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Moving solitons in a one-dimensional fermionic superfluidAug 27 2014Feb 18 2015A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov-de Gennes equations, which are solved exactly in the Andreev approximation. The soliton ... More

A Strongly-Interacting Dirac Liquid on the Surface of a Topological Kondo InsulatorApr 22 2014Aug 27 2014A topological Kondo insulator (TKI) is a strongly-correlated material, where hybridization between the conduction electrons and localized f-electrons gives rise to a crossover from a metallic behavior at high temperatures to a topologically non-trivial ... More

Fluctuational internal Josephson effect in topological insulator filmApr 04 2013Jul 29 2013Tunneling between opposite surfaces of topological insulator thin film populated by electrons and holes is considered. We predict considerable enhancement of tunneling conductivity by Cooper electron-hole pair fluctuations that are precursor of their ... More

Many-Body Theory of Trion Absorption Features in Two-Dimensional SemiconductorsSep 20 2016Recent optical studies of monolayer transition metal dechalcogenides have demonstrated that their excitonic absorption feature splits into two widely separated peaks at finite carrier densities. The additional peak is usually attributed to the presence ... More

Self-consistent theory of ferromagnetism on the surface of a topological insulatorJan 29 2014Mar 27 2014The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities, mediated by Dirac surface states on the surface of a topological insulator, leads to impurities ferromagnetic ordering. We present a self-consistent theory of the ordering, ... More

Emergence of Topologically Protected Helical States in Minimally Twisted Bilayer GrapheneFeb 08 2018Bilayer graphene samples in which inversion symmetry is broken have quantum valley Hall ground states that support counterpropogating topologically protected helical (TPH) edge states localized along domain walls between AB and BA stacking regions. Moreover, ... More

Spin-plasmons in topological insulatorJul 23 2011Collective plasmon excitations in a helical electron liquid on the surface of strong three-dimensional topological insulator are considered. The properties and internal structure of these excitations are studied. Due to spin-momentum locking in helical ... More

Anomalous Coulomb Drag in Electron-Hole Bilayers due to the Formation of ExcitonsMay 31 2015Jan 27 2016Several recent experiments have reported an anomalous temperature dependence of the Coulomb drag effect in electron-hole bilayers. Motivated by these puzzling data, we study theoretically a low-density electron-hole bilayer, where electrons and holes ... More

Non-Markovian quantum friction of bright solitons in superfluidsDec 23 2015May 04 2016We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov ... More

Amperean Pairing at the Surface of Topological InsulatorsMar 13 2016Aug 12 2016The surface of a 3D topological insulator is described by a helical electron state with the electron's spin and momentum locked together. We show that in the presence of ferromagnetic fluctuations the surface of a topological insulator is unstable towards ... More

Transport of Dirac electrons in a random magnetic field in topological heterostructuresMar 01 2016We consider the proximity effect between Dirac states at the surface of a topological insulator and a ferromagnet with easy plane anisotropy, which is described by the \emph{XY}-model and undergoes a Berezinskii-Kosterlitz-Thouless (BKT) phase transition. ... More

Comment on the article "On the Existence of the N-Body Efimov Effect" by X. P. WangApr 25 2012It is shown that the proof of the main theorem in the article "On the Existence of the N-Body Efimov Effect" by X. P. Wang, J. Funct. Anal. 209 (2004) pp. 137--161, is incorrect.

Essential spectrum of a limit of self--adjoint operatorsAug 23 2012Aug 27 2012For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence.

Universal Angular Probability Distribution of Three Particles near Zero Energy ThresholdDec 02 2011Mar 12 2013We study bound states of a 3--particle system in $\mathbb{R}^3$ described by the Hamiltonian $H(\lambda_n) = H_0 + v_{12} + \lambda_n (v_{13} + v_{23})$, where the particle pair $\{1,2\}$ has a zero energy resonance and no bound states, while other particle ... More

Zero Energy Bound States in Many--Particle SystemsDec 01 2011It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed ... More

Integrals of open 2D latticesDec 21 2009We present an explicit formula for integrals of the open 2D Toda lattice of type $A_n$. This formula is applicable for various reductions of this lattice. To illustrate the concept we find integrals of the Toda $G_2$ lattice. We also reveal a connection ... More

Universal low-energy behavior in three-body systemsJan 24 2014Mar 03 2015We consider a pairwise interacting quantum 3-body system in 3-dimensional space with finite masses and the interaction term $V_{12} + \lambda(V_{13} + V_{23})$, where all pair potentials are assumed to be nonpositive. The pair interaction of the particles ... More

Resonant Faraday and Kerr effects due to in-gap states on the surface of a topological insulatorAug 21 2014Nov 25 2014When Dirac electrons on the surface of a topological insulator are gapped, the resulting quantum anomalous Hall effect leads to universal magneto-optical Faraday and Kerr effects in the low frequency limit. However, at higher frequencies different excitations ... More

Charged skyrmions on the surface of a topological insulatorDec 02 2014Feb 13 2015We consider the interplay between magnetic skyrmions in an insulating thin film and the Dirac surface states of a 3D topological insulator (TI), coupled by proximity effect. The magnetic texture of skyrmions can lead to confinement of Dirac states at ... More

Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrumOct 18 2012Feb 06 2013We consider a system of $N$ pairwise interacting particles described by the Hamiltonian $H$, where $\sigma_{ess} (H) = [0,\infty)$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs and obey ... More

Zero Energy Bound States in Three--Particle SystemsDec 02 2009Jan 22 2010Under certain restrictions on pair--potentials it is proved that the eigenvalues in the three--particle system are absorbed at zero energy threshold if there is no negative energy bound states and zero energy resonances in particle pairs.

Manifestation of Universality in the Asymmetric Helium Trimer and in the Halo Nucleus $^{22}$CApr 20 2016We prove that the corner angle distributions in the bound three-body system AAB, which consists of two particles of type A and one particle of type B, approach universal form if the pair AA has a virtual state at zero energy and the binding energy of ... More

On non-Abelian Toda $A_2^{(1)}$ model and related hierarchiesDec 21 2009We study limiting cases of the two known integrable chiral-type models with tree-dimensional configuration space. One of the initial models is the non-Abelian Toda $A_2^{(1)}$ model and the other was found by means of the symmetry approach by A.G. Meshkov ... More

Selecting fast folding proteins by their rate of convergenceApr 02 2012Feb 06 2013We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using only the very ... More

Lagrangian Relaxation for MAP Estimation in Graphical ModelsSep 28 2007We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph, but subject ... More

A microprocessor based on a two-dimensional semiconductorDec 03 2016The advent of microcomputers in the 1970s has dramatically changed our society. Since then, microprocessors have been made almost exclusively from silicon, but the ever-increasing demand for higher integration density and speed, lower power consumption ... More

Nuclear interactions with modern three-body forces lead to the instability of neutron matter and neutron starsJun 24 2013Jul 30 2014It is shown that the neutron matter interacting through Argonne V18 pair-potential plus modern variants of Urbana or Illinois three-body forces is unstable. For the energy of $N$ neutrons $E(N)$, which interact through these forces, we prove mathematically ... More

Drag effect and Cooper electron-hole pair fluctuations in a topological insulator filmAug 12 2013Nov 19 2013Manifestations of fluctuating Cooper pairs formed by electrons and holes populating opposite surfaces of a topological insulator film in the Coulomb drag effect are considered. Fluctuational Aslamazov-Larkin contribution to the transresistance between ... More

Resonant manifestations of chiral excitons in magnetooptical Faraday and Kerr effects in topological insulator filmAug 16 2012Jun 20 2013Manifestation of chiral excitons on surfaces of topological insulator thin film with magnetically induced energy gap in the surface spectrum in magnetooptical Kerr and Faraday effects is analyzes. Excitonic contribution to a surface optical conductivity ... More

On Small Gaps in the Length SpectrumFeb 15 2016We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the gaps. On the ... More

Metastable states and macroscopic quantum tunneling in a cold atom Josephson ringSep 18 2009We study macroscopic properties of a system of weakly interacting neutral bosons confined in a ring-shaped potential with a Josephson junction. We derive an effective low energy action for this system and evaluate its properties. In particular we find ... More

Catalog of Nearby Galaxies and the Local Cosmic WebOct 04 2004We compiled an all-sky catalog of 451 nearby galaxies, each having an individual distance estimate $D \la 10$ Mpc or the radial velocity $V_{LG} < 550$ km s$^{-1}$. The catalog contains data on basic optical and HI properties of the galaxies: their diameters, ... More

A remark on approximation of open sets with regular bounded onesDec 08 2010We show that any open set in $\R^n$ is a union of an ascending sequence of bounded open sets with analytic boundary. This is just a technical result, which is probably known. We believe, however, that it can be useful for studing BVPs on irregular open ... More

Topological Semantics and DecidabilityMar 05 2007Jun 01 2007It is well-known that the basic modal logic of all topological spaces is $S4$. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of $T_0$, ... More

On the derivative of two functions from Denjoy-Tichy-Uitz familyFeb 14 2013Dec 01 2013The family of functions, we investigate in this article, was originally introduced by A.Denjoy and later rediscovered by R Tichy and J. Uitz. We denote the functions of the family by $g_{\lambda}(x),$ where $\lambda\in(0,1)$. The definition will be given ... More

Asymptotic dimension of one relator groupsJul 21 2006We show that one relator groups viewed as metric spaces with respect to the word-length metric have finite asymptotic dimension in the sense of Gromov and give an estimate of their asymptotic dimension in terms of the relator length.

On subexponential tails for the maxima of negatively driven compound renewal and Lévy processesAug 31 2016We study subexponential tail asymptotics for the distribution of the maximum $M_t:=\sup_{u\in[0,t]}X_u$ of a process $X_t$ with negative drift for the entire range of $t>0$. We consider compound renewal processes with linear drift and L\'evy processes. ... More

Unbalanced Renormalization of Tunneling in MOSFET-type Structures in Strong High-Frequency Electric FieldsAug 12 2007Two-dimensional electron gas coupled to adjacent impurity sites in high-frequency out-of-plane ac control electric field is investigated. Modification of tunneling rates as a function of the field amplitude is calculated. Nonlinear dependence on the ac ... More

The quotient girth of normed spaces, and an extension of Schäffer's dual girth conjecture to GrassmanniansNov 22 2011Dec 01 2011In this note we introduce a natural Finsler structure on convex surfaces, referred to as the projective Finsler structure, which is dual in a sense to the obvious inclusion of a convex surface in a normed space. It has an associated projective girth, ... More

Clown: a Microprocessor Simulator for Operating System StudiesJul 21 2012In this paper, I present the design and implementation of Clown--a simulator of a microprocessor-based computer system specifically optimized for teaching operating system courses at undergraduate or graduate levels. The package includes the simulator ... More

Error bounds for approximations with deep ReLU networksOct 03 2016We study how approximation errors of neural networks with ReLU activation functions depend on the depth of the network. We establish rigorous error bounds showing that deep ReLU networks are significantly more expressive than shallow ones as long as approximations ... More

Commuting symplectomorphisms and Dehn twists in divisorsMay 18 2014Jun 02 2016Two commuting symplectomorphisms of a symplectic manifold give rise to actions on Floer cohomologies of each other. We prove the elliptic relation saying that the supertraces of these two actions are equal. In the case when a symplectomorphism $f$ commutes ... More

A Theory of Intermittency Renormalization of 1D Gaussian Multiplicative Chaos MeasuresSep 29 2016A theory of intermittency differentiation is developed for a general class of 1D Gaussian Multiplicative Chaos measures including the measure of Bacry and Muzy on the interval and circle as special cases. An exact, non-local functional equation is derived ... More

New models of income distribution, graduation as the explanation of Gini coefficientSep 15 2013The paper covers the new model of wage distribution in typical group of people. The model provides the opportunity to reparameterize applicable income distribution model: Pareto, logarithmically normal, logarithmically logistic, Dagum etc. The model ensures ... More

Attainable numbers and the Lagrange spectrumJun 06 2016Oct 14 2016The paper is devoted to the properties of the Lagrange spectrum left endpoints and so-called attainable numbers.

Storage option an Analytic approachNov 04 2010May 28 2012The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show ... More

On extension for infinite horizon game of pursuit-evasionDec 16 2010The extension of a conflict control problem with infinite horizon is constructed. This extension is the projective limit of restricted games. Relations between "sensitivity to target set" and the existence of the optimal control are studied. Special attention ... More

Classical Interaction Cannot Replace Quantum NonlocalityJan 08 2009We present a two-player communication task that can be solved by a protocol of polylogarithmic cost in the simultaneous message passing model with classical communication and shared entanglement, but requires exponentially more communication in the classical ... More

Classical Interaction Cannot Replace a Quantum MessageMar 23 2007Feb 21 2008We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O (log n) but requires exponentially more communication in the classical interactive (bounded error) model.

Free energy in the Sherrington-Kirkpatrick model with constrained magnetizationMay 18 2004Oct 12 2004This paper has been withdrawn since a trivial proof of the result has been pointed out to the author.

Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation ProcedureNov 01 2016We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes ... More

Enstrophy growth in the viscous Burgers equationFeb 09 2012We study bounds on the enstrophy growth for solutions of the viscous Burgers equation on the unit circle. Using the variational formulation of Lu and Doering, we prove that the maximizer of the enstrophy's rate of change is sharp in the limit of large ... More

Asymptotic properties of excited states in the Thomas--Fermi limitNov 24 2009Excited states are stationary localized solutions of the Gross--Pitaevskii equation with a harmonic potential and a repulsive nonlinear term that have zeros on a real axis. Existence and asymptotic properties of excited states are considered in the semi-classical ... More

A classification of Lie algebras of pseudounitary groups in the techniques of Clifford algebrasMay 23 2007In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudounitary groups. Our main ... More

Courant-Dorfman algebras and their cohomologyFeb 27 2009Nov 30 2009We introduce a new type of algebra, the Courant-Dorfman algebra. These are to Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson algebras to Poisson manifolds. We work with arbitrary rings and modules, without any regularity, ... More

Chemistry of a protoplanetary disk with grain settling and Lyman alpha radiationNov 01 2010We present results from a model of the chemical evolution of protoplanetary disks. In our models we directly calculate the changing propagation and penetration of a high energy radiation field with Lyman alpha radiation included. We also explore the effect ... More

Production of Gas Phase Zinc Oxide Nanoclusters by Pulsed Laser AblationJun 10 2004We present experimental results on the photoluminescence (PL) of gas-suspended zinc oxide nanoclusters prepared during ablation of sintered ZnO targets by a pulsed ArF laser in the presence of oxygen ambient gas. The PL spectra in the UV spectral region ... More

The Frequency of Rapid Rotation Among K Giant StarsMar 07 2011We present the results of a search for unusually rapidly rotating giant stars in a large sample of K giants (~1300 stars) that had been spectroscopically monitored as potential targets for the Space Interferometry Mission's Astrometric Grid. The stars ... More

Microlocal CategoryNov 29 2015Given a compact symplectic manifold whose symplectic form has integer periods, one associates to it a dg category based on the microlocal analysis according to Kashiwara-Schapira

Medical Process Modeling: an Artifact-Centric ApproachMar 19 2013In this position paper we argue that just as traditional business process modeling has been adopted to deal with clinical pathways, also the artifact-centric process modeling technique may be successfully used to model various kinds of medical processes: ... More

Moment inversion problem for piecewise D-finite functionsJan 29 2009Jul 01 2009We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial ... More

Quantization of Poisson structures on $\R^2$May 09 1997An 'isomorphism' between the 'moduli space' of star products on $\R^2$ and the 'moduli space' of all formal Poisson structures on $\R^2$ is established.

Introduction to the SK modelNov 30 2014This is a review paper for the "Current Developments in Mathematics 2014" conference.

The Parisi formula for mixed $p$-spin modelsDec 19 2011Mar 31 2014The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for ... More

Spin glass models from the point of view of spin distributionsMay 16 2010May 24 2013In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can think of this ... More

The Baum-Connes conjecture for countable subgroups of SL(2)Dec 21 2007We present an alternative approach to the result of Guentner, Higson, and Weinberger concerning the Baum-Connes conjecture for finitely generated subgroups of SL(2,C). Using finite-dimensional methods, we show that the Baum-Connes assembly map for such ... More

Multiplicity One Theorems and Invariant DistributionsJul 06 2009This is my PhD thesis submitted to the Weizmann Institute of Science. It is based on the papers [AG08c], [AG08d], [AGRS07], [AGS08], [AGS09], [Aiz08] and [SZ08]. This thesis includes an introduction to Gelfand pairs and invariant distributions, a list ... More

A Family of Unitary Operators Satisfying a Poisson-type Summation FormulaNov 20 2011We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operator which satisfies this formula. We next find the diagonal form of this ... More

Validity of approximations applied in calculations of single-wall metallic carbon nanotube current-voltage characteristicsNov 11 2013The calculation results of dependencies of electric current in the infinitely long single-wall metallic carbon nanotubes of armchair type with different diameter values on the strength of constant and uniform longitudinal electric field applied to them ... More

Cavity method in the spherical Sherrington-Kirkpatrick modelApr 04 2006Aug 18 2007We develop a cavity method in the spherical Sherrington-Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.

Free energy in the generalized Sherrington-Kirkpatrick mean field modelMay 18 2004Jun 14 2005Recently Michel Talagrand gave a rigorous proof of the Parisi formula in the Sherrington-Kirkpatrick model. In this paper we build upon the methodology developed by Talagrand and extend his result to the class of SK type models in which the spins have ... More

Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier DataNov 04 2012Mar 17 2014In this paper we provide a reconstruction algorithm for piecewise-smooth functions with a-priori known smoothness and number of discontinuities, from their Fourier coefficients, posessing the maximal possible asymptotic rate of convergence -- including ... More

Large regular QCD coupling at Low Energy?Jul 09 2008The issue is the expediency of the QCD notions use in the low energy region down to the confinement scale, and, in particular, the efficacy of the QCD invariant coupling \bar{\alpha}_s(Q^2) with a minimal analytic modification in this domain. To this ... More

Gromov's macroscopic dimension conjectureApr 30 2009In this note we construct a closed 4-manifold having torsion-free fundamental group and whose universal covering is of macroscopic dimension 3. This yields a counterexample to Gromov's conjecture about the falling of macroscopic dimension.

The number of multinomial coefficients based on a set of partitions of n into k parts and divided by k evenlyApr 30 2012In this paper we obtained an original integer sequence based on the properties of the multinomial coefficient. We investigated a property of the sequence that shows connection with a primality testing. For any prime n the n-th term in the sequence is ... More

Residue Formulation of Chern Character on Smooth ManifoldsMay 07 2005The Chern character of a complex vector bundle is most conveniently defined as the exponential of a curvature of a connection. It is well known that its cohomology class does not depend on the particular connection chosen. It has been shown by Quillen ... More

On the collisions of singular points of complex algebraic plane curvesAug 09 2007Apr 21 2009We study the "generic" degenerations of curves with two singular points when the points merge. First, the notion of generic degeneration is defined precisely. Then a method to classify the possible results of generic degenerations is proposed in the case ... More

An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximationApr 09 2009Aug 06 2009Let $Y_0$ be a not very well approximable $m\times n$ matrix, and let $M$ be a connected analytic submanifold in the space of $m\times n$ matrices containing $Y_0$. Then almost all $Y\in M$ are not very well approximable. This and other similar statements ... More

Some applications of homogeneous dynamics to number theoryOct 18 2002This survey paper is not a complete reference guide to number-theoretical applications of ergodic theory. Instead, it considers an approach to a class of problems involving Diophantine properties of $n$-tuples of real numbers, namely, describes a specific ... More

Chaos in temperature in generic 2p-spin modelsFeb 12 2015Dec 18 2015We prove chaos in temperature for even $p$-spin models which include sufficiently many $p$-spin interaction terms. Our approach is based on a new invariance property for coupled asymptotic Gibbs measures, similar in spirit to the invariance property that ... More

On the structure of graded symplectic supermanifolds and Courant algebroidsMar 12 2002This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles (E\to M_{0}) by canonically associating to such a bundle ... More

Quasi-Lie bialgebroids and twisted Poisson manifoldsDec 17 2001Nov 21 2002We develop a theory of quasi-Lie bialgebroids using a homological approach. This notion is a generalization of quasi-Lie bialgebras, as well as twisted Poisson structures with a 3-form background which have recently appeared in the context of string theory, ... More

Courant algebroids, derived brackets and even symplectic supermanifoldsOct 15 1999In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant algebroids to generalize the notion of the Drinfeld double to ... More

On a criterion of properness of multimapsNov 09 2009The close relation between properness and closedness of maps is well-known. For instance, for Fredholm mappings of infinite dimensional Banach manifolds, these properties are equivalent. On the other hand, properness of maps plays an important role for ... More

Quantum Money with Classical VerificationSep 02 2011Mar 15 2012We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. ... More

A Note on Shared Randomness and Shared Entanglement in CommunicationMay 12 2005Aug 06 2005We consider several models of 1-round classical and quantum communication, some of these models have not been defined before. We "almost separate" the models of simultaneous quantum message passing with shared entanglement and the model of simultaneous ... More

Improved bounds for arithmetic progressions in product setsFeb 12 2015Let $B$ be a set of natural numbers of size $n$. We prove that the length of the longest arithmetic progression contained in the product set $B.B = \{bb'| \, b, b' \in B\}$ cannot be greater than $O(n \log n)$ which matches the lower bound provided in ... More

Instabilities of dispersion-managed solitons in the normal dispersion regimeMar 13 2000Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of different pulse ... More

Translationally invariant nonlinear Schrodinger latticesMar 10 2006Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed. The discrete NLS equation with the most general cubic polynomial function is considered. ... More

Free energy in the Potts spin glassDec 01 2015Dec 28 2015We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi variational ... More

Recombination formulae for the spectrum of curve singularities and some applicationsMar 23 2014May 16 2014We obtain some recombination formulae for the spectra of (complex, reduced) plane curve singularities. As an application we prove: a generalization of Durfee's bound; a generalization of Givental's bound; the multiplicity of the curve singularity is determined ... More

An extension of quantitative nondivergence and applications to Diophantine exponentsAug 25 2005May 19 2008We present a sharpening of nondivergence estimates for unipotent (or more generally polynomial-like) flows on homogeneous spaces. Applied to metric Diophantine approximation, it yields precise formulas for Diophantine exponents of affine subspaces of ... More

Badly approximable systems of affine formsAug 12 1998Jan 20 1999We prove an inhomogeneous analogue of W. M. Schmidt's (1969) theorem on Hausdorff dimension of the set of badly approximable systems of linear forms. The proof is based on ideas and methods from the theory of dynamical systems, in particular, on abundance ... More

Diophantine exponents of measures: a dynamical approachJun 24 2005We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional Diophantine approximation ... More

Beam-Beam Resonances for Different Collision SchemesJun 25 2008One of the main advantages of proposed by P. Raimondi "Crab Waist" collision scheme is a strong suppression of betatron resonances excited by beam-beam interaction. Some qualitative explanations with numerical examples, describing beam-beam resonances ... More

On Riemann zeroes, Lognormal Multiplicative Chaos, and Selberg IntegralJun 21 2015Nov 29 2015Rescaled Mellin-type transforms of the exponential functional of the Bourgade-Kuan-Rodgers statistic of Riemann zeroes are conjecturally related to the distribution of the total mass of the limit lognormal stochastic measure of Mandelbrot-Bacry-Muzy. ... More

On weak Lie 2-algebrasDec 20 2007A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between ... More

A note on the residue Chern characterNov 09 2005The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth differential ... More

Structure of finite-RSB asymptotic Gibbs measures in the diluted spin glass modelsJun 18 2014Feb 25 2015We suggest a possible approach to proving the M\'ezard-Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we show that a ... More

On the replica symmetric solution of the K-sat modelApr 22 2013In this paper we translate Talagrand's solution of the K-sat model at high temperature into the language of asymptotic Gibbs measures. Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions ... More