Laguerre weightMay 10 2017Let $w_\alpha(t) := t^{\alpha}\,e^{-t}$, where $\alpha > -1$, be the Laguerre weight function, and let $\|\cdot\|_{w_\alpha}$ be the associated $L_2$-norm, $$ \|f\|_{w_\alpha} = \left\{\int_{0}^{\infty} |f(x)|^2 w_\alpha(x)\,dx\right\}^{1/2}\,. $$ By ... 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

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.

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

The genetic code, algebra of projection operators and problems of inherited biological ensemblesJul 30 2013Dec 31 2014This article is devoted to applications of projection operators to simulate phenomenological properties of the molecular-genetic code system. Oblique projection operators are under consideration, which are connected with matrix representations of the ... 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

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

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

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

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 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.

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

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

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

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

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

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