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Entanglement Entropy in 2D Non-abelian Pure Gauge TheoryMar 20 2014We compute the Entanglement Entropy (EE) of a bipartition in 2D pure non-abelian $U(N)$ gauge theory. We obtain a general expression for EE on an arbitrary Riemann surface. We find that due to area-preserving diffeomorphism symmetry EE does not depend ... More

Chiral Topological Elasticity and Fracton OrderDec 18 2017Feb 18 2019We analyze the "higher rank" gauge theories, that capture some of the phenomenology of the Fracton order. It is shown that these theories lose gauge invariance when arbitrarily weak and smooth curvature is introduced. We propose a resolution to this problem ... More

Towards classification of Fracton phases: the multipole algebraDec 12 2018We present an effective field theory approach to the Fracton phases. The approach is based the notion of a multipole algebra. It is an extension of space(-time) symmetries of a charge-conserving matter that includes global symmetries responsible for the ... More

Geometric Defects in Quantum Hall StatesApr 13 2016We describe a geometric (or gravitational) analogue of the Laughlin quasiholes in the fractional quantum Hall states. Analogously to the quasiholes these defects can be constructed by an insertion of an appropriate vertex operator into the conformal block ... More

Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac bracketsDec 21 2017We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that ... More

Anyonic Chains, Topological Defects, and Conformal Field TheoryJan 10 2017Feb 20 2017Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to an enormously ... More

Supersymmetric waves in Bose-Fermi mixturesApr 29 2015Dec 23 2015Interacting Bose-Fermi mixtures possess a fermionic (super)symmetry when bosons and fermions in the mixture have equal masses, and when the interaction strengths are appropriately tuned. This symmetry is spontaneously broken in the ground state of the ... More

Density-curvature response and gravitational anomalyMar 23 2014We study constraints imposed by the Galilean invariance on linear electromagnetic and elastic responses of two-dimensional gapped systems in background magnetic field. Exact relations between response functions following from the Ward identities are derived. ... More

Bimetric Theory of Fractional Quantum Hall StatesMay 18 2017Nov 15 2017We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist of a topological ... More

Transport signatures of Hall viscosityJun 12 2017Sep 22 2017Hall viscosity is a non-dissipative response function describing momentum transport in two-dimensional systems with broken parity. It is quantized in the quantum Hall regime, and contains information about the topological order of the quantum Hall state. ... More

Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic fieldJan 15 2014We compute electromagnetic, gravitational and mixed linear response functions of two- dimensional free fermions in external quantizing magnetic field at an integer filling factor. The results are presented in the form of the effective action and as an ... More

Thermal Hall Effect and Geometry with TorsionJul 10 2014We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes the classic Luttinger's ... More

Exact Electromagnetic Response of Landau Level ElectronsOct 11 2016We present a simple method that allows to calculate the electromagnetic response of non-interacting electrons in strong magnetic field to arbitrary order in the gradients of external electric and magnetic fields. We illustrate the method on both non-relativistic ... More

On the Derivation of the Exact Slope FunctionApr 30 2012Jan 22 2013In this note we give a simple derivation of the exact slope function conjectured by Basso for the anomalous dimensions of Wilson operators in the sl2 sector of planar N=4 Super-Yang-Mills theory. We also discuss generalizations of this result for higher ... More

Investigating anisotropic quantum Hall states with bi-metric geometryMar 03 2017Nov 27 2017We construct a low energy effective theory of anisotropic fractional quantum Hall (FQH) states. We develop a formalism similar to that used in the bi-metric approach to massive gravity, and apply it to describe abelian anisotropic FQH states in the presence ... More

Boundary effective action for quantum Hall statesJun 23 2015Jul 20 2015We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the low-energy effective ... More

Soliton solutions of Calogero model in harmonic potentialMar 31 2011A classical Calogero model in an external harmonic potential is known to be integrable for any number of particles. We consider here reductions which play a role of "soliton" solutions of the model. We obtain these solutions both for the model with finite ... More

Geometric quench and nonequilibrium dynamics of fractional quantum Hall statesFeb 28 2018Oct 26 2018We introduce a quench of the geometry of Landau level orbitals as a probe of nonequilibrium dynamics of fractional quantum Hall (FQH) states. We show that such geometric quenches induce coherent many-body dynamics of neutral degrees of freedom of FQH ... More

Particle-Hole Duality in the Lowest Landau LevelDec 22 2016We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various ... More

Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theorySep 17 2018Jan 24 2019We investigate the recently introduced geometric quench protocol for fractional quantum Hall (FQH) states within the framework of exactly solvable quantum Hall matrix models. In the geometric quench protocol a FQH state is subjected to a sudden change ... More

Synthetic Landau levels for photonsNov 23 2015Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties[1-7]. Making photons experience a Lorentz force imbues them with handedness, providing unique opportunities ... More

Synthetic Landau levels for photonsNov 23 2015Jan 24 2017Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties[1-5]. Photons experiencing a Lorentz force develop handedness, providing opportunities to study ... More

The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometryOct 02 2008More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically different ... More

Fermionic determinant for dyons and instantons with nontrivial holonomyApr 04 2005Aug 04 2005We calculate exactly the functional determinant for fermions in fundamental representation of SU(2) in the background of periodic instanton with non-trivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy ... More

Universal dynamics of a soliton after an interaction quenchAug 15 2014Mar 09 2016We propose a new type of experimentally feasible quantum quench protocol in which a quantum system is prepared in a coherent, localized excited state of a Hamiltonian. During the evolution of this solitonic excitation, the microscopic interaction is suddenly ... More

Measuring Electromagnetic and Gravitational Responses of Photonic Landau LevelsFeb 13 2018The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it changes its ... More

Controllability of 2D Euler and Navier-Stokes Equations by Forcing 4 ModesJul 18 2005We study controllability issues for the 2D Euler and Navier-Stokes (NS) systems under periodic boundary conditions. These systems describe motion of homogeneous ideal or viscous incompressible fluid on a two-dimensional torus $\mathbb{T}^2$. We assume ... More

Framing Anomaly in the Effective Theory of Fractional Quantum Hall EffectOct 24 2014Mar 25 2015We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain correct gravitational linear response functions. ... More

NNLO BFKL Pomeron eigenvalue in N=4 SYMJul 14 2015Aug 13 2015We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4 using Quantum Spectral Curve (QSC) integrability based method. The result is verified with more than ... More

Surgery for partially hyperbolic dynamical systems I. Blow-ups of invariant submanifoldsSep 19 2016We suggest a method to construct new examples of partially hyperbolic diffeomorphisms. We begin with a partially hyperbolic diffeomorphism $f\colon M\to M$ which leaves invariant a submanifold $N\subset M$. We assume that $N$ is an Anosov submanifold ... More

On dynamical smash productAug 30 2007In the theory of dynamical Yang-Baxter equation, with any Hopf algebra $H$ and a certain $H$-module and $H$-comodule algebra $L$ (base algebra) one associates a monoidal category. Given an algebra $A$ in that category, one can construct an associative ... More

New solvable stochastic volatility models for pricing volatility derivativesMay 16 2012Jun 30 2012Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter $\gamma$ takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 ... More

Splitting and Matrix Exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumpsMay 23 2014May 27 2014This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order ... More

Efficient Solution of Backward Jump-Diffusion PIDEs with Splitting and Matrix ExponentialsApr 10 2013Apr 12 2014We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on financial processes ... More

Pricing options with VG model using FFTMar 16 2005Jan 15 2010We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, Carr-Madan's FFT method could blow up for certain values of the model parameters ... More

The Maupertuis principle and integrable systemsSep 25 2000We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals of motion, ... More

Duality between integrable Stackel systemsNov 27 1998For the Stackel family of the integrable systems a non-canonical transformation of the time variable is considered. This transformation may be associated to the ambiguity of the Abel map on the corresponding hyperelliptic curve. For some Stackel's systems ... More

Canonical transformations of the extended phase space, Toda lattices and Stackel family of integrable systemsSep 10 1999We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to transformations ... More

Dynamical boundary conditions for integrable latticesJan 09 1998Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.

Universal Nonlinear Small-Scale DynamoSep 21 2011We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds numbers (Re). We argue that it is universal in a sense that magnetic energy grows at a rate which is a constant fraction C_E of the total turbulent dissipation rate. On the basis ... More

The Spectral Slope and Kolmogorov Constant of MHD turbulenceNov 10 2010The spectral slope of strong MHD turbulence has recently been a matter of controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3 slope of turbulence, shallower slopes were often reported by numerical studies. We argue that earlier ... More

Quotients of cubic surfacesJun 16 2015Let $\Bbbk$ be any field of characteristic zero, $X$ be a cubic surface in $\mathbb{P}^3_{\Bbbk}$ and $G$ be a group acting on $X$. We show that if $X(\Bbbk) \ne \varnothing$ and $G$ is not trivial and not a group of order $3$ acting in a special way ... More

Brane world cosmological constant in the models with large extra dimensionsJan 16 2001We consider ``brane universe'' with nonzero tension in the models with large extra dimensions. We find exact solutions of higher-dimensional Einstein equations with single flat Minkowsky brane of arbitrary large tension (or brane cosmological constant) ... More

Semantic clustering of Russian web search results: possibilities and problemsSep 04 2014Oct 26 2014The paper deals with word sense induction from lexical co-occurrence graphs. We construct such graphs on large Russian corpora and then apply this data to cluster Mail.ru Search results according to meanings of the query. We compare different methods ... More

Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial CyclesOct 01 2007Nov 19 2007We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification of three-geometries) ... More

Sequential multiple hypothesis testing in presence of control variablesDec 15 2008Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ at this stage can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the problem ... More

Optimal sequential testing of two simple hypotheses in presence of control variablesDec 07 2008Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the classical problem ... More

Contravariant form on tensor product of highest weight modulesSep 25 2017May 07 2018We give a criterion for complete reducibility of tensor product $V\otimes Z$ of two irreducible highest weight modules over a classical or quantum reductive group in terms of a contravariant form on $V\otimes Z$. We endow the tensor product of modules ... More

The Dirac equation as one fourth-order equation for one function -- a general, manifestly covariant formFeb 09 2015Oct 21 2017Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac spinor function. ... More

One real function instead of the Dirac spinor functionAug 28 2010Aug 19 2011Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of the fourth order for the ... More

Efficient Heating of Thin Cylindrical Targets by Broad Electromagnetic Beams IMay 18 2004In many high-profile applications, such as nuclear fusion and pumping of active media of short-wavelength lasers, it is necessary to achieve high specific input of power of an electromagnetic beam in a target. Diffraction sets the lower limit to the transverse ... More

On dilaton-assisted generation of the Fermi scale from the Planck scaleMar 27 2019In scale-invariant theories of gravity the Planck mass $M_P$, which appears due to spontaneous symmetry breaking, can be the only scale at the classical level. It was argued that the second scale can be generated by a quantum non-perturbative gravitational ... More

Multilayered Model of SpeechJan 08 2018Human speech is the most important part of General Artificial Intelligence and subject of much research. The hypothesis proposed in this article provides explanation of difficulties that modern science tackles in the field of human brain simulation. The ... More

Smooth conjugacy of Anosov diffeomorphisms on higher dimensional toriApr 24 2008Sep 27 2008Let $L$ be a hyperbolic automorphism of $\mathbb T^d$, $d\ge3$. We study the smooth conjugacy problem in a small $C^1$-neighborhood $\mathcal U$ of $L$. The main result establishes $C^{1+\nu}$ regularity of the conjugacy between two Anosov systems with ... More

On a Generalization of Bernoulli and Euler NumbersJul 20 2011May 08 2013We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and identical distribution ... More

Notes on Chern-Simons Theory in the Temporal GaugeOct 27 2009We analyze the perturbative series expansion of vacuum expectation values (vevs) for Wilson loop operators in Chern-Simons (CS) gauge theory in the temporal gauge $A_{0}=0$. Following J. Labastida and E. P\'erez we introduce the notion of the kernels ... More

Explicit Rational Solution of the KZ Equation (example)Sep 07 2007We investigate the Knizhnik-Zamolodchikov linear differential system. The coefficients of this system are rational functions. We have proved that the solution of the KZ system is rational when k is equal to two and n is equal to three (see [5]) . In this ... More

Rational Solution of the KZ equation (example)Dec 06 2006We investigate the Knizhnik-Zamolodchikov linear differential system. The coefficients of this system are rational functions. We prove that the solution of the KZ system is rational when $k$ is equal to two and $n$ is equal to three. While doing so, we ... More

Classification of KdV vessels with constant parameters and two dimensional outer spaceJul 06 2014In this article we classify vessels producing solutions of some completely integrable PDEs, presenting a \textit{unified} approach for them. The classification includes such important examples as Korteweg-de Vries (KdV) and evolutionary Non Linear Schr\" ... More

Regularization of Mickelsson generators for non-exceptional quantum groupsDec 29 2015Let $\mathfrak{g}'\subset \mathfrak{g}$ be the pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces $\mathbb{C}^{N-2}\subset \mathbb{C}^N$ and $U_q(\mathfrak{g}')\subset U_q(\mathfrak{g})$ the ... More

Ideals on the Quantum Plane's jet spaceMar 20 2016The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime ideals. We will prove some results (theorems 1-4) about the prime spectrum ... More

Modal logic of some products of neighborhood framesMay 26 2014We consider modal logics of products of neighborhood frames and prove that for any pair $L$ and $L'$ of logics from set $\{S4, D4, D, T\}$ modal logic of products of $L$-neighborhood frames and $L'$-neighborhood frames is the fusion of $L$ and $L'$.

On dynamical adjoint functorMar 27 2012We give an explicit formula relating the dynamical adjoint functor and dynamical twist over nonalbelian base to the invariant pairing on parabolic Verma modules. As an illustration, we give explicit $U(sl(n))$- and $U_\hbar(sl(n))$-invariant star product ... More

Reflection equation and twisted YangiansDec 23 2006Jul 14 2007With any involutive anti-algebra and coalgebra automorphism of a quasitriangular bialgebra we associate a reflection equation algebra. A Hopf algebraic treatment of the reflection equation of this type and its universal solution is given. Applications ... More

The functional mechanics: evolution of the moments of distribution function and the Poincare recurrence theoremMay 17 2013This paper consider the functional mechanics as one of modern approaches to a problem of the correspondence between classical mechanics and the statistical physics. Deviations from classical trajectories are calculated and evolution of the moments of ... More

LSV models with stochastic interest rates and correlated jumpsNov 04 2015Dec 14 2015Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be extended by ... More

Nonlinear PDEs risen when solving some optimization problems in finance, and their solutionsOct 16 2015We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and discuss the ... More

To sigmoid-based functional description of the volatility smileJul 01 2014Dec 08 2014We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied volatilities which ... More

Quotients of conic bundlesDec 24 2013Apr 21 2015Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over projective line by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any quotient is ... More

On the Thermal History of Calculable Gauge MediationJul 23 2009Oct 27 2009Many messenger models with realistic gaugino masses are based on meta-stable vacua. In this work we study the thermal history of some of these models. Analyzing R-symmetric models, we point out that while some of the known messenger models clearly prefer ... More

Weil-Petersson Volumes of the Moduli Spaces of CY ManifoldsAug 04 2004Mar 25 2007In this paper it is proved that the volumes of the moduli spaces of polarized CY manifolds with respect to the Weil-Petersson metrics are finite and they are rational numbers.

Reply to Comment on "Spectra of strong magnetohydrodynamic turbulence from high-resolution simulations"Oct 03 2014In a Comment by Perez et al (2014) it is claimed that recently published simulations of Beresnyak (2014) are grossly underresolved, compared to theirs, and that Beresnyak (2014) failed to estimate numerical error. Both claims are contrary to the fact. ... More

The Flow Around a Cosmic String, Part I: Hydrodynamic SolutionJan 15 2015Cosmic strings are linear topological defects which are hypothesized to be produced during inflation. Most searches for strings have been relying on the string's lensing of background galaxies or CMB. In this paper I obtained the solution for the supersonic ... More

On the mechanism of prompt emission of gamma-ray burstsNov 05 2003We propose a model in which prompt gamma emission of gamma-ray bursts is the synchrotron radiation of electron-positron plasma in the ordered magnetic field in the direct vicinity of horizon of a young black hole formed in the core collapse of a massive ... More

Brane collisions in anti-de Sitter spaceSep 11 2001From the requirement of continuous matching of bulk metric around the point of brane collision we derive a conservation law for collisions of p-branes in (p+2)-dimensional space-time. This conservation law relates energy densities on the branes before ... More

Penalty Method for Obliquely Reflected DiffusionsSep 06 2015Sep 20 2016Consider a multidimensional obliquely reflected diffusion in a smooth domain. We approximate it by solutions of SDEs without reflection using the penalty method. We emulate the "hard barrier" of reflection by a "soft barrier" of a properly chosen drift ... More

Saturation model in the non-Glauber approachJul 15 2007Jul 31 2007In this paper a new saturation model is presented. This model is based on the theoretical solution for the generating functional, and it is quite different and not more complicated than the Glauber-like approach used before. The model describes the structure ... More

Optimal sequential multiple hypothesis testsNov 08 2008This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized. ... More

Kato perturbation expansion in classical mechanics and an explicit expression for a Deprit generatorJul 12 2013Aug 26 2014This work explores the structure of Poincare-Lindstedt perturbation series in Deprit operator formalism and establishes its connection to Kato resolvent expansion. A discussion of invariant definitions for averaging and integrating perturbation operators ... More

Penalty Method for Obliquely Reflected DiffusionsSep 06 2015Nov 13 2017Consider a multidimensional normally or obliquely reflected diffusion in a smooth domain. We approximate it by solutions of stochastic differential equations without reflection using the penalty method. That is, we approximate the reflection term with ... More

Clifford algebra and the projective model of Minkowski (pseudo-Euclidean) spacesJul 16 2013Jul 18 2013I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The emphasis is ... More

Clifford algebra and the projective model of Elliptic spacesOct 10 2013I apply the algebraic framework developed in arXiv:1101.4542 to study geometry of elliptic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in arXiv:1307.2917. ... More

Kolmogorov Complexity and the Garden of Eden TheoremDec 09 2012Suppose $\tau$ is a cellular automaton over an amenable group and a finite alphabet. Celebrated Garden of Eden theorem states, that pre-injectivity of $\tau$ is equivalent to non-existence of Garden of Eden configuration. In this paper we will prove, ... More

Elliptic stable envelope for Hilbert scheme of points in the planeApr 23 2018Apr 30 2018We find an explicit formula for the elliptic stable envelope in the case of the Hilbert scheme of points on a complex plane. The formula has a structure of a sum over trees in Young diagrams. In the limit we obtain the formulas for the stable envelope ... More

Polynomials associated with fixed points on the instanton moduli spaceApr 21 2014Using the Okounkov-Maulik stable map, we identify the equivariant cohomology of instanton moduli spaces with the space of polynomials on an infinite number of variables. We define the generalized Jack polynomials as the polynomials representing the classes ... More

Degenerate Sklyanin AlgebrasMar 08 2009New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for $sl(2,\mathbb{C})$. These solutions are shown to be related ... More

Solution of the Boussinesq equation using evolutionary vesselsJan 11 2013In this work we present a solution of the Boussinesq equation. The derived formulas include solitons, Schwartz class solutions and solutions, possessing singularities on a closed set Z of the (x,t) domain, obtained from the zeros of the tau function. ... More

The nonlocal Darboux transformation of the 2D stationary Schrödinger equation and its relation to the Moutard transformationMar 23 2013Mar 16 2014The nonlocal Darboux transformation of the two - dimensional stationary Schr\"odinger equation is considered and its relation to the Moutard transformation is established. It is shown that a special case of the nonlocal Darboux transformation provides ... More

How typical are pathological foliations in partially hyperbolic dynamics: an exampleJul 21 2009Jun 24 2010We show that for a large space of volume preserving partially hyperbolic diffeomorphisms of the 3-torus with non-compact central leaves the central foliation generically is non-absolutely continuous.

Non-Levi closed conjugacy classes of SO_q(N)Dec 11 2011Jul 14 2013We construct explicit quantization of semisimple conjugacy classes of the complex orthogonal group SO(N) with non-Levi isotropy subgroups through an operator realization on highest weight modules of the quantum group U_q(so(N)).

Non-Levi closed conjugacy classes of SP_q(2n)Oct 12 2011Jun 22 2012We construct explicit quantization of closed conjugacy classes of the complex symplectic group SP(2n) with non-Levi isotropy subgroups through an operator realization on highest weight modules over the quantum group U_q(sp(2n)).

Triple and Simultaneous Collisions of Competing Brownian ParticlesJan 24 2014Jan 29 2015Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. A triple collision occurs if ... More

Weak Convergence of Obliquely Reflected DiffusionsSep 06 2015Jun 15 2017Burdzy and Chen (1998) proved results on weak convergence of multidimensional normally reflected Brownian motions. We generalize their work by considering obliquely reflected diffusion processes. We require weak convergence of domains, which is stronger ... More

Equivariant vector bundles over quantum projective spacesMay 07 2018We construct equivariant vector bundles over quantum projective spaces making use of parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of projective space as a subalgebra in ... More

Fermion masses and quantum numbers from extra dimensionsJun 28 2001We study the localization of fermions on a brane embedded in a space-time with $AdS_n \times M^k$ geometry. Quantum numbers of localized fermions are associated with their rotation momenta around the brane. Fermions with different quantum numbers have ... More

Weak Convergence of Obliquely Reflected DiffusionsSep 06 2015Aug 20 2016Burdzy and Chen (1998) proved results on weak convergence of multidimensional normally reflected Brownian motions. We generalize their work by considering obliquely reflected diffusion processes. We require weak convergence of domains, which is stronger ... More

Proalgebraic crossed modules of quasirational presentationsJul 11 2015Sep 24 2016We introduce the concept of quasirational relation modules for discrete and pro-$p$ presentations of discrete and pro-$p$ groups and show that aspherical presentations and their subpresentations are quasirational. In the pro-$p$-case quasirationality ... More

A Simple Recurrence Within the $3$-adics and Mixed-Radix $\textbf{2}$-adics of the 3x+1 Accelerated First-Inverse MapJun 25 2015Feb 18 2016This article analyzes the $3x+1$ Accelerated First-Inverse map: we will consider the functional powers of the function $\mathcal{B}: Z_3 \to Z_3$ defined as $$ \mathcal{B}\left(3q+r\right) = \begin{cases} 3q, & r = 0\\ \notag 4q+1, & r = 1\\ \notag 2q+1, ... More

Cohomology theories for highly structured ring spectraNov 18 2002This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological Andr\'e-Quillen cohomology and of topological derivations are described. We give sample calculations of ... More

Exploring mutexes, the Oracle RDBMS retrial spinlocksDec 29 2012Spinlocks are widely used in database engines for processes synchronization. KGX mutexes is new retrial spinlocks appeared in contemporary Oracle versions for submicrosecond synchronization. The mutex contention is frequently observed in highly concurrent ... More