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Real or Imaginary? (On pair creation in de Sitter space)Sep 21 2009Jul 06 2010Using properly defined Feynman propagator we obtain non--zero imaginary contribution to the scalar field effective action in even dimensional de Sitter space. Such a propagator follows from the path integral in de Sitter space and obeys composition principle ... More

Lectures on General Theory of RelativityJan 19 2016Nov 19 2016These are lectures on General Theory of Relativity that were given to students of the Mathematical Faculty of the Higher School of Economics in Moscow.

Expansion in Feynman Graphs as Simplicial String TheoryJul 02 2004Aug 22 2004We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory -- the theory describing embeddings of the two--dimensional simplicial complexes into ... More

Non-Abelian Structures in BSFT and RR couplingsSep 29 2001Oct 04 2001In this talk we show that the tachyon annihilation combined with an approximation, in which string theory non-commutativity structure is captured by the algebra of differential operators on space-time, gives a unified point of view on: non-Abelian structures ... More

Towards the Theory of Non--Abelian Tensor Fields IIJun 03 2005We go on with the definition of the theory of the non--Abelian two--tensor fields and find the gauge transformation rules and curvature tensor for them. To define the theory we use the surface {\it exponent} proposed in hep--th/0503234. We derive the ... More

Simplicial vs. Continuum String Theory and Loop EquationsFeb 19 2005Apr 07 2005We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory -- the theory describing embeddings of two--dimensional simplicial complexes into the space--time of the matrix field theory. This ... More

Classical radiation by free-falling charges in de Sitter spacetimeJun 16 2010Aug 06 2010We study the classical radiation emitted by free-falling charges in de Sitter spacetime coupled to different kinds of fields. Specifically we consider the cases of the electromagnetic field, linearized gravity and scalar fields with arbitrary mass and ... More

A simple way to take into account back reaction on pair creationDec 17 2009Mar 08 2010We propose a simple and systematic way of accounting for the back reaction on the background field due to the pair creation in the four--dimensional scalar QED. This method is straightforwardly generalizable to the gravity backgrounds. In the case of ... More

On the relation between Unruh and Sokolov--Ternov effectsOct 29 2006May 13 2007We show that the Sokolov--Ternov effect -- the depolarization of particles in storage rings coming from synchrotron radiation due to spin flip transitions -- is physically equivalent to the Unruh effect for circular acceleration if one uses a spin 1/2 ... More

On the physical meaning of the Unruh effectMay 17 2007Oct 19 2007We present simple arguments that detectors moving with constant acceleration (even acceleration for a finite time) should detect particles. The effect is seen to be universal. Moreover, detectors undergoing linear acceleration and uniform, circular motion ... More

Hawking temperature in the tunneling pictureAug 15 2006Sep 24 2006We examine Hawking radiation from a Schwarzschild black hole in several reference frames using the quasi-classical tunneling picture. It is shown that when one uses, $\Gamma \propto \exp(Im [\oint p dr])$, rather than, $\Gamma \propto \exp(2 Im [\int ... More

Interacting Field Theories in de Sitter Space are Non-UnitaryAug 29 2008Sep 27 2008It is well known that there should be a total cancellation of the IR divergences in unitary interacting field theories, such as QED and gravity. The cancellation should be at all orders between loop and tree level contributions to cross--sections. This ... More

Subtleties in the quasi-classical calculation of Hawking radiationMay 17 2008Oct 02 2008he quasi-classical method of deriving Hawking radiation is investigated. In order to recover the original Hawking temperature one must take into account a previously ignored contribution coming from the temporal part of the action. This contribution plus ... More

Majorana neutrinos and other Majorana particles:Theory and experimentDec 10 2014This is a somewhat modified version of Chapter 15 of the book "The Physics of Ettore Majorana", by Salvatore Esposito with contributions by Evgeny Akhmedov (Ch. 15) and Frank Wilczek (Ch. 14), Cambridge University Press, 2014.

Optimal quadrature formulas for the Cauchy type singular integral in the Sobolev space $L_2^{(2)}(0,1)$Jul 02 2017In the present paper in $L_2^{(2)}(0,1)$ S.L.Sobolev space the optimal quadrature formula is constructed for approximate calculation of Cauchy type singular integral.

A way to distinguish very compact stellar objects from black holesJan 15 2016Feb 15 2016We propose a way to distinguish compact stellar object, whose size is very close to its Schwarzschild radius, from the collapsing stars. Namely, we show that {\it massive} fields in the vicinity of a very compact stellar object have discrete energy levels. ... More

On Unification of RR CouplingsMay 22 2001May 30 2001We consider the couplings of RR fields with open string sector for $Dp$-${\overline{Dp}}$ backgrounds of various $p$. Proposed approach, based on the approximation of the open string algebra by the algebra of differential operators, provides the unified ... More

Thermal radiation of various gravitational backgroundsMay 14 2006Feb 17 2007We present a simple and general procedure for calculating the thermal radiation coming from any stationary metric. The physical picture is that the radiation arises as the quasi--classical tunneling of particles through a gravitational barrier. We show ... More

Running couplings and triviality of field theories on non-commutative spacesOct 01 2000Oct 07 2000We examine the issue of renormalizability of asymptotically free field theories on non-commutative spaces. As an example, we solve the non-commutative O(N) invariant Gross-Neveu model at large N. On commutative space this is a renormalizable model with ... More

De Sitter space and perpetuum mobileMay 17 2009Feb 14 2010We give general arguments that any interacting non--conformal {\it classical} field theory in de Sitter space leads to the possibility of constructing a perpetuum mobile. The arguments are based on the observation that massive free falling particles can ... More

Ultraviolet phenomena in AdS self-interacting quantum field theoryFeb 08 2018We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $\phi^4$ field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general ... More

Hawking radiation and secularly growing loop correctionsAug 29 2015Dec 20 2015We study the expectation value of the energy momentum tensor during thin shell collapse for a massive, real, scalar field theory. At tree-level, we find thermal, Hawking-type, behaviour for the energy flux. Using the Schwinger-Keldysh technique, we calculate ... More

Non-commutative Gross-Neveu model at large NMar 23 2001Apr 05 2001The non-commutative O(N) Gross-Neveu model is solved in the large N limit in two and three space-time dimensions. The commutative version of the two dimensional model is a renormalizable quantum field theory, both in a coupling constant expansion and ... More

The Existence of Quasimeromorphic MappingsApr 30 2004We prove that a Kleinian group $G$ acting upon $\mathbb{H}^{n}$ admits a non-constant $G$-automorphic function, even if it has torsion elements, provided that the orders of the elliptic (torsion) elements are uniformly bounded. This is accomplished by ... More

The minimal resolution of a cointerval edge ideal is multiplicativeSep 23 2016We show that the minimal resolution of the quotient of the polynomial algebra over a field by a cointerval edge ideal can be given the structure of a DG-algebra.

Resolutions of modules with initially linear syzygiesJun 09 2011Dec 16 2011We introduce the class of modules with initially linear syzygies, which includes ideals with linear quotients, and study their minimal resolutions. Using a contracting homotopy for the resolutions, we see that the minimal resolution of a matroidal monomial ... More

Estimating Global Errors in Time SteppingMar 17 2015May 10 2017This study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky's procedure; however, the proposed approach ... More

Ramsey properties of randomly perturbed dense graphsFeb 06 2019We investigate Ramsey properties of a random graph model in which random edges are added to a given dense graph. Specifically, we determine lower and upper bounds on the function $p=p(n)$ that ensures that for any dense graph $G_n$ a.a.s. every 2-colouring ... More

Paradoxes of neutrino oscillationsMay 12 2009Jun 20 2009Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss, in the framework of the wave packet approach, a number of such issues, including the relevance of the "same energy" ... More

Comment on "New conditions for a total neutrino conversion in a medium"Oct 21 1999Oct 22 1999We show that the conditions for total neutrino conversion found in [1] are equivalent to the conditions of maximal depth (parametric resonance) and ($\pi/2 + \pi k$) - phase of parametric oscillations. Therefore the effects considered in [1] are a particular ... More

Decoherence by wave packet separation and collective neutrino oscillationsMay 28 2014Mar 01 2017In dense neutrino backgrounds present in supernovae and in the early Universe, neutrino oscillations may exhibit complex collective phenomena, such as synchronized oscillations, bipolar oscillations and spectral splits and swaps. In this Letter we consider ... More

Gluing of Surfaces with Polygonal BoundariesDec 17 2007Aug 24 2008By pairwise gluing of edges of a polygon, one produces two-dimensional surfaces with handles and boundaries. In this paper, we count the number ${\cal N}_{g,L}(n_1, n_2, ..., n_L)$ of different ways to produce a surface of given genus $g$ with $L$ polygonal ... More

Neutrino oscillograms of the Earth: effects of 1-2 mixing and CP-violationApr 09 2008Jun 18 2008We develop a comprehensive description of three flavor neutrino oscillations inside the Earth in terms of neutrino oscillograms in the whole range of nadir angles and for energies above 0.1 GeV. The effects of the 1-2 mass splitting and mixing as well ... More

Baryogenesis via neutrino oscillationsMar 05 1998Jul 29 1998We propose a new mechanism of leptogenesis in which the asymmetries in lepton numbers are produced through the CP-violating oscillations of ``sterile'' (electroweak singlet) neutrinos. The asymmetry is communicated from singlet neutrinos to ordinary leptons ... More

On the Asymptotic Formula for the Number of Plane Partitions of Positive IntegersJan 11 2006Jan 24 2006The paper presents a discussion on the asymptotic formula for the number of plane partitions of a large positive integer.

Graded gamma ringsDec 30 2014Jan 06 2017We introduce graded gamma rings from a more general point of view via methods developed by Krasner and Halberstadt for graded rings. We propose three equivalent aspects of studying graded gamma rings, nonhomogeneous, semihomogeneous and homogeneous. The ... More

Residual-based iterations for the generalized Lyapunov equationJul 27 2018This paper treats iterative solution methods to the generalized Lyapunov equation. Specifically it expands the existing theoretical justification for the alternating linear scheme (ALS) from the stable Lyapunov equation to the stable generalized Lyapunov ... More

A Multiple Prior Monte Carlo Method for the Backward Heat Diffusion ProblemMay 16 2014We consider the nonlinear inverse problem of reconstructing the heat conductivity of a cooling fin, modeled by a 2-dimensional steady-state equation with Robin boundary conditions. The Metropolis Hastings Markov Chain Monte Carlo algorithm is studied ... More

Quantization of Topological Invariants under Symmetry-Breaking DisorderJul 09 2015Nov 10 2015In the strictly periodic setting, the electric polarization of inversion-symmetric solids with and without time-reversal symmetry and the isotropic magneto-electric response function of time-reversal symmetric insulators are known to be topological invariants ... More

Characterization of the Quantized Hall Insulator Phase in the Quantum Critical RegimeJan 22 2013Feb 07 2014The conductivity $\sigma$ and resistivity $\rho$ tensors of the disordered Hofstadter model are mapped as functions of Fermi energy $E_F$ and temperature $T$ in the quantum critical regime of the plateau-insulator transition (PIT). The finite-size errors ... More

Forman's Ricci curvature - From networks to hypernetworksOct 17 2018Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the common name ... More

Comments on QED with background electric fieldsJan 05 2009Feb 23 2009It is well known that there is a total cancellation of the \emph{factorizable} IR divergences in unitary interacting field theories, such as QED and quantum gravity. In this note we show that such a cancellation does not happen in QED with background ... More

A few more comments on secularly growing loop corrections in strong electric fieldsDec 04 2014Aug 25 2015We extend the observations of our previous paper JHEP 1409, 071 (2014) [arXiv:1405.5285]. In particular, we show that the secular growth of the loop corrections to the two--point correlation functions is gauge independent: we observe the same growth in ... More

Comment on the Surface Exponential for Tensor FieldsApr 19 2005Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e. in tensors of ... More

An exact statement for Wilsonian and Holographic renormalization groupJan 22 2010Mar 03 2010We show that Polchinski equations in the D--dimensional matrix scalar field theory can be reduced at large $N$ to the Hamiltonian equations in a (D+1)-dimensional theory. In the subsector of the $\Tr \phi^l$ (for all $l$) operators we find the exact form ... More

Quantum integrability in the multistate Landau-Zener problemDec 16 2014We analyze Hamiltonians linear in the time variable for which the multistate Landau-Zener problem is known to have an exact solution. We show that they either belong to families of mutually commuting Hamiltonians polynomial in time or reduce to the 2 ... More

Weighted Thresholding and Nonlinear ApproximationNov 06 2017We present a new method for performing nonlinear approximation with redundant dictionaries. The method constructs an $m-$term approximation of the signal by thresholding with respect to a weighted version of its canonical expansion coefficients, thereby ... More

A Characterization of Sparse Nonstationary Gabor ExpansionsJun 28 2016Apr 19 2017We investigate the problem of constructing sparse time-frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames in the framework of decomposition spaces. Given a painless nonstationary Gabor frame, ... More

Dynamical semigroups in the Birkhoff polytope of order 3 as a tool for analysis of quantum channelsNov 23 2018In the present paper we show a link between bistochastic quantum channels and classical maps. The primary goal of this work is to analyse the multiplicative structure of the Birkhoff polytope of order 3 (the simplest non-trivial case). A suitable complex ... More

On the relation between effective supersymmetric actions in different dimensionsFeb 05 2002We make two remarks: (i) Renormalization of the effective charge in a 4--dimensional (supersymmetric) gauge theory is determined by the same graphs and is rigidly connected to the renormalization of the metric on the moduli space of the classical vacua ... More

Implications of Gallium Solar Neutrino Data for the Resonant Spin-Flavor Precession ScenarioJan 14 1993We consider the implications of the recent results of SAGE and GALLEX experiments for the solution of the solar neutrino problem in the framework of the resonant neutrino spin-flavor precession scenario. It is shown that this scenario is consistent with ... More

Infrared dynamics of the massive $φ^4$ theory on de Sitter spaceMar 05 2013Nov 15 2013We study massive real scalar $\phi^4$ theory in the expanding Poincare patch of de Sitter space. We calculate the leading two-loop infrared contribution to the two-point function in this theory. We do that for the massive fields both from the principal ... More

T violation in neutrino oscillations in matterMay 03 2001May 29 2001We consider the interplay of fundamental and matter-induced T violation effects in neutrino oscillations in matter. After discussing the general features of these effects we derive a simple approximate analytic expression for the T-violating probability ... More

Neutrinos with Mixing in Twisting Magnetic FieldsJan 06 1993Transitions in a system of neutrinos with vacuum mixing and magnetic moments, propagating in matter and transverse magnetic field, are considered. It is shown that in the realistic case of magnetic field direction varying along the neutrino path qualitatively ... More

Non-homogeneous square functions on general sets: suppression and big pieces methodsJun 14 2016We aim to showcase the wide applicability and power of the big pieces and suppression methods in the theory of local $Tb$ theorems. The setting is new: we consider conical square functions with cones $\{x \in \mathbb{R}^n \setminus E: |x-y| < 2 \operatorname{dist}(x,E)\}$, ... More

Power Control for D2D Underlay in Multi-cell Massive MIMO NetworksNov 02 2018This paper proposes a new power control and pilot allocation scheme for device-to-device (D2D) communication underlaying a multi-cell massive MIMO system. In this scheme, the cellular users in each cell get orthogonal pilots which are reused with reuse ... More

Uplink Spectral Efficiency of Massive MIMO with Spatially Correlated Rician FadingMay 21 2018This paper considers the uplink (UL) of a multi-cell Massive MIMO (multiple-input multiple-output) system with spatially correlated Rician fading channels. The channel model is composed of a deterministic line-of-sight (LoS) path and a stochastic non-line-of-sight ... More

Secularly growing loop corrections in strong electric fieldsMay 21 2014Nov 25 2014We calculate one--loop corrections to the vertexes and propagators of photons and charged particles in the strong electric field backgrounds. We use the Schwinger--Keldysh diagrammatic technique. We observe that photon's Keldysh propagator receives growing ... More

Hints on integrability in the Wilsonian/holographic renormalization groupJun 10 2010Sep 20 2011The Polchinski equations for the Wilsonian renormalization group in the $D$--dimensional matrix scalar field theory can be written at large $N$ in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) ... More

Dynamical Analysis of an $n-H-T$ Cosmological Quintessence Real Gas Model with a General Equation of StateFeb 01 2019The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter, and ... More

Vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flowAug 11 2012We show that for a certain family of initial data, there exist non-unique weak solutions to the 3D incompressible Euler equations satisfying the weak energy inequality, whereas the weak limit of every sequence of Leray-Hopf weak solutions for the Navier-Stokes ... More

Weak-strong uniqueness for measure-valued solutions of some compressible fluid modelsMar 17 2015We prove weak-strong uniqueness in the class of admissible measure-valued solutions for the isentropic Euler equations in any space dimension and for the Savage-Hutter model of granular flows in one and two space dimensions. For the latter system, we ... More

Humans and Machines can be Jointly Spatially Multiplexed by Massive MIMOAug 28 2018Future cellular networks are expected to support new communication paradigms such as machine-type communication (MTC) services along with conventional human-type communication (HTC) services. This requires base stations to serve a large number of devices ... More

Optimal Base Station Design with Limited Fronthaul: Massive Bandwidth or Massive MIMO?Sep 15 2017To reach a cost-efficient 5G architecture, the use of remote radio heads connected through a fronthaul to baseband controllers is a promising solution. However, the fronthaul links must support high bit rates as 5G networks are projected to use wide bandwidths ... More

Software Engineers' Information Seeking Behavior in Change Impact Analysis - An Interview StudyMar 06 2017Software engineers working in large projects must navigate complex information landscapes. Change Impact Analysis (CIA) is a task that relies on engineers' successful information seeking in databases storing, e.g., source code, requirements, design descriptions, ... More

Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk StatesAug 11 2014The effect of strong disorder on chiral-symmetric 3-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the non-commutative winding number, as functions of disorder strength ... More

Node Centrality Metrics for Hotspots Analysis in Telecom Big DataMar 13 2019In this work, we are interested in the applications of big data in the telecommunication domain, analysing two weeks of datasets provided by Telecom Italia for Milan and Trento. Our objective is to identify hotspots which are places with very high communication ... More

Optimized Power Control for Massive MIMO with Underlaid D2D CommunicationsMar 06 2019In this paper, we consider device-to-device (D2D) communication that is underlaid in a multi-cell massive multiple-input multiple-output (MIMO) system and propose a new framework for power control and pilot allocation. In this scheme, the cellular users ... More

Joint Transmit and Circuit Power Minimization in Massive MIMO with Downlink SINR Constraints: When to Turn on Massive MIMO?Nov 28 2017Feb 21 2019In this work, we consider the downlink of a multi-cell multiple-input multiple-output (MIMO) system and find the jointly optimal number of base station (BS) antennas and transmission powers that minimize the power consumption while satisfying each user's ... More

Unsteady PDE-constrained optimization with spectral elements using PETSc and TAOJun 04 2018Solving optimization problems where the objective function depends on the solution to partial differential equations (PDEs) entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization algorithms. ... More

Techniques for System Information Broadcast in Cell-Free Massive MIMOJan 28 2019We consider transmission of system information in a cell-free massive MIMO system, when the transmitting access points do not have any channel state information and the receiving terminal has to estimate the channel based on downlink pilots. We analyze ... More

Optimal Coordinated Beamforming in the Multicell Downlink with Transceiver ImpairmentsSep 04 2012Physical wireless transceivers suffer from a variety of impairments that distort the transmitted and received signals. Their degrading impact is particularly evident in modern systems with multiuser transmission, high transmit power, and low-cost devices, ... More

Forman-Ricci flow for change detection in large dynamic data setsApr 22 2016Jun 28 2016We present a viable solution to the challenging question of change detection in complex networks inferred from large dynamic data sets. Building on Forman's discretization of the classical notion of Ricci curvature, we introduce a novel geometric method ... More

On applications of Razborov's flag algebra calculus to extremal 3-graph theoryOct 07 2011Feb 10 2012In this paper, we prove several new Tur\'an density results for 3-graphs with independent neighbourhoods. We show: \pi(K_4^-, C_5, F_{3,2})=12/49, \pi(K_4^-, F_{3,2})=5/18, and \pi(J_4, F_{3,2})=\pi(J_5, F_{3,2})=3/8, where J_t is the 3-graph consisting ... More

Solar Neutrino Data, Neutrino Magnetic Moments and Flavor MixingNov 15 1994The results of all currently operating solar neutrino experiments are analyzed in the framework of the resonant neutrino spin--flavor precession scenario including the effects of neutrino mixing. Nine different profiles of the solar magnetic field are ... More

Pontecorvo's Original Oscillations RevisitedJan 18 1993We show that a left-handed neutrino $\nu_L$ can oscillate into its $CP$- conjugated state $\bar{\nu}_R$ with maximal amplitude, in direct analogy with $K^0-\bar{K}^0$ oscillations. Peculiarities of such oscillations under different conditions are studied. ... More

Characters of different secular effects in various patches of de Sitter spaceJan 22 2019There are at least three different types of secular effects in the two-point correlation functions in scalar quantum field theories in de Sitter space-time. The first one is specific to de Sitter massless and tachyonic minimally coupled scalar fields. ... More

Note on new symplectic 4-manifolds with nonnegative signatureJul 09 2012In this short note, we present a construction of new symplectic 4-manifolds with non-negative signature using the complex surfaces on Bogomolov-Miyaoka-Yau line $c_1^2 = 9\chi_h$, the fake projective planes and Cartwright-Steger surfaces. Our construction ... More

Groups not acting on compact metric spaces by homeomorphismsMar 17 2016We show that the direct sum of uncountably many non-Abelian groups does not embed into the group of homeomorphisms of a compact metric space.

Construction of New Symplectic Cohomology S^2xS^2Nov 06 2006Apr 18 2007In this article, we present new symplectic 4-manifolds with same integral cohomology as $S^{2}\times S^{2}$. The generalization of this construction is given as well, an infinite family of symplectic 4-manifolds cohomology equivalent to $#_{(2g-1)}{(S^{2}\times ... More

Atmospheric neutrinos, $nu_e-nu_s$ oscillations, and a novel neutrino evolution equationJun 23 2016Sep 28 2016If a sterile neutrino nu_s with an eV-scale mass and a sizeable mixing to the electron neutrino exists, as indicated by the reactor and gallium neutrino anomalies, a strong resonance enhancement of nu_e-nu_s oscillations of atmospheric neutrinos should ... More

Finiteness of the topological rank of diffeomorphism groupsOct 14 2015Oct 15 2015For a compact smooth manifold $M$ (with boundary) we prove that the topological rank of the diffeomorphism group Diff$_0^k(M)$ is finite for all $k\geq 1$. This extends a result from [2] where the same claim is proved in the special case of dim M = k ... More

Questions and Remarks on Discrete and Dense Subgroups of Diff(I)Nov 26 2013Nov 27 2013We are raising questions on discrete and dense subgroups of Diff(I). Most of the questions are around the problems discussed in [A1]-[A4].

A weak Zassenhaus lemma for discrete subgroups of Diff(I)Nov 06 2012Oct 02 2013We prove a weaker version of Zassenhaus Lemma (also known as Margulis Lemma) for subgroups of Diff(I). We also show that a group with commutator subgroup containing a free subsemigroup does not admit a C_0-discrete faithful representation in Diff(I).

Simply Connected Symplectic Calabi-Yau 6-ManifoldsJul 13 2011Jul 25 2011In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplectic non-K\"{a}hler Calabi-Yau 6-manifolds with fundamental group ... More

A new metric criterion for non-amenability IFeb 27 2009By studying the so-called traveling salesman groups, we obtain a new metric criterion for non-amenability. As an application, we give a new and very short proof of non-amenability of free Burnside groups with sufficiently big odd exponent.

On groups of diffeomorphisms of the interval with finitely many fixed points IIMar 12 2015In [6], it is proved that any subgroup of $\mathrm{Diff}_{+}^{\omega }(I)$ (the group of orientation preserving analytic diffeomorphisms of the interval) is either metaabelian or does not satisfy a law. A stronger question is asked whether or not the ... More

Cayley graphs with an infinite Heesch numberDec 01 2014Mar 12 2015We construct a 2-generated group $\Gamma $ such that its Cayley graph possesses finite connected subsets with arbitrarily big finite Heesch number.

On the height of subgroups of Homeo(I)Mar 11 2014Sep 23 2014In [Bl1], it is proved that a subgroup of $PL_{+}(I)$ has a finite height if and only if it is solvable. We prove the "only if" part for any subgroup of Homeo$_{+}(I)$, and present a construction which indicates a plethora of examples of solvable groups ... More

On Dense Subgroups of Homeo(I)Dec 05 2013We prove that a dense subgroup of $\mathrm{Homeo}_{+}(I)$ is not elementary amenable and (if it is finitely generated) has infinite girth. We also show that the topological group $\mathrm{Homeo}_{+}(I)$ does not satisfy the Stability of the Generators ... More

On free discrete subgroups of Diff(I)Apr 12 2010We prove that a free group F_2 admits a faithful discrete representation into Diff_{+}(I). We also prove that F_2 admits a faithful discrete representation into Homeo_{+}(I). Some properties of these representations have been studied. In the last section ... More

Construction of Exotic Smooth StructuresNov 05 2006Nov 08 2006In this article, we construct infinitley many simply connected, nonsymplectic and pairwise nondiffeomorphic 4-manifolds starting from E(n) and applying the sequence of knot surgery, ordinary blowups and rational blowdown. We also compute the Seiberg-Witten ... More

Surface Bundles With Non-Zero SignatureMar 22 2007Apr 28 2007In this paper we develop a new technique that yields infinitely many surface bundles with non-zero signature.

Stability and leptogenesis in the left-right symmetric seesaw mechanismDec 15 2006May 15 2007We analyze the left-right symmetric type I+II seesaw mechanism, where an eight-fold degeneracy among the mass matrices of heavy right-handed neutrinos M_R is known to exist. Using the stability property of the solutions and their ability to lead to successful ... More

Non-amenability of R.Thompson's group FOct 16 2013Dec 20 2013We present a short proof of non-amenability of R.Thompson's group F.

Amenable subgroups of Homeo(R) with large characterizing quotientsNov 26 2012Feb 09 2016We construct a finitely generated solvable subgroup of Homeo(R) with a non-metaabelian characterizing quotient.

About the asymptotic formula for spectral function of the Laplace-Beltrami operator on sphereAug 04 2008In this work we established asymptotical behavior for Riesz means of the spectral function of the Laplace operator on unit sphere.

About the almost everywhere convergence of the spectral expansions of functions from $L_1^\a(S^N)$Jun 29 2008In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace-Beltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and ... More

On groups of diffeomorphisms of the interval with finitely many fixed points IMar 12 2015We strengthen the results of [1], consequently, we improve the claims of [2] obtaining the best possible results. Namely, we prove that if a subgroup $\Gamma $ of $\mathrm{Diff}_{+}(I)$ contains a free semigroup on two generators then $\Gamma $ is not ... More