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Identifying topological edge states in 2D optical lattices using light scatteringSep 10 2012Feb 11 2013We recently proposed in a Letter [Physical Review Letters 108 255303] a novel scheme to detect topological edge states in an optical lattice, based on a generalization of Bragg spectroscopy. The scope of the present article is to provide a more detailed ... More

Nonlinear dynamics of Aharonov-Bohm cagesOct 17 2018Mar 12 2019The interplay of $\pi$-flux and lattice geometry can yield full localization of quantum dynamics in lattice systems, a striking interference phenomenon known as Aharonov-Bohm caging. At the level of the single-particle energy spectrum, this full-localization ... More

Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atomsMay 16 2013Sep 26 2013We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological (Chern) insulating phase, and driven by a constant force. We show that the time evolution of the center of mass, after releasing ... More

Tensor Berry connections and their topological invariantsNov 06 2018Jan 30 2019The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector potential defined ... More

Floquet approach to $\mathbb{Z}_{2}$ lattice gauge theories with ultracold atoms in optical latticesJan 21 2019Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based ... More

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux-attachment to Z2 lattice gauge theoriesOct 05 2018Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly-controllable environment. Despite being dynamically tunable, such ... More

A localization marker from many-body quantum geometry measurementsApr 26 2019In condensed matter, the quantum geometric tensor characterizes the geometry of single-particle Bloch states. Here, we generalize this notion by introducing a many-body geometric tensor, which is defined in the parameter space of twist angles associated ... More

Nonlinear dynamics of Aharonov-Bohm cagesOct 17 2018The interplay of $\pi$-flux and lattice geometry can yield full localization of quantum dynamics in lattice systems, a striking interference phenomenon known as Aharonov-Bohm caging. At the level of the single-particle energy spectrum, this full-localization ... More

Detecting Chiral Edge States in the Hofstadter Optical LatticeMar 06 2012Apr 27 2012We propose a realistic scheme to detect topological edge states in an optical lattice subjected to a synthetic magnetic field, based on a generalization of Bragg spectroscopy sensitive to angular momentum. We demonstrate that using a well-designed laser ... More

Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb latticeJan 16 2012Apr 26 2012We investigate the properties of an edge-centered honeycomb lattice, and show that this lattice features both spin-1/2 and spin-1 Dirac-Weyl fermions at different filling fractions f (f=1/5,4/5 for spin-1/2 and f=1/2 for spin-1). This five-band system ... More

Synthetic Dimensions for Cold Atoms from Shaking a Harmonic TrapMay 30 2016Jun 23 2016We introduce a simple scheme to implement synthetic dimensions and gauge fields in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our ... More

Preparing and probing Chern bands with cold atomsJul 28 2015The present Chapter discusses methods by which topological Bloch bands can be prepared in cold-atom setups. Focusing on the case of Chern bands for two-dimensional systems, we describe how topological properties can be triggered by driving atomic gases, ... More

The efficiency of convective tidal viscosity in close solar-type binariesOct 06 2008The value of the effective convective viscosity, in the framework of the mixing length theory (MLT), is 2 orders of magnitude too small compared to that required by the observational data. Moreover, the reduction of the effective viscosity due to the ... More

A note related to the CS decomposition and the BK inequality for discrete determinantal processesMay 09 2019We prove that for a discrete determinantal process the BK inequality occurs for increasing events generated by simple points. We give also some elementary, but nonetheless appealing relationship, between a discrete determinantal process and the well-known ... More

Lessons Drawn from Implementation of Online Tutoring System in Physics CoursesMar 30 2007The online tutoring system CAPA was implemented at Afeka College in the academic year 2000-2001 in calculus based physics courses. It was used also in the academic year 2001-2002 and was very successful in improving understanding and achievements of the ... More

Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical LatticesApr 14 2008Apr 18 2008In this work we study ultracold Fermions confined in a two-dimensional optical lattice and we explore the Mott-insulator transition with the Fermi-Hubbard model. On the basis of a mean-field approach, we study the phase diagrams in the presence of a harmonic ... More

Characterizing the Hofstadter butterfly's outline with Chern numbersAug 11 2008Jan 28 2009In this work, we report original properties inherent to independent particles subjected to a magnetic field by emphasizing the existence of regular structures in the energy spectrum's outline. We show that this fractal curve, the well-known Hofstadter ... More

Spatial patterns in optical lattices submitted to gauge potentialsJul 25 2007Sep 06 2007We study the vortex formation in optical lattices submitted to artificial gauge potentials. We compute the superfluid density for Abelian and non-Abelian gauge potentials with a mean-field approach of the Bose-Hubbard model and we determine the rule describing ... More

Dynamic optical lattices of sub-wavelength spacing for ultracold atomsJun 01 2015Oct 02 2015We propose a scheme to realize lattice potentials of sub-wavelength spacing for ultracold atoms. It is based on spin-dependent optical lattices with a time-periodic modulation. We show that the atomic motion is well described by the combined action of ... More

Topological Hofstadter Insulators in a Two-Dimensional QuasicrystalDec 01 2014Mar 17 2015We investigate the properties of a two-dimensional quasicrystal in the presence of a uniform magnetic field. In this configuration, the density of states (DOS) displays a Hofstadter butterfly-like structure when it is represented as a function of the ... More

Tunable axial gauge fields in engineered Weyl semimetals: Semiclassical analysis and optical lattice implementationsAug 28 2017Jan 19 2018In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally ... More

Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall SystemsMar 02 2018Jun 14 2018The dissipative response of a quantum system upon a time-dependent drive can be exploited as a probe of its geometric and topological properties. In this work, we explore the implications of such phenomena in the context of two-dimensional gases subjected ... More

An Elementary Proof of the Fundamental Theorem of Tropical AlgebraJul 17 2007In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm for factoring ... More

Phase segregation for binary mixtures of Bose-Einstein CondensatesMay 27 2015Dec 16 2015We study the strong segregation limit for mixtures of Bose-Einstein condensates modelled by a Gross-Pitaievskii functional. Our first main result is that in presence of a trapping potential, for different intracomponent strengths, the Thomas-Fermi limit ... More

Similarities Between the Inner Solar System and the Planetary System of PSR B1257+12Dec 27 1994We call attention to the surprising similarity between the newly discovered planetary system around PSR B1257+12 and the inner solar system. The similarity is in the ratios of the orbital radii and the masses of the three planets.

Crooked surfaces and anti-de Sitter geometryFeb 20 2013Nov 25 2014Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes. They were extended by Frances to closed polyhedral surfaces in the conformal compactification of Minkowski space (Einstein space) which we ... More

Useful Statistical Methods for Human Factors Research in Software Engineering: A Discussion on Validation with Quantitative DataApr 04 2019In this paper we describe the usefulness of statistical validation techniques for human factors survey research. We need to investigate a diversity of validity aspects when creating metrics in human factors research, and we argue that the statistical ... More

Locally homogeneous geometric manifoldsMar 14 2010Apr 21 2010Motivated by Felix Klein's notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally ... More

Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fieldsApr 16 2014Jun 10 2015Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter systems. Here, ... More

Quantum Hall-like effect for cold atoms in non-Abelian gauge potentialsSep 19 2006May 23 2007We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and ... More

Stability of $SU(N_c)$ QCD3 from the $ε$-ExpansionJun 22 2016QCD with gauge group $SU(N_c)$ flows to an interacting conformal fixed point in three spacetime dimensions when the number of four-component Dirac fermions $N_f \gg N_c$. We study the stability of this fixed point via the $\epsilon$-expansion about four ... More

Higgs Bundles and Geometric Structures on SurfacesMay 12 2008This paper concerns the relationship between locally homogeneous geometric structures on topological surfaces and the moduli of polystable Higgs bundles on Riemann surfaces, due to Hitchin and Simpson. In particular we discuss the uniformization of Riemann ... More

Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimatesMay 20 2019We study a family of non-convex functionals $\{\mathcal{E}\}$ on the space of measurable functions$u: \Omega_1\times\Omega_2 \subset \mathbb{R}^{n_1}\times\mathbb{R}^{n_2} \to \mathbb{R}$. These functionals vanish on the non-convex subset $S(\Omega_1\times\Omega_2)$ ... More

Bulging deformations of convex $RP^2$-manifoldsFeb 04 2013We define deformations of $RP^2$-manifolds.

Topological tameness of Margulis spacetimesApr 24 2012Oct 27 2017We show that Margulis spacetimes without parabolic holonomy are topologically tame. A Margulis spacetime is the quotient of the $3$-dimensional Minkowski space by a free proper isometric action of the free group of rank $\geq 2$. We will use our particular ... More

Mapping Class Group Dynamics on Surface Group RepresentationsSep 06 2005Jan 28 2006Deformation spaces Hom($\pi$,G)/G of representations of the fundamental group $\pi$ of a surface $\Sigma$ in a Lie group $G$ admit natural actions of the mapping class group $Mod_\Sigma$, preserving a Poisson structure. When $G$ is compact, the actions ... More

Quantum graphs and the integer quantum Hall effectSep 11 2007We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establish ... More

The complex-symplectic geometry of SL(2,C)-characters over surfacesApr 21 2003Oct 03 2003The SL(2)-character variety X of a closed surface M enjoys a natural complex-symplectic structure invariant under the mapping class group G of M. Using the ergodicity of G on the SU(2)-character variety, we deduce that every G-invariant meromorphic function ... More

Explaining Pure Spinor SuperspaceDec 04 2006Mar 26 2008In the pure spinor formalism for the superstring and supermembrane, supersymmetric invariants are constructed by integrating over five $\theta$'s in d=10 and over nine $\theta$'s in d=11. This pure spinor superspace is easily explained using the superform ... More

Pure Spinor Formalism as an N=2 Topological StringSep 15 2005Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted $\hat c$=3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one ... More

The Ramond Sector of Open Superstring Field TheorySep 12 2001Although the equations of motion for the Neveu-Schwarz (NS) and Ramond (R) sectors of open superstring field theory can be covariantly expressed in terms of one NS and one R string field, picture-changing problems prevent the construction of an action ... More

Super-Poincare Invariant Superstring Field TheoryMar 15 1995Using the topological techniques developed in an earlier paper with Vafa, a field theory action is constructed for any open string with critical N=2 worldsheet superconformal invariance. Instead of the Chern-Simons-like action found by Witten, this action ... More

A Ten-Dimensional Super-Yang-Mills Action with Off-Shell SupersymmetryAug 27 1993Sep 05 1993After adding seven auxiliary scalar fields, the action for ten-dimensional super-Yang-Mills contains an equal number of bosonic and fermionic non-gauge fields. Besides being manifestly Lorentz and gauge-invariant, this action contains nine spacetime supersymmetries ... More

Lorentz-Covariant Green-Schwarz Superstring AmplitudesNov 04 1992In a recent paper, the BRST formalism for the gauge-fixed N=2 twistor-string was used to calculate Green-Schwarz supersring scattering amplitudes with an arbitrary number of loops and external massless states. Although the gauge-fixing procedure preserved ... More

The Heterotic Green-Schwarz Superstring on an N=(2,0) Super-WorldsheetJan 03 1992By defining the heterotic Green-Schwarz superstring action on an N=(2,0) super-worldsheet, rather than on an ordinary worldsheet, many problems with the interacting Green-Schwarz superstring formalism can be solved. In the light-cone approach, superconformally ... More

ICTP Lectures on Covariant Quantization of the SuperstringSep 06 2002These ICTP Trieste lecture notes review the pure spinor approach to quantizing the superstring with manifest D=10 super-Poincare invariance. The first section discusses covariant quantization of the superparticle and gives a new proof of equivalence with ... More

Review of Open Superstring Field TheoryMay 23 2001I review the construction of an action for open superstring field theory which does not suffer from the contact term problems of other approaches. This action resembles a Wess-Zumino-Witten action and can be constructed in a manifestly D=4 super-Poincar\'e ... More

The Tachyon Potential in Open Neveu-Schwarz String Field TheoryJan 13 2000Jan 20 2000A classical action for open superstring field theory has been proposed which does not suffer from contact term problems. After generalizing this action to include the non-GSO projected states of the Neveu-Schwarz string, the pure tachyon contribution ... More

A New Description of the SuperstringApr 19 1996Aug 01 2000This is a review of the new manifestly spacetime-supersymmetric description of the superstring. The new description contains N=2 worldsheet supersymmetry, and is related by a field redefinition to the standard RNS description. It is especially convenient ... More

New Spacetime-Supersymmetric Methods for the SuperstringJun 06 1995In this talk, the new spacetime-supersymmetric description of the superstring is reviewed and some of its applications are described. These applications include the manifestly spacetime-supersymmetric calculation of scattering amplitudes, the construction ... More

Vanishing Theorems for the Self-Dual N=2 StringDec 20 1994It is proven that up to possible surface terms, the only non-vanishing momentum-dependent amplitudes for the self-dual N=2 string in $R^{2,2}$ are the tree-level two and three-point functions, and the only non-vanishing momentum-independent amplitudes ... More

Covariant Quantization of the Green-Schwarz Superstring in a Calabi-Yau BackgroundApr 26 1994After adding a scalar chiral boson to the usual superspace variables, the four-dimensional Green-Schwarz superstring is quantized in a manifestly SO(3,1) super-Poincar\'e covariant manner. The constraints are all first-class and form an N=2 superconformal ... More

Can elemental bismuth be a liquid crystal?Mar 28 2010A number of anomalies have been reported in molten Bi, including a first-order liquid-liquid transition at 1010K and ambient pressure, which is irreversible at cooling rates of several degrees per minute. An interpretation of these effects as due to long-range ... More

Clusters, Coxeter-sortable elements and noncrossing partitionsJul 08 2005Dec 14 2005We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in terms of their ... More

Two Algorithms to Compute Symmetry Groups for Landau-Ginzburg ModelsFeb 19 2018Jun 27 2018Landau-Ginzburg mirror symmetry studies isomorphisms between graded Frobenius algebras, known as A- and B-models. Fundamental to constructing these models is the computation of the finite, Abelian $\textit{maximal symmetry group}$ $G_{W}^{\max}$ of a ... More

A bound for the "torsion conductor" of a non-CM elliptic curveNov 09 2007Given a non-CM elliptic curve E over Q, define the ``torsion conductor'' m_E to be the smallest positive integer so that the Galois representation on the torsion of E has image Pi^{-1}(Gal(Q(E[m_E])/Q), where Pi denotes the natural projection GL_2(\hat{Z}) ... More

On sets of integers which contain no three terms in geometric progressionOct 08 2013The problem of looking for subsets of the natural numbers which contain no 3-term arithmetic progressions has a rich history. Roth's theorem famously shows that any such subset cannot have positive upper density. In contrast, Rankin in 1960 suggested ... More

Cohomology of line bundles on a toric variety and constructible sheaves on its polytopeNov 15 2006We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.

A Slow Relative of Hofstadter's Q-SequenceNov 24 2016Hofstadter's Q-sequence remains an enigma fifty years after its introduction. Initially, the terms of the sequence increase monotonically by 0 or 1 at a time. But, Q(12)=8 while Q(11)=6, and monotonicity fails shortly thereafter. In this paper, we add ... More

Quasipolynomial Solutions to the Hofstadter Q-RecurrenceNov 20 2015In 1991, Solomon Golomb discovered a quasilinear solution to Hofstadter's Q-recurrence. In this paper, we construct eventual quasipolynomial solutions of all positive degrees to Hofstadter's recurrence.

Homology of the curve complex and the Steinberg module of the mapping class groupOct 31 2007Nov 03 2011By the work of Harer, the reduced homology of the complex of curves is a fundamental cohomological object associated to all torsion free finite index subgroups of the mapping class group. We call this homology group the Steinberg module of the mapping ... More

The Theory of Fallible Probability and The Dynamics of Degrees of BeliefMar 05 2008This monograph is an account of the theory of fallible probability and of the dynamics of degrees of belief. It discusses the first order subjective theory in which first order degrees of belief are expressed by subjective probabilities and are updated ... More

Pure spinors, twistors, and emergent supersymmetryMay 05 2011May 06 2011Starting with a classical action whose matter variables are a d=10 spacetime vector $x^m$ and a pure spinor $\lambda^\alpha$, the pure spinor formalism for the superstring is obtained by gauge-fixing the twistor-like constraint $\partial x^m (\gamma_m ... More

Super-Poincare Covariant Two-Loop Superstring AmplitudesMar 25 2005The super-Poincare covariant formalism for the superstring is used to compute massless four-point two-loop amplitudes in ten-dimensional superspace. The computations are much simpler than in the RNS formalism and include both external bosons and fermions. ... More

Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the SuperstringJun 05 2004Sep 22 2004A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined ... More

N=2 Sigma Models for Ramond-Ramond BackgroundsOct 08 2002Using the U(4) hybrid formalism, manifestly N=(2,2) worldsheet supersymmetric sigma models are constructed for the Type IIB superstring in Ramond-Ramond backgrounds. The Kahler potential in these N=2 sigma models depends on four chiral and antichiral ... More

Relating the RNS and Pure Spinor Formalisms for the SuperstringApr 27 2001Recently, the superstring was covariantly quantized using the BRST-like operator $Q = \oint \lambda^\alpha d_\alpha$ where $\lambda^\alpha$ is a pure spinor and $d_\alpha$ are the fermionic Green-Schwarz constraints. By performing a field redefinition ... More

Super-Poincare Covariant Quantization of the SuperstringJan 07 2000Jan 10 2000Using pure spinors, the superstring is covariantly quantized. For the first time, massless vertex operators are constructed and scattering amplitudes are computed in a manifestly ten-dimensional super-Poincar\'e covariant manner. Quantizable non-linear ... More

A New Approach to Superstring Field TheoryDec 14 1999I review the construction of an action for open superstring field theory which does not suffer from the contact term problems of other approaches. I also discuss a possible generalization of this action for closed superstring field theory.

Quantization of the Superstring in Ramond-Ramond BackgroundsOct 29 1999Nov 18 1999Sigma model actions are constructed for the Type II superstring compactified to four and six dimensional curved backgrounds which can contain non-vanishing Ramond-Ramond fields. These actions are N=2 worldsheet superconformally invariant and can be covariantly ... More

Quantization of the Type II Superstring in a Curved Six-Dimensional BackgroundAug 04 1999A sigma model action with N=2 D=6 superspace variables is constructed for the Type II superstring compactified to six curved dimensions with Ramond-Ramond flux. The action can be quantized since the sigma model is linear when the six-dimensional spacetime ... More

An Introduction to Superstring Theory and its Duality SymmetriesJul 29 1997In these proceedings for the First School on Field Theory and Gravitation (Vit\'oria, Brasil), a brief introduction is given to superstring theory and its duality symmetries. This introduction is intended for beginning graduate students with no prior ... More

Calculation of Green-Schwarz Superstring Amplitudes Using the N=2 Twistor-String FormalismAug 13 1992The manifestly SU(4)xU(1) super-Poincare invariant free-field N=2 twistor- string action for the ten-dimensional Green-Schwarz superstring is quantized using standard BRST methods. Unlike the light-cone and semi-light-cone gauge-fixed Green-Schwarz actions, ... More

Covariant Quantization of the Superparticle Using Pure SpinorsMay 05 2001Aug 03 2001The ten-dimensional superparticle is covariantly quantized by constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor variable. This same method was recently used for covariantly quantizing the superstring, ... More

Quantization of the Superstring with Manifest U(5) Super-Poincare InvarianceFeb 12 1999Feb 17 1999The superstring is quantized in a manner which manifestly preserves a U(5) subgroup of the (Wick-rotated) ten-dimensional super-Poincar\'e invariance. This description of the superstring contains critical N=2 worldsheet superconformal invariance and is ... More

Local Actions with Electric and Magnetic SourcesOct 17 1996Oct 28 1996Superstring field theory was recently used to derive a covariant action for a self-dual five-form field strength. This action is shown to be a ten-dimensional version of the McClain-Wu-Yu action. By coupling to D-branes, it can be generalized in the presence ... More

A New Approach to the Green-Schwarz SuperstringJun 21 1993By replacing two of the bosonic scalar superfields of the N=2 string with fermionic scalar superfields (which shifts $d_{critical}$ from (2,2) to (9,1)), a quadratic action for the ten-dimensional Green-Schwarz superstring is obtained. Using the usual ... More

Finiteness and Unitarity of Lorentz-Covariant Green-Schwarz Superstring AmplitudesMar 22 1993Mar 24 1993In two recent papers, a new method was developed for calculating ten-dimensional superstring amplitudes with an arbitrary number of loops and external massless particles, and for expressing them in manifestly Lorentz-invariant form. By explicitly checking ... More

A discrete mean value of the derivative of the Riemann zeta functionJun 12 2007In this article we compute a discrete mean value of the derivative of the Riemann zeta function. This mean value will be important for several applications concerning the size of $\zeta'(\rho)$ where $\zeta(s)$ is the Riemann zeta function and $\rho$ ... More

The Kontsevich integral and quantized Lie superalgebrasNov 02 2004Sep 27 2005Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: 1) quantum group invariants using the R-matrix, 2) the Kontsevich universal link invariant followed by the Lie algebra based weight ... More

Logarithms Over a Real Associative AlgebraAug 03 2017Extending the work of Freese and Cook, which develop the basic theory of calculus and power series over real associative algebras, we examine what can be said about the logarithmic functions over an algebra. In particular, we find that for any multiplicative ... More

Noncrossing partitions, clusters and the Coxeter planeDec 26 2009Feb 18 2010When W is a finite Coxeter group of classical type (A, B, or D), noncrossing partitions associated to W and compatibility of almost positive roots in the associated root system are known to be modeled by certain planar diagrams. We show how the classical-type ... More

Spectra of Wishart Matrices with size-dependent entriesOct 17 2017We prove the convergence of the empirical spectral measure of Wishart matrices with size-dependent entries and characterize the limiting law by its moments. We apply our result to the cases where the entries are Bernoulli variables with parameter c=n ... More

Chains in the noncrossing partition latticeJun 19 2007Jul 27 2007We establish recursions counting various classes of chains in the noncrossing partition lattice of a finite Coxeter group. The recursions specialize a general relation which is proven uniformly (i.e. without appealing to the classification of finite Coxeter ... More

The Order Dimension of the Poset of Regions in a Hyperplane ArrangementMay 23 2003Aug 12 2003We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified approach which, in ... More

MacWilliams Identities for $m$-tuple Weight EnumeratorsMay 07 2012Jan 13 2014Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of $m$-tuple support enumerators. ... More

Homological Stability For Moduli Spaces of Odd Dimensional ManifoldsNov 22 2013Feb 14 2014We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to $\#^{g}(S^{n+1}\times S^{n})$, provided $n \geq 4$. This is an odd dimensional analogue of a recent homological stability result of S. Galatius and O. Randal ... More

Bosonic Chern-Simons Field Theory of Anyon SuperconductivityApr 13 1992We study the Quantum Field Theory of nonrelativistic bosons coupled to a Chern--Simons gauge field at nonzero particle density. This field theory is relevant to the study of anyon superconductors in which the anyons are described as {\bf bosons} with ... More

The distribution of the summatory function of the Möbius functionOct 23 2003Let the summatory function of the M\"{o}bius function be denoted $M(x)$. We deduce in this article conditional results concerning $M(x)$ assuming the Riemann Hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the Riemann zeta function. ... More

On the weak tightness, Hausdorff spaces, and power homogeneous compactaSep 23 2017Motivated by results of Juh\'asz and van Mill in [13], we define the cardinal invariant $wt(X)$, the weak tightness of a topological space $X$, and show that $|X|\leq 2^{L(X)wt(X)\psi(X)}$ for any Hausdorff space $X$ (Theorem 2.8). As $wt(X)\leq t(X)$ ... More

Doing Algebra over an Associative AlgebraAug 03 2017A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to $\mathbb{R}$ ... More

Dominance phenomena: mutation, scattering and cluster algebrasFeb 27 2018Jun 14 2018An exchange matrix $B$ dominates an exchange matrix $B'$ if the signs of corresponding entries weakly agree, with the entry of $B$ always having weakly greater absolute value. When $B$ dominates $B'$, interesting things happen in many cases (but not always): ... More

The cd-index of Bruhat intervalsOct 08 2003We study flag enumeration in intervals in the Bruhat order on a Coxeter group by means of a structural recursion on intervals in the Bruhat order. The recursion gives the isomorphism type of a Bruhat interval in terms of smaller intervals, using basic ... More

Parametrized Morse Theory and Positive Scalar CurvatureMay 08 2017We use the cobordism category constructed in arXiv:1703.01047 to the study the homotopy type of the space of positive scalar curvature metrics on a spin manifold of dimension > 4. Our methods give an alternative proof and extension of a recent theorem ... More

A combinatorial approach to scattering diagramsJun 13 2018Scattering diagrams arose in the context of mirror symmetry, but a special class of scattering diagrams (the cluster scattering diagrams) were recently developed to prove key structural results on cluster algebras. This paper studies cluster scattering ... More

On The Probability of a Rational Outcome for Generalized Social Welfare Functions on Three AlternativesMay 26 2009Nov 19 2009In [G. Kalai, A Fourier-theoretic Perspective on the Condorcet Paradox and Arrow's Theorem, Adv. in Appl. Math. 29(3) (2002), pp. 412--426], Kalai investigated the probability of a rational outcome for a generalized social welfare function (GSWF) on three ... More

One-Parameter Toric Deformations of Cyclic Quotient SingularitiesJan 15 2008Oct 17 2008In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions. In particular, we describe to which components each such deformation maps, show how to induce ... More

Finding Linear-Recurrent Solutions to Hofstadter-Like Recurrences Using Symbolic ComputationSep 20 2016The Hofstadter Q-sequence, with its simple definition, has defied all attempts at analyzing its behavior. Defined by a simple nested recurrence and an initial condition, the sequence looks approximately linear, though with a lot of noise. But, nobody ... More

Spectral Properties of Complex Unit Gain GraphsOct 20 2011Nov 15 2011A complex unit gain graph is a graph where each orientation of an edge is given a complex unit, which is the inverse of the complex unit assigned to the opposite orientation. We extend some fundamental concepts from spectral graph theory to complex unit ... More

Some remarks on quantized Lie superalgebras of classical typeAug 23 2005Apr 26 2007In this paper we use the Etingof-Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld-Jimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that the D-J type ... More