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Gyroscopes based on nitrogen-vacancy centers in diamondMay 01 2012Sep 04 2012We propose solid-state gyroscopes based on ensembles of negatively charged nitrogen-vacancy (${\rm NV^-}$) centers in diamond. In one scheme, rotation of the nitrogen-vacancy symmetry axis will induce Berry phase shifts in the ${\rm NV^{-}}$ electronic ... More

Miniature cavity-enhanced diamond magnetometerJun 07 2017We present a highly sensitive miniaturized cavity-enhanced room-temperature magnetic-field sensor based on nitrogen-vacancy (NV) centers in diamond. The magnetic resonance signal is detected by probing absorption on the 1042\,nm spin-singlet transition. ... More

Sidebands in Optically Detected Magnetic Resonance Signals of Nitrogen Vacancy Centers in DiamondDec 23 2012Jun 06 2013We study features in the optically detected magnetic resonance (ODMR) signals associated with negatively charged nitrogen-vacancy (NV) centers coupled to other paramagnetic impurities in diamond. Our results are important for understanding ODMR line shapes ... More

Electromagnetically-induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensingMar 27 2013May 24 2013We use electromagnetically-induced transparency (EIT) to probe the narrow electron-spin resonance of nitrogen-vacancy centers in diamond. Working with a multi-pass diamond chip at temperatures 6-30 K, the zero-phonon absorption line (637 nm) exhibits ... More

Hybrid optical pumping of K and Rb atoms in a paraffin coated vapor cellAug 29 2017Dynamic hybrid optical pumping effects with a radio-frequency-field-driven nonlinear magneto-optical rotation (RF NMOR) scheme are studied in a dual-species paraffin coated vapor cell. By pumping K atoms and probing $^{87}$Rb atoms, we achieve an intrinsic ... More

Waveplate retarders based on overhead transparenciesFeb 25 2007Feb 28 2007We describe procedures for constructing inexpensive waveplates of desired retardation out of ordinary commercially available transparencies. Various relevant properties of the transparencies are investigated: the dependence of retardation on rotation ... More

Sawtooth wave adiabatic passage slowing of dysprosiumSep 17 2018We report on sawtooth wave adiabatic passage (SWAP) slowing of bosonic and fermionic dysprosium isotopes by using a 136 kHz wide transition at 626 nm. A beam of precooled atoms is further decelerated in one dimension by the SWAP force and the amount of ... More

All-Optical Spin Locking in Alkali-Vapor MagnetometersSep 28 2018The nonlinear Zeeman effect can induce splittings and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. We demonstrate a scheme to suppress the nonlinear Zeeman effect all optically based on spin locking. Spin locking is ... More

Nondestructive in-line sub-picomolar detection of magnetic nanoparticles in flowing complex fluidsJan 17 2018Over the last decades, the use of magnetic nanoparticles in research and commercial applications has increased dramatically. However, direct detection of trace quantities remains a challenge in terms of equipment cost, operating conditions and data acquisition ... More

Sensitive Magnetic Control of Ensemble Nuclear Spin Hyperpolarisation in DiamondNov 30 2012Dynamic nuclear polarisation, which transfers the spin polarisation of electrons to nuclei, is routinely applied to enhance the sensitivity of nuclear magnetic resonance; it is also critical in spintronics, particularly when spin hyperpolarisation can ... More

Hyperfine level structure in nitrogen-vacancy centers near the ground-state level anticrossingMay 03 2018Energy levels of the nitrogen-vacancy centers in diamond were investigated using optically detected magnetic-resonance spectroscopy near the electronic ground-state level anticrossing (GSLAC) at an axial magnetic field around 102.4 mT in diamond samples ... More

Directional infrared emission resulting from cascade population inversion and four-wave mixing in Rb vapoursNov 01 2013Directional infrared emission at 1367 and 5230 nm is generated in Rb vapours that are step-wise excited by low-power resonant light. The mid-infrared radiation originating from amplified spontaneous emission on the 5D-6P transition consists of forward- ... More

Dynamics of a Ferromagnetic Particle Levitated Over a SuperconductorOct 20 2018Jan 08 2019Under conditions where the angular momentum of a ferromagnetic particle is dominated by intrinsic spin, applied torque is predicted to cause gyroscopic precession of the particle. If the particle is sufficiently isolated from the environment, a measurement ... More

Infrared laser magnetometry with a NV doped diamond intracavity etalonOct 18 2018We propose an hybrid laser system consisting of a semiconductor external cavity laser associated to an intra-cavity diamond etalon doped with nitrogen-vacancy color centers. We consider laser emission tuned to the infrared absorption line that is enhanced ... More

Rules for collaborative scientific writingJun 21 2016Several years ago, one of us, having noticed that inexperienced scientists tend to make largely the same mistakes while writing their first papers, was compelled to write a one-page note summarizing some dos and don'ts intended to help take care of common ... More

Magnetometry with nitrogen-vacancy ensembles in diamond based on infrared absorption in a doubly resonant optical cavityJan 04 2013We propose to use an optical cavity to enhance the sensitivity of magnetometers relying on the detection of the spin state of high-density nitrogen-vacancy ensembles in diamond using infrared optical absorption. The role of the cavity is to obtain a contrast ... More

Search for axionlike dark matter with a liquid-state nuclear spin comagnetometerJan 30 2019Feb 13 2019We report the results of a search for axionlike dark matter using nuclear magnetic resonance (NMR) techniques. This search is part of the multi-faceted Cosmic Axion Spin Precession Experiment (CASPEr) program. In order to distinguish axionlike dark matter ... More

A Precessing Ferromagnetic Needle MagnetometerFeb 08 2016Apr 20 2016A ferromagnetic needle is predicted to precess about the magnetic field axis at a Larmor frequency $\Omega$ under conditions where its intrinsic spin dominates over its rotational angular momentum, $N\hbar \gg I\Omega$ ($I$ is the moment of inertia of ... More

Polarized alkali vapor with minute-long transverse spin-relaxation timeMay 10 2010We demonstrate lifetimes of atomic populations and coherences in excess of 60 seconds in alkali vapor cells with inner walls coated with an alkene material. This represents two orders of magnitude improvement over the best paraffin coatings. Such anti-relaxation ... More

Alkali-vapor magnetic resonance driven by fictitious radiofrequency fieldsSep 22 2014Sep 26 2014We demonstrate an all-optical $^{133}$Cs scalar magnetometer, operating in nonzero magnetic field,in which the magnetic resonance is driven by an effective oscillating magnetic field provided by the AC Stark shift of an intensity-modulated laser beam. ... More

Eddy current imaging with an atomic radio-frequency magnetometerMar 16 2016We use a radio-frequency $^{85}$Rb alkali-vapor cell magnetometer based on a paraffin-coated cell with long spin-coherence time and a small, low-inductance driving coil to create highly resolved conductivity maps of different objects. We resolve sub-mm ... More

Suppression of nonlinear Zeeman effect and heading error in earth-field-range alkali-vapor magnetometersAug 17 2017The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear ... More

Detection of the Meissner Effect with a Diamond MagnetometerNov 13 2009Sep 24 2010We examine the possibility of probing superconductivity effects in metal nanoclusters via diamond magnetometry. Metal nanoclusters have been proposed as constitutive elements of high T$_c$ superconducting nanostructured materials. Magnetometry based on ... More

Nonlinear processes responsible for mid-infrared and blue light generation in alkali vapoursOct 10 2013The nonlinear processes responsible for frequency up- and down-conversion of resonant low-intensity laser radiation in Rb vapour have been evaluated from the spatial and temporal properties of blue and mid-IR light resulting from wave mixing.

Optical polarization of nuclear ensembles in diamondFeb 06 2012Jan 21 2013We report polarization of a dense nuclear-spin ensemble in diamond and its dependence on magnetic field and temperature. The polarization method is based on the transfer of electron spin polarization of negatively charged nitrogen vacancy color centers ... More

Multi-Channel Data Acquisition System with Absolute Time SynchronizationNov 22 2013A low-cost, stand-alone Global-Positioning-System-time-synchronized data acquisition system is described. The constructed prototype allows recoding up to four analog signals with a 16-bit resolution in variable ranges and a maximum sampling rate of 1000 ... More

Sensitive optical atomic magnetometer based on nonlinear magneto-optical rotationMar 07 2010A self-oscillating magnetometer based on nonlinear magneto-optical rotation using amplitude-modulated pump light and unmodulated probe light (AM-NMOR) in 87Rb has been constructed and tested towards a goal of airborne detection of magnetic anomalies. ... More

Search for ultralight scalar dark matter with atomic spectroscopyMar 24 2015Apr 08 2015We report new limits on ultralight scalar dark matter (DM) with dilaton-like couplings to photons that can induce oscillations in the fine-structure constant alpha. Atomic dysprosium exhibits an electronic structure with two nearly degenerate levels whose ... More

Continuous-wave mirrorless lasing at 2.21 μm in sodium vaporsAug 31 2018We demonstrate backward-directed continuous-wave (cw) emission at 2.21 {\mu}m generated on the 4P3/2-4S1/2 population-inverted transition in Na vapors two-photon excited with resonant laser light at 589 and 569 nm. Our study of power and atom-number-density ... More

Constraints on bosonic dark matter from ultralow-field nuclear magnetic resonanceFeb 12 2019The nature of dark matter, the invisible substance making up over $80\%$ of the matter in the Universe, is one of the most fundamental mysteries of modern physics. Ultralight bosons such as axions, axion-like particles or dark photons could make up most ... More

Efficient polarization of high-angular-momentum systemsAug 31 2016We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw ... More

Cosmic Axion Spin Precession Experiment (CASPEr)Jun 25 2013May 29 2014We propose an experiment to search for QCD axion and axion-like-particle (ALP) dark matter. Nuclei that are interacting with the background axion dark matter acquire time-varying CP-odd nuclear moments such as an electric dipole moment. In analogy with ... More

Bulk Nuclear Polarization Enhanced at Room-Temperature by Optical PumpingNov 25 2012Jun 05 2013Bulk 13C polarization can be strongly enhanced in diamond at room-temperature based on the optical pumping of nitrogen-vacancy color centers. This effect was confirmed by irradiating suitably aligned single-crystals at a ~50 mT field promoting anti-crossings ... More

Magneto-Optical Cooling of AtomsSep 23 2013We propose an alternative method to laser cooling. Our approach utilizes the extreme brightness of a supersonic atomic beam, and the adiabatic atomic coilgun to slow atoms in the beam or to bring them to rest. We show how internal-state optical pumping ... More

Detection of a single cobalt microparticle with a microfabricated atomic magnetometerJul 11 2011Jul 12 2011We present magnetic detection of a single, 2 {\mu}m diameter cobalt microparticle using an atomic magnetometer based on a microfabricated vapor cell. These results represent an improvement by a factor of 105 in terms of the detected magnetic moment over ... More

Constraints on exotic spin-dependent interactions between electrons from helium fine-structure spectroscopyAug 20 2016Agreement between theoretical calculations of atomic structure and spectroscopic measurements is used to constrain possible contribution of exotic spin-dependent interactions between electrons to the energy differences between states in helium-4. In particular, ... More

Parahydrogen enhanced zero-field nuclear magnetic resonanceFeb 26 2011Nuclear magnetic resonance (NMR), conventionally detected in multi-tesla magnetic fields, is a powerful analytical tool for the determination of molecular identity, structure, and function. With the advent of prepolarization methods and alternative detection ... More

Liquid-state nuclear spin comagnetometersJan 21 2012Jan 24 2012We discuss nuclear spin comagnetometers based on ultra-low-field nuclear magnetic resonance in mixtures of miscible solvents, each rich in a different nuclear spin. In one version thereof, Larmor precession of protons and ${\rm ^{19}F}$ nuclei in a mixture ... More

Electron Spin Resonance Shift and Linewidth Broadening of Nitrogen-Vacancy Centers in Diamond as a Function of Electron Irradiation DoseDec 29 2009Aug 09 2012A high-nitrogen-concentration diamond sample was subject to 200-keV electron irradiation using a transmission electron microscope. The optical and spin-resonance properties of the nitrogen-vacancy (NV) color centers were investigated as a function of ... More

Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixingMay 11 2012We present a theoretical analysis of the propagation of light pulses through a medium of four-level atoms, with two strong pump fields and a weak signal field in an N-scheme arrangement. We show that the generation of four-wave mixing has a profound effect ... More

Light shift averaging in paraffin-coated alkali vapor cellsNov 17 2015Light shifts are an important source of noise and systematics in optically pumped magnetometers. We demonstrate that the long spin coherence time in paraffin-coated cells leads to spatial averaging of the light shifts over the entire cell volume. This ... More

Solid-state electronic spin coherence time approaching one secondNov 29 2012Dec 06 2012Solid-state electronic spin systems such as nitrogen-vacancy (NV) color centers in diamond are promising for applications of quantum information, sensing, and metrology. However, a key challenge for such solid-state systems is to realize a spin coherence ... More

Four-wave mixing in a ring cavityApr 17 2014We investigate a four-wave mixing process in an N interaction scheme in Rb vapor placed inside a low-finesse ring cavity. We observe strong amplification and generation of a probe signal, circulating in the cavity, in the presence of two strong optical ... More

High magnetic fields for fundamental physicsMar 20 2018Various fundamental-physics experiments such as measurement of the birefringence of the vacuum, searches for ultralight dark matter (e.g., axions), and precision spectroscopy of complex systems (including exotic atoms containing antimatter constituents) ... More

Linewidth of collimated wavelength-converted emission in Rb vapoursJan 30 2013Oct 09 2013We present a study of the spectral linewidth of collimated blue light (CBL) that results from wave mixing of low-power cw laser radiation at 780 nm and 776 nm and an internally-generated mid-IR field at 5.23 um in Rb vapour. Using a high-finesse Fabry-Perot ... More

A Remotely Interrogated All-Optical $^{87}$Rb MagnetometerAug 06 2012Atomic magnetometry was performed at Earth's magnetic field over a free-space distance of ten meters. Two laser beams aimed at a distant alkali-vapor cell excited and detected the $^{87}$Rb magnetic resonance, allowing the magnetic field within the cell ... More

Efficient polarization of high-angular-momentum systemsAug 31 2016Oct 21 2016We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw ... More

Tailorable Dispersion in a Four-Wave Mixing LaserMay 08 2017We present experimental results demonstrating controllable dispersion in a ring laser by monitoring the lasing-frequency response to cavity-length variations. Pumping on an N-type level configuration in ${}^{87}$Rb, we tailor the intra-cavity dispersion ... More

Characterization of high-temperature performance of cesium vapor cells with anti-relaxation coatingSep 15 2016Vapor cells with antirelaxation coating are widely used in modern atomic physics experiments due to the coating's ability to maintain the atoms' spin polarization during wall collisions. We characterize the performance of vapor cells with different coating ... 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

Coherent phase slips in superconducting nanoringsJul 15 2011We study quantum fluctuations of persistent current in a small superconducting ring. Based on a microscopic model of the ring we argue that under certain conditions such ring will exhibit coherent quantum phase slips, similar to those in a flux qubit. ... More

Kinetics of the Phase Separation Transition in Cold-Atom Boson-Fermion MixturesDec 04 2007Apr 16 2008We study the kinetics of the first order phase separation transition in boson-fermion cold-atom mixtures. At sufficiently low temperatures such a transition is driven by quantum fluctuations responsible for the formation of critical nuclei of a stable ... More

Cold Atom QubitsMay 29 2010Dec 20 2010We discuss a laser-trapped cold-atom superfluid qubit system. Each qubit is proposed as a macroscopic two-state system based on a set of Bose-Einstein condensate (BEC) currents circulating in a ring, cut with a Josephson barrier. We review the effective ... More

Investigation of two-frequency Paul traps for antihydrogen productionMar 31 2016Oct 13 2016Radio-frequency (rf) Paul traps operated with multifrequency rf trapping potentials provide the ability to independently confine charged particle species with widely different charge-to-mass ratios. In particular, these traps may find use in the field ... More

Search for plant biomagnetism with a sensitive atomic magnetometerJun 17 2010Aug 16 2011We report what we believe is the first experimental limit placed on plant biomagnetism. Measurements with a sensitive atomic magnetometer were performed on the Titan arum (Amorphophallus titanum) inflorescence, known for its fast bio-chemical processes ... More

Microwave-free magnetometry with nitrogen-vacancy centers in diamondJun 09 2016We use magnetic-field-dependent features in the photoluminescence of negatively charged nitrogen-vacancy centers to measure magnetic fields without the use of microwaves. In particular, we present a magnetometer based on the level anti-crossing in the ... More

Polarization-driven spin precession of mesospheric sodium atomsSep 11 2018We report experimental results on the first on-sky observation of atomic spin precession of mesospheric sodium driven by polarization modulation of a continuous-wave laser. The magnetic resonance was remotely detected from the ground by observing the ... More

Optical quenching and recovery of photoconductivity in single-crystal diamondJul 28 2016Oct 11 2016We study the photocurrent induced by pulsed-light illumination (pulse duration is several nanoseconds) of single-crystal diamond containing nitrogen impurities. Application of additional continuous-wave light of the same wavelength quenches pulsed photocurrent. ... More

Remote sensing of geomagnetic fields and atomic collisions in the mesosphereFeb 09 2018Magnetic-field sensing has contributed to the formulation of the plate-tectonics theory, the discovery and mapping of underground structures on Earth, and the study of magnetism in other planets. Filling the gap between space-based and near-Earth observation, ... 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

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

The Weierstrass representation of discrete isotropic surfaces in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$Jul 03 2009Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation of time-like surfaces parametrized along isotropic directions in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$. The corresponding discrete surfaces have ... More

Extremal subspaces and their submanifoldsOct 23 2002Apr 03 2003It is known that the properties of almost all points of R^n being not very well (multiplicatively) approximable are inherited by nondegenerate in R^n (read: not contained in a proper affine subspace) smooth submanifolds. In this paper we consider submanifolds ... More

The $c_2$ invariant is invariantDec 27 2013Oct 13 2015The $c_2$ invariants in all 4 different representations of the Feynman period (parametric and dual parametric representations, position and momentum spaces) coincide for all log-divergent graphs that satisfy the combinatorial condition called duality ... More

Hopf algebra of ribbon graphs and renormalizationDec 17 2001Apr 24 2002Connes and Kreimer have discovered a Hopf algebra structure behind renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is naturally defined ... More

Reducibility of Killing tensors in d>4 NHEK geometrySep 05 2013Mar 31 2014An extremal rotating black hole in arbitrary dimension, along with time translations and rotations, possesses a number of hidden symmetries characterized by the second rank Killing tensors. As is known, in the near horizon limit the isometry group of ... 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

On the Dovbysh-Sudakov representation resultMay 11 2009We present a detailed proof of the Dovbysh-Sudakov representation for symmetric positive definite weakly exchangeable infinite random arrays, called Gram-de Finetti matrices, which is based on the representation result of Aldous and Hoover for arbitrary ... More

A note on the free energy of the coupled system in the Sherrington-Kirkpatrick modelMay 18 2004In this paper we consider a system of spins that consists of two configurations $\vsi^1,\vsi^2\in\Sigma_N=\{-1,+1\}^N$ with Gaussian Hamiltonians $H_N^1(\vsi^1)$ and $H_N^2(\vsi^2)$ correspondingly, and these configurations are coupled on the set where ... More

The Higgs Boson is found: What is next?May 21 2014The situation in particle physics after the discovery of the Higgs boson is discussed. Is the Standard Model complete? Are there still mysteries which have no answer? Answering these questions we consider the Higgs sector, the neutrino sector and the ... More

Concepts of trace, determinant and inverse of Clifford algebra elementsAug 27 2011In our paper we consider the notion of determinant of Clifford algebra elements. We present some new formulas for determinant of Clifford algebra elements for the cases of dimension 4 and 5. Also we consider the notion of trace of Clifford algebra elements. ... 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

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

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

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

Decimated generalized Prony systemsAug 03 2013We continue studying robustness of solving algebraic systems of Prony type (also known as the exponential fitting systems), which appear prominently in many areas of mathematics, in particular modern "sub-Nyquist" sampling theories. We show that by considering ... 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

Complex structures on nilpotent Lie algebras and descending central seriesDec 01 2014We study the algebraic constraints on the structure of nilpotent Lie algebra $\mathbb{g}$, which arise because of the presence of an integrable complex structure $J$. Particular attention is paid to non-abelian complex structures. Constructed various ... More

A Review of Conjectured Laws of Total Mass of Bacry-Muzy GMC Measures on the Interval and Circle and Their ApplicationsMar 18 2018Selberg and Morris integral probability distributions are long conjectured to be distributions of the total mass of the Bacry-Muzy Gaussian Multiplicative Chaos measures with non-random logarithmic potentials on the unit interval and circle, respectively. ... More

On the $K$-sat model with large number of clausesAug 22 2016Apr 01 2017We show that in the $K$-sat model with $N$ variables and $\alpha N$ clauses, the expected ratio of the smallest number of unsatisfied clauses to the number of variables is $\alpha/2^K - \sqrt{\alpha} c_*(N)/2^K$ up to smaller order terms $o(\sqrt{\alpha})$ ... More

Near-zero-field nuclear magnetic resonanceJul 08 2011We investigate nuclear magnetic resonance (NMR) in near-zero-field, where the Zeeman interaction can be treated as a perturbation to the electron mediated scalar interaction (J-coupling). This is in stark contrast to the high field case, where heteronuclear ... More

Constraints on exotic spin-dependent interactions between matter and antimatter from antiprotonic helium spectroscopyJan 01 2018Heretofore undiscovered spin-0 or spin-1 bosons can mediate exotic spin-dependent interactions between standard-model particles. Here we carry out the first search for semileptonic spin-dependent interactions between matter and antimatter. We compare ... More

Accurate solution of near-colliding Prony systems via decimation and homotopy continuationDec 31 2014Oct 21 2016We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the system is a-priori ... More

Faster Lightweight Lempel-Ziv ParsingApr 25 2015Jun 08 2015We present an algorithm that computes the Lempel-Ziv decomposition in $O(n(\log\sigma + \log\log n))$ time and $n\log\sigma + \epsilon n$ bits of space, where $\epsilon$ is a constant rational parameter, $n$ is the length of the input string, and $\sigma$ ... More