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Frequency Modulation Spectroscopy at High Modulation Depth in an Indium Atomic BeamOct 24 2013We present a detailed analysis of an application of frequency modulation (FM) spectroscopy in the high modulation depth limit. We have recently completed and reported a measurement of the Stark shift in the indium $5p_{1/2}\rightarrow 6s_{1/2}$ 410 nm ... More

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

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

Observation of Cavity Rydberg PolaritonsNov 05 2015Nov 12 2015We demonstrate hybridization of optical cavity photons with atomic Rydberg excitations using electromagnetically induced transparency (EIT). The resulting dark state Rydberg polaritons exhibit a compressed frequency spectrum and enhanced lifetime indicating ... More

Photons and polaritons in a time-reversal-broken non-planar resonatorAug 31 2017Dec 01 2017From generation of backscatter-free transmission lines, to optical isolators, to chiral Hamiltonian dynamics, breaking time-reversal symmetry is a key tool for development of next-generation photonic devices and materials. Of particular importance is ... More

Interacting Floquet polaritonsJun 27 2018Ordinarily, photons do not interact with one another. However, atoms can be used to mediate photonic interactions, raising the prospect of forming synthetic materials and quantum information systems from photons. One promising approach uses electromagnetically-induced ... More

A Strongly Interacting Polaritonic Quantum DotMay 21 2017Polaritons are an emerging platform for exploration of synthetic materials [1] and quantum information processing [2] that draw properties from two disparate particles: a photon and an atom. Cavity polaritons are particularly promising, as they are long-lived ... More

30-Fold Increase in Atom-Cavity Coupling Using a Parabolic Ring CavityFeb 15 2018Optical cavities are one of the best ways to increase atom-light coupling and will be a key ingredient for future quantum technologies that rely on light-matter interfaces. We demonstrate that traveling-wave "ring" cavities can achieve a greatly reduced ... More

Superstrings in Graviphoton Background and N=1/2+3/2 SupersymmetryJun 24 2003Jun 30 2003Motivated by Ooguri and Vafa, we study superstrings in flat R^4 in a constant self-dual graviphoton background. The supergravity equations of motion are satisfied in this background which deforms the N=2 d=4 flat space super-Poincare algebra to another ... 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

Large gaps between the zeros of the Riemann zeta functionOct 25 2005We show that the generalized Riemann hypothesis implies that there are infinitely many consecutive zeros of the Riemann zeta function whose spacing is 2.9125 times larger than the average spacing. This is deduced from the calculation of the second moment ... 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

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

Step Size in Stein's Method of Exchangeable PairsApr 02 2009Stein's method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we analyze how modifying ... 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

How to speed up R code: an introductionMar 03 2015Most calculations performed by the average R user are unremarkable in the sense that nowadays, any computer can crush the related code in a matter of seconds. But more and more often, heavy calculations are also performed using R, something especially ... More

On Aperiodic Subtraction Games with Bounded Nim SequenceJul 10 2014Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to define, sub- traction ... 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

Divisorial instability and Vojta's Main Conjecture for $\mathbb{Q}$-Fano varietiesJan 23 2019We study Diophantine arithmetic properties of birational divisors in conjunction with concepts that surround $\mathrm{K}$-stability for Fano varieties. There is also an interpretation in terms of the barycentres of Newton-Okounkov bodies. Our main results ... More

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.

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.

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

Dimer models and Calabi-Yau algebrasJan 29 2009Aug 20 2010In this article we study dimer models, as introduced in string theory, which give a way of writing down a class of non-commutative `superpotential' algebras. Some examples are 3-dimensional Calabi-Yau algebras, as defined by Ginzburg, and some are not. ... More

Exposing Software Defined Radio Functionality To Native Operating System Applications via Virtual DevicesJul 13 2004Many reconfigurable platforms require that applications be written specifically to take advantage of the reconfigurable hardware. In a PC-based environment, this presents an undesirable constraint in that the many already available applications cannot ... More

Introduction to $Z_N$ Symmetry in $SU_N$ Gauge Theories at Finite TemperaturesNov 05 1993There have been several talks at this workshop on the physical interpretation and consequences of the $Z_N$ symmetry which is present in the Euclidean Path Integral formulation of $SU_N$ Gauge Theories at finite temperature. The purpose of this paper ... More

Observational indicators of the transition from fully convective stars to stars with radiative coresJun 24 2010We present a discussion of the similarities and key differences between the transition onto (at the turn-on) and away from (at the turn-off) the main sequence, the latter termed the Hertzsprung gap. Using a set of model isochrones and adopting an initial ... More

The Kinematics of Arp 295 in H-alpha Emission: an Interacting Galaxy with Highly Asymmetric RotationOct 13 2006Dec 12 2006We investigate Arp 295, a pair of interacting spirals at z=0.023. We measure scalelengths 5.24 kpc for Arp 295a and 2.52 kpc for 295b. There is a much smaller Im galaxy associated with the larger spiral. Arp 295b is asymmetric with the disk more extended ... More

Ten-Dimensional Super-Twistors and Super-Yang-MillsOct 09 2009Oct 11 2009Four-dimensional super-twistors provide a compact covariant description of on-shell N=4 d=4 super-Yang-Mills. In this paper, ten-dimensional super-twistors are introduced which similarly provide a compact covariant description of on-shell d=10 super-Yang-Mills. ... More

Off-shell Supersymmetry versus Hermiticity in the SuperstringApr 19 1996We point out that off-shell four-dimensional supersymmetry implies strange hermiticity properties for the N=1 RNS superstring. However, these hermiticity properties become natural when the N=1 superstring is embedded into an N=2 superstring.

Super-Poincare Invariant Koba-Nielsen Formulas for the SuperstringApr 19 1996The new spacetime-supersymmetric description of the superstring is used to compute tree-level scattering amplitudes for an arbitrary number of massless four-dimensional states. The resulting Koba-Nielsen formula is manifestly SO(3,1) super-Poincare invariant ... More

A New Sigma Model Action for the Four-Dimensional Green-Schwarz Heterotic SuperstringMar 03 1993The sigma model action described in this paper differs in four important features from the usual sigma model action for the four-dimensional Green-Schwarz heterotic superstring in a massless background. Firstly, the action is constructed on an N=(2,0) ... More

Simplifying and Extending the AdS_5xS^5 Pure Spinor FormalismDec 30 2008Although the AdS_5xS^5 worldsheet action is not quadratic, some features of the pure spinor formalism are simpler in an AdS_5xS^5 background than in a flat background. The BRST operator acts geometrically, the left and right-moving pure spinor ghosts ... More

Towards Covariant Quantization of the SupermembraneJan 20 2002Apr 16 2002By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, ... More

Extra Dimensions in Superstring TheoryApr 14 1997Jun 04 1997It was earlier shown that an SO(9,1) $\theta^\a$ spinor variable can be constructed from RNS matter and ghost fields. $\theta^\a$ has a bosonic worldsheet super-partner $\lambda^\a$ which plays the role of a twistor variable, satisfying $\lambda\Gamma^\mu\lambda ... More

Radically weakening the Lehmer and Carmichael conditionsOct 06 2012Lehmer's totient problem asks if there exist composite integers n satisfying the condition phi(n)|(n-1), (where phi is the Euler-phi function) while Carmichael numbers satisfy the weaker condition lambda(n)|(n-1) (where lambda is the Carmichael universal ... More

Non-equilibrium Josephson-like effects in mesoscopic S-N-S junctionsAug 30 1997Wide mesoscopic superconducting - normal-metal - superconducting (S-N-S) junctions exhibit Andreev bound states which carry substantial supercurrents, even at temperatures for which the equilibrium Josephson effect is exponentially small --- the currents ... More

Bell's Theorem and the Causal Arrow of TimeJul 13 2008May 06 2010Einstein held that the formalism of Quantum Mechanics (QM) entails "spooky actions at a distance". Indeed, in the 60's Bell showed that the predictions of QM disagree with the results of any locally causal description. Accepting non-local descriptions ... More

Semiclassical analysis of the quantum interference corrections to the conductance of mesoscopic systemsMay 12 1995The Kubo formula for the conductance of a mesoscopic system is analyzed semiclassically, yielding simple expressions for both weak localization and universal conductance fluctuations. In contrast to earlier work which dealt with times shorter than $O(\log ... More

Segre embeddings and the canonical image of a curveJan 10 2012We prove that there is no g for which the canonical embedding of a general curve of genus g lies on the Segre embedding of any product of three or more projective spaces.

Primitive and geometric-progression-free sets without large gapsSep 22 2018Feb 04 2019We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of prime numbers. ... More

On The Influences of Variables on Boolean Functions in Product SpacesMay 26 2009In this paper we consider the influences of variables on Boolean functions in general product spaces. Unlike the case of functions on the discrete cube where there is a clear definition of influence, in the general case at least three definitions were ... More

The sixth moment of the Riemann zeta function and ternary additive divisor sumsOct 17 2016Hardy and Littlewood initiated the study of the $2k$-th moments of the Riemann zeta function on the critical line. In 1918 Hardy and Littlewood established an asymptotic formula for the second moment and in 1926 Ingham established an asymptotic formula ... More

From the Tamari lattice to Cambrian lattices and beyondSep 23 2011Oct 05 2011In this chapter, we trace the path from the Tamari lattice, via lattice congruences of the weak order, to the definition of Cambrian lattices in the context of finite Coxeter groups, and onward to the construction of Cambrian fans. We then present sortable ... More

Sortable elements and Cambrian latticesDec 14 2005We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice ... More

Lattice congruences of the weak orderJan 28 2004We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the ... More

Noncrossing partitions and the shard intersection orderSep 17 2009We define a new lattice structure on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC(W) as a sublattice. The new construction of NC(W) ... More

Establishing Conditions on the Degree of Regularity of Linear Homogeneous EquationsJan 28 2017In 1933, Rado conjectured that for any positive integer n, there is always a linear homogeneous equation with degree of regularity n. In proving this conjecture, Alexeev and Tsimerman, and independently Golowich, found that some equations in n variables ... More

Degree of irrationality of very general abelian surfacesFeb 15 2019The degree of irrationality of a projective variety $X$ is defined to be the smallest degree rational dominant map to a projective space of the same dimension. For abelian surfaces, Yoshihara computed this invariant in specific cases, while Stapleton ... More

Realising the C*-algebra of a higher-rank graph as an Exel crossed productDec 23 2009Jun 07 2011We use the boundary-path space of a finitely-aligned k-graph \Lambda to construct a compactly-aligned product system X, and we show that the graph algebra C^*(\Lambda) is isomorphic to the Cuntz-Nica-Pimsner algebra NO(X). In this setting, we introduce ... More

Extreme values of zeta prime rhoJun 12 2007In this article we exhibit small and large values of $\zeta'(\rho)$ by applying Soundararajan's resonance method. Our results assume the Riemann hypothesis.

The fourth moment of ζ^{'}(ρ)Oct 23 2003Discrete moments of the Riemann zeta function were studied by Gonek and Hejhal in the 1980's. They independently formulated a conjecture concerning the size of these moments. In 1999, Hughes, Keating, and O'Connell, by employing a random matrix model, ... More

Averages of elliptic curve constantsNov 21 2007We compute the averages over elliptic curves of the constants occurring in the Lang-Trotter conjecture, the Koblitz conjecture, and the cyclicity conjecture. The results obtained confirm the consistency of these conjectures with the corresponding ``theorems ... More

Status of the Kazakov--Migdal ModelJan 16 1995In this talk I discuss both the present status and some recent work on the Kazakov--Migdal Model which was originally proposed as a soluble, large $N$ realization of QCD. After a brief description of the model and a discussion of its solubility in the ... More

Imaging and Spectroscopy of Arp 104: A Post-starburst Interacting Pair with Cross-Fuelling?Apr 29 2006We perform UBR imaging and optical spectroscopy of the interacting galaxy pair Arp 104, at z=0.0098. This consists of NGC5218, a disturbed Sb barred spiral with an inclined outer shell, the round spheroidal NGC5216, a connecting bridge of length 50 kpc ... 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

Methods for scaling a large member baseFeb 20 2006The technical challenges of scaling websites with large and growing member bases, like social networking sites, are numerous. One of these challenges is how to evenly distribute the growing member base across all available resources. This paper will explore ... More

Constrained BV Description of String Field TheoryJan 09 2012In the conventional BV description of string field theory, the string field Phi is split as Phi = Psi+Psi* where Psi includes all states with ghost number less than or equal to G and describes the spacetime fields, and Psi* includes all states with ghost ... More

Explaining the Pure Spinor Formalism for the SuperstringDec 03 2007Dec 18 2007After adding a pair of non-minimal fields and performing a similarity transformation, the BRST operator in the pure spinor formalism is expressed as a conventional-looking BRST operator involving the Virasoro constraint and (b,c) ghosts, together with ... More

Quantum Consistency of the Superstring in AdS_5 x S^5 BackgroundNov 18 2004Dec 15 2004Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS_5 x S^5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments ... More

BRST Cohomology and Nonlocal Conserved ChargesSep 15 2004A relation is found between nonlocal conserved charges in string theory and certain ghost-number two states in the BRST cohomology. This provides a simple proof that the nonlocal conserved charges for the superstring in an AdS_5 x S^5 background are BRST-invariant ... More

Conformal Field Theory for the Superstring in a Ramond-Ramond Plane Wave BackgroundMar 26 2002A quantizable worldsheet action is constructed for the superstring in a supersymmetric plane wave background with Ramond-Ramond flux. The action is manifestly invariant under all isometries of the background and is an exact worldsheet conformal field ... More

Covariant Quantization of the SuperstringAug 17 2000Aug 28 2000After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators ... More

Cohomology in the Pure Spinor Formalism for the SuperstringJun 01 2000Aug 01 2000A manifestly super-Poincar\'e covariant formalism for the superstring has recently been constructed using a pure spinor variable. Unlike the covariant Green-Schwarz formalism, this new formalism is easily quantized with a BRST operator and tree-level ... More

Construction of $R^4$ Terms in N=2 D=8 SuperspaceSep 16 1997Sep 18 1997Using linearized superfields, $R^4$ terms in the Type II superstring effective action compactified on $T^2$ are constructed as integrals in N=2 D=8 superspace. The structure of these superspace integrals allows a simple proof of the $R^4$ non-renormalization ... More

The Ten-Dimensional Green-Schwarz Superstring is a Twisted Neveu-Schwarz-Ramond StringAug 27 1993An action for the ten-dimensional Green-Schwarz superstring with N=2 worldsheet superconformal invariance has recently been used to calculate superstring scattering amplitudes and prove their finiteness. In this paper, it is shown that the N=2 stress-energy ... More

A New Limit of the AdS_5 x S^5 Sigma ModelMar 30 2007Apr 01 2007Using the pure spinor formalism, a quantizable sigma model has been constructed for the superstring in an AdS_5 x S^5 background with manifest PSU(2,2|4) invariance. The PSU(2,2|4) metric g_{AB} has both vector components g_{ab} and spinor components ... More

Conformal Compensators and Manifest Type IIB S-DualityJan 04 1998Jan 07 1998Using the conformal compensator superfields of N=2 D=4 supergravity, the Type IIB S-duality transformations are expressed as a linear rotation which mixes the compensator and matter superfields. The classical superspace action for D=4 compactifications ... More

A Problem with the Superstring Action of Deriglazov and GalajinskyDec 05 1997Dec 12 1997Deriglazov and Galajinsky have recently proposed a new covariant action for the Green-Schwarz superstring which can be constructed in any spacetime dimension. In this short note, I show that their action contains extra on-shell degrees of freedom as compared ... More

Random Scattering Matrices and the Circuit Theory of Andreev ConductancesAug 20 1996The conductance of a normal-metal mesoscopic system in proximity to superconducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a ``circuit'' with ``leads'' and ``junctions''. The junctions are each ... More

The AJ-Conjecture for Cables of Two Bridge KnotsDec 02 2014Mar 02 2015The $AJ$-conjecture for a knot $K \subset S^3$ relates the $A$-polynomial and the colored Jones polynomial of $K$. If a two-bridge knot $K$ satisfies the $AJ$-conjecture, we give sufficient conditions on $K$ for the $(r,2)$-cable knot $C$ to also satisfy ... More

Generic rectangulationsMay 16 2011Jan 05 2012A rectangulation is a tiling of a rectangle by a finite number of rectangles. The rectangulation is called generic if no four of its rectangles share a single corner. We initiate the enumeration of generic rectangulations up to combinatorial equivalence ... More

Homological Stability for Diffeomorphism Groups of High Dimensional HandlebodiesOct 09 2015Jun 21 2016In this paper we prove a homological stability theorem for the diffeomorphism groups of high dimensional manifolds with boundary, with respect to forming the boundary connected sum with the product $D^{p+1}\times S^{q}$ for $|q - p| < \min\{p, q\} - 2$. ... More

Linear Recurrent Subsequences of Meta-Fibonacci SequencesAug 07 2015In a recent paper, Frank Ruskey asked whether every linear recurrent sequence can occur in some solution of a meta-Fibonacci sequence. In this paper, we answer his question in the affirmative for recurrences with positive coefficients.

Transposing Noninvertible PolynomialsMar 10 2015Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted $\mathcal{A}$ and $\mathcal{B}$) that are constructed from a nondegenerate quasihomogeneous polynomial $W$ and a related group of symmetries $G$. Duality ... More

An Isomorphism Extension Theorem for Landau-Ginzburg B-ModelsJul 05 2016Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known that given two ... More

New Bounds for the Laplacian Spectral Radius of a Signed GraphMar 23 2011We obtain new bounds for the Laplacian spectral radius of a signed graph. Most of these new bounds have a dependence on edge sign, unlike previously known bounds, which only depend on the underlying structure of the graph. We then use some of these bounds ... More

A tight quantitative version of Arrow's impossibility theoremMar 20 2010The well-known Impossibility Theorem of Arrow asserts that any Generalized Social Welfare Function (GSWF) with at least three alternatives, which satisfies Independence of Irrelevant Alternatives (IIA) and Unanimity and is not a dictatorship, is necessarily ... More

A simple reduction from a biased measure on the discrete cube to the uniform measureJan 07 2010Nov 24 2010We show that certain statements related to the Fourier-Walsh expansion of functions with respect to a biased measure on the discrete cube can be deduced from the respective results for the uniform measure by a simple reduction. In particular, we present ... More

Weight enumerators of Reed-Muller codes from cubic curves and their dualsSep 24 2018Let $\mathbb{F}_q$ be a finite field of characteristic not equal to $2$ or $3$. We compute the weight enumerators of some projective and affine Reed-Muller codes of order $3$ over $\mathbb{F}_q$. These weight enumerators answer enumerative questions about ... More

Lattice congruences, fans and Hopf algebrasFeb 04 2004We give a unified explanation of the geometric and algebraic properties of two well-known maps, one from permutations to triangulations, and another from permutations to subsets. Furthermore we give a broad generalization of the maps. Specifically, for ... More

Coarsening polyhedral complexesApr 23 2010Given a polyhedral complex C with convex support, we characterize, by a local codimension-2 condition, polyhedral complexes that coarsen C. The proof of the characterization draws upon a surprising general shortcut for showing that a collection of polyhedra ... More

Improved Error-Scaling for Adiabatic Quantum State TransferMay 31 2011Sep 15 2011We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate. These improvements ... More

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

Noncyclic covers of knot complementsJan 12 2004May 31 2005Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\Phi (c)$, such that if $K$ is a nontrivial knot in ... 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

Almost all elliptic curves are Serre curvesNov 03 2006Using a multidimensional large sieve inequality, we obtain a bound for the mean square error in the Chebotarev theorem for division fields of elliptic curves that is as strong as what is implied by the Generalized Riemann Hypothesis. As an application ... More