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An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological InsulatorsMay 04 2011We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine ... More

Experimental observation of anomalous topological edge modes in a slowly-driven photonic latticeApr 19 2016Apr 20 2016The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of topological band theory, ... More

Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguidesApr 03 2016Sep 07 2016We report on the experimental realization of a photonic system that simulates the one-dimensional two-particle Hubbard model. This analogy is realized by means of two-dimensional arrays of coupled optical waveguides, fabricated using femtosecond laser ... 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

Topological PhotonicsFeb 12 2018Topological photonics is a rapidly-emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators ... 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

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

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

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

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

A hopping mechanism for cargo transport by molecular motors in crowded microtubulesJun 26 2010Most models designed to study the bidirectional movement of cargos as they are driven by molecular motors rely on the idea that motors of different polarities can be coordinated by external agents if arranged into a motor-cargo complex to perform the ... More

The Palm measure and the Voronoi tessellation for the Ginibre processOct 07 2006Jan 14 2010We prove that the Palm measure of the Ginibre process is obtained by removing a Gaussian distributed point from the process and adding the origin. We obtain also precise formulas describing the law of the typical cell of Ginibre--Voronoi tessellation. ... 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

Neutrino Oscillations and Energy-Momentum ConservationApr 19 1996Jun 15 2010A description of neutrino oscillation phenomena is presented which is based on relativistic quantum mechanics and includes both entangled state and source dependent aspects, unlike both of the conventional approaches which use either equal energies or ... More

A geometric approach for convexity in some variational problem in the Gauss spaceOct 26 2011In this short note we prove the convexity of minimizers of some variational problem in the Gauss space. This proof is based on a geometric version of an older argument due to Korevaar.

Continuous Primal-Dual Methods for Image ProcessingMar 31 2010Sep 21 2010In this article we study a continuous Primal-Dual method proposed by Appleton and Talbot and generalize it to other problems in image processing. We interpret it as an Arrow-Hurwicz method which leads to a better description of the system of PDEs obtained. ... More

Implications of Mirror Dark Matter on Neutron StarsDec 07 2011We study the implications of asymmetric dark matter on neutron stars. we construct a "mixed neutron star" model composed of ordinary baryons and of asymmetric dark matter baryons. We derive the general relativistic structure equations for each specie, ... 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

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

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

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

A phenomenological study of photon production in low energy neutrino nucleon scatteringAug 31 2009Low energy photon production is an important background to many current and future precision neutrino experiments. We present a phenomenological study of t-channel radiative corrections to neutral current neutrino nucleus scattering. After introducing ... More

Some Radiative Corrections to Neutrino Scattering: I Neutral CurrentsJun 04 2009With the advent of high precision neutrino scattering experiments comes the need for improved radiative corrections. We present a phenomenological analysis of some contributions to the production of photons in neutrino neutral current scattering that ... More

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

Two papers which changed my life: Milnor's seminal work on flat manifolds and flat bundlesAug 01 2011Apr 09 2012We survey developments arising from Milnor's 1958 paper, "On the existence of a connection with curvature zero" and his 1977 paper, "On fundamental groups of complete affinely flat manifolds".

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

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

On the regularity of stationary points of a nonlocal isoperimetric problemMay 18 2014In this article we establish $C^{3,\alpha}$-regularity of the reduced boundary of stationary points of a nonlocal isoperimetric problem in a domain $\Omega \subset \mathbb{R}^n$. In particular, stationary points satisfy the corresponding Euler-Lagrange ... More

On the optimality of stripes in a variational model with non-local interactionsNov 22 2016We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a $\Gamma$--convergence analysis, we show that as the parameter J converges to ... More

The Mapping Class Group acts reducibly on SU(n)-character varietiesSep 06 2005Sep 22 2005When $G$ is a connected compact Lie group, and $\pi$ is a closed surface group, then $Hom(\pi,G)$ contains an open dense $Out(\pi)$-invariant subset which is a smooth symplectic manifold. This symplectic structure is $Out(\pi)$-invariant and therefore ... More

"Atmospheric Neutrino" and "Proton Decay" Data Exclude Some New Dark Matter ScenariosJun 23 2004Models in which the "dark" halo particles have mutual and potentially also appreciable nuclear interactions have been considered by various authors. In this note we briefly point out strategies for a most sensitive search for these particles. We show ... More

Turbulent Convection in Thin Accretion DisksJan 03 1995A self-consistent solution for a thin accretion disk with turbulent convection is presented. The disk viscosity and the convective flux are derived from a physical model for turbulence, and expressed in terms of the local physical conditions of the disk ... More

Phase segregation for binary mixtures of Bose-Einstein CondensatesMay 27 2015Nov 30 2016We 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

Nucleation barriers at corners for cubic-to-tetragonal phase transformationNov 22 2013We are interested in the energetic cost of a martensitic inclusion of volume $V$ in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of [Kn\"upfer, Kohn, Otto: Comm. Pure Appl. Math. 66 (2013), no. 6, 867--904], we ... More

Volume-constrained minimizers for the prescribed curvature problem in periodic mediaMar 26 2011Mar 15 2013We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also show convergence ... 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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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.

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

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

Homological Stability For The Moduli Spaces of Products of SpheresAug 08 2014Sep 26 2014We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds, with respect to forming the connected sum with the product of spheres $S^{p}\times S^{q}$, for $p < q < 2p - 2$. This result is analogous to recent ... 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

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

Cambrian LatticesFeb 05 2004Jul 18 2005For an arbitrary finite Coxeter group W we define the family of Cambrian lattices for W as quotients of the weak order on W with respect to certain lattice congruences. We associate to each Cambrian lattice a complete fan, which we conjecture is the normal ... More

Nested Archimedean copulas: a new class of nonparametric tree structure estimatorsJul 01 2014Any nested Archimedean copula is defined starting from a rooted phylogenetic tree, for which a new class of nonparametric estimators is presented. An estimator from this new class relies on a two-step procedure where first a binary tree is built and second ... More

Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n+1Nov 10 2014Feb 26 2016Let $n \geq 2$. We prove a homological stability theorem for the diffeomorphism groups of $(4n+1)$-dimensional manifolds, with respect to forming the connected sum with $(2n-1)$-connected, $(4n+1)$-dimensional manifolds that are stably parallelizable. ... 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

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

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

New Higher-Derivative $R^4$ TheoremsSep 01 2006The non-minimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative $R^4$ conjectures of Green, Russo and Vanhove. The first theorem states that when $0<n<12$, $\partial^n ... More

Covariant Multiloop Superstring AmplitudesOct 07 2004In these proceedings, the multiloop amplitude prescription using the super-Poincare invariant pure spinor formalism for the superstring is reviewed. Unlike the RNS prescription, there is no sum over spin structures and surface terms coming from the boundary ... More

Self-Dual Super-Yang-Mills as a String Theory in $(x,θ)$ SpaceMar 29 2004Different string theories in twistor space have recently been proposed for describing ${\cal N}=4$ super-Yang-Mills. In this paper, my Strings 2003 talk is reviewed in which a string theory in $(x,\theta)$ space was constructed for self-dual ${\cal N}=4$ ... More

An Alternative String Theory in Twistor Space for N=4 Super-Yang-MillsFeb 05 2004In this letter, an alternative string theory in twistor space is proposed for describing perturbative N=4 super-Yang-Mills theory. Like the recent proposal of Witten, this string theory uses twistor worldsheet variables and has manifest spacetime superconformal ... More

Perturbative Super-Yang-Mills from the Topological AdS_5xS^5 Sigma ModelJun 12 2008Jul 22 2008A topological sigma model based on the pure spinor formalism was recently proposed for the small radius limit of the AdS_5xS^5 superstring. Physical states in this model can be constructed by connecting holes on the worldsheet with Wilson lines of the ... More

Ramond-Ramond Central Charges in the Supersymmetry Algebra of the SuperstringJun 03 1997The free action for the massless sector of the Type II superstring was recently constructed using closed RNS superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N=2 D=10 SUSY algebra with Ramond-Ramond central ... More

Super-Maxwell Actions with Manifest DualityOct 28 1996Superstring field theory was recently used to derive a four-dimensional Maxwell action with manifest duality. This action is related to the McClain-Wu-Yu Hamiltonian and can be locally coupled to electric and magnetic sources. In this letter, the manifestly ... More

Manifest Electromagnetic Duality in Closed Superstring Field TheoryJul 09 1996Jul 25 1996The free action for massless Ramond-Ramond fields is derived from closed superstring field theory using the techniques of Siegel and Zwiebach. For the uncompactified Type IIB superstring, this gives a manifestly Lorentz-covariant action for a self-dual ... 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