Results for "Nathan Goldman"

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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
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
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
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
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
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
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
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
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
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".
On algebraic properties of low rank approximations of Prony systemsMar 25 2018We consider the reconstruction of spike train signals of the form $$F(x) = \sum_{i=1}^d a_i \delta(x-x_i),$$ from their moments measurements $m_k(F)=\int x^k F(x) dx = \sum_{i=1}^d a_ix^k$. When some of the nodes $x_i$ near collide the inversion becomes ... 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
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
"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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Shock waves in virus fitness evolutionAug 20 2005We consider a nonlinear partial differential equation of conservation type to describe the dynamics of vesicular stomatitis virus observed in aliquots of fixed particle number taken from an evolving clone at periodic intervals of time \cite{novella 95}. ... 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
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
Constructing the Primitive Roots of Prime PowersSep 12 2008We use only addition and multiplication to construct the primitive roots of $p^{k+1}$ from the primitive roots of $p^{k}$, where $p$ is an odd prime and $k$ is at least 2.
Cobordism categories of manifolds with Baas-Sullivan singularities, Part 2Jun 18 2013Dec 15 2014For a given list of closed manifolds $\Sigma_k=(P_1,...,P_k)$, we construct a cobordism category $\mathbf{Cob}_{d}^{\Sigma_{k}}$ of embedded manifolds with Baas-Sullivan singularities of type $\Sigma_k$. Our main results identify the homotopy type of ... More
Cobordism Category of Manifolds With Baas-Sullivan Singularities, Part IDec 27 2012Dec 12 2014For a fixed closed manifold $P$, we construct a cobordism category of embedded manifolds with a single Baas-Sullivan singularity of type $P$. Our main theorem identifies the homotopy type of the classifying space of this cobordism category with that of ... More
The Kontsevich integral and re-normalized link invariants arising from Lie superalgebrasApr 02 2009We show that the coefficients of the re-normalized link invariants of the paper "Multivariable link invariants arising from Lie superalgebras of type I" are Vassiliev invariants which give rise to a canonical family of weight systems.
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
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
Universal geometric cluster algebrasSep 18 2012Sep 17 2013We consider, for each exchange matrix B, a category of geometric cluster algebras over B and coefficient specializations between the cluster algebras. The category also depends on an underlying ring R, usually the integers, rationals, or reals. We broaden ... 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
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
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
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
Geodesics on Margulis spacetimesFeb 02 2011Aug 15 2011Let M be a Margulis spacetime whose associated complete hyperbolic surface S has compact convex core. Generalizing the correspondence between closed geodesics on M and closed geodesics on S, we establish an orbit equivalence between recurrent spacelike ... More
Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physicsOct 13 2015Apr 23 2016Recent technological advances in integrated photonics have spurred on the study of topological phenomena in engineered bosonic systems. Indeed, the controllability of silicon ring-resonator arrays has opened up new perspectives for building lattices for ... 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
McShane-type Identities for Affine DeformationsJul 07 2015Oct 07 2016We derive an identity for Margulis invariants of affine deformations of a complete orientable one-ended hyperbolic sur- face following the identities of McShane, Mirzakhani and Tan- Wong-Zhang. As a corollary, a deformation of the surface which infinitesimally ... 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
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
Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladderJun 26 2015Sep 12 2015We consider a spin-1/2 fermionic ladder with spin-orbit coupling and a perpendicular magnetic field, which shares important similarities with topological superconducting wires. We fully characterize the symmetry-protected topological phase of this ladder ... More