Results for "Scott Manifold"
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The Hilbert Schemes of Degree Three Curves are ConnectedMar 14 1996In this paper we show that the Hilbert scheme $H(3,g)$ of locally Cohen-Macaulay curves in $\Pthree$ of degree three and genus $g$ is connected. In contrast to $H(2,g)$, which is irreducible, $H(3,g)$ generally has many irreducible components (roughly ... More Oracles Are Subtle But Not MaliciousApr 12 2005Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not prevent us from ... More Quantum Lower Bound for Recursive Fourier SamplingSep 09 2002Dec 18 2004One of the earliest quantum algorithms was discovered by Bernstein and Vazirani, for a problem called Recursive Fourier Sampling. This paper shows that the Bernstein-Vazirani algorithm is not far from optimal. The moral is that the need to "uncompute" ... More How much can we learn about the physics of inflation?Mar 25 2014Mar 28 2014The recent BICEP2 measurement of B-modes in the polarization of the cosmic microwave background suggests that inflation was driven by a field at an energy scale of $2\times 10^{16}$ GeV. I explore the potential of upcoming CMB polarization experiments ... More UV Perturbations in Brane Gas CosmologyFeb 02 2004We consider the effect of the ultraviolet (UV) or short wavelength modes on the background of Brane Gas Cosmology. We find that the string matter sources are negligible in the UV and that the evolution is given primarily by the dilaton perturbation. We ... More SU(3) Ghosts with SpinJun 15 2007A new Lorentz-covariant gauge is presented for SU(3). In this gauge, both the ghosts and the gauge fields in the (4, 5, 6, 7) gauge directions acquire half-integral spin. As a result, the ghosts in these directions have the correct relationship between ... More Symmetry Breaking in BRST Quantization of SU(3)Jan 21 2007New BRST-invariant states for SU(3) gauge field theory are presented. The states have finite norms and unlike the states that are usually used to derive path integrals, they break SU(3) symmetry by choosing preferred gauge directions. This symmetry breaking ... More New Ghost States in SU(3) Gauge Field TheoryDec 26 2006The ghost sector of SU(3) gauge field theory is studied, and new BRST-invariant states are presented that do not have any analog in other SU(N) field theories. The new states come in either ghost doublets or triplets, and they appear exclusively in SU(3) ... More PT-Invariance and Indefinite MetricOct 27 2009A new proof is given for why the non-Hermitian, PT-Invariant cubic oscillator with imaginary coupling has real eigenvalues. The proof consists of two steps. In the first step, it is shown that for many PT-Invariant Hamiltonians, one can define corresponding ... More Viscosity at RHIC: Theory and PracticeSep 01 2008Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared ... More Formulating Viscous Hydrodynamics for Large Velocity GradientsNov 25 2007Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity g radients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, ... More The Long Slow Death of the HBT PuzzleDec 26 2008Femtoscopic measurements at RHIC have been hailed as a source of insight into the bulk properties of QCD matter. However, hydrodynamic models, which have been successful in reproducing other observables have failed to satisfactorily explain femtoscopic ... More Correlations and Fluctuations, A Summary of Quark Matter 2002Aug 06 2003Results for correlations and fluctuations presented at Quark Matter 2002 are summarized. These results include Hanbury-Brown Twiss interferometry of a wide variety of species, large scale fluctuations and correlations in $p_t$ and multiplicity, and charge ... More A selective version of Lin's TheoremAug 14 2018Aug 24 2018We prove a selective version of Lin's Theorem for nearly commuting operators. This is accomplished by establishing the tracial stability of a certain class of graph products of $C^*$-algebras. This result involves the development of the "pincushion class" ... More Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More CP-odd Phases in Slepton Pair ProductionMar 23 1998Mar 27 1998The effects of CP-odd supersymmetric phases on slepton pair production are considered. It is shown that CP-even observables in $e^+ e^-$ and $e^- e^-$ collisions, such as the total selectron cross section, can depend on CP-odd supersymmetric phases through ... More Graph products of completely positive mapsJun 22 2017Jul 06 2017We define the graph product of unital completely positive maps on a universal graph product of unital C*-algebras and show that it is unital completely positive itself. To accomplish this, we introduce the notion of the non-commutative length of a word, ... More Rank of Submatrices of the Pascal MatrixFeb 10 2017In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem. In this paper, ... More A note on Cauchy integrabilitySep 23 2014We show that for any bounded function $f:[a,b]\rightarrow{\mathbb R}$ and $\epsilon>0$ there is a partition $P$ of $[a,b]$ with respect to which the Riemann sum of $f$ using right endpoints is within $\epsilon$ of the upper Darboux sum of $f$. This leads ... More A family of critically finite maps with symmetryJul 03 2003May 17 2005The symmetric group S_n acts as a reflection group on CP^{n-2} (for $n\geq 3$) . Associated with each of the $\binom{n}{2}$ transpositions in S_n is an involution on CP^{n-2} that pointwise fixes a hyperplane--the mirrors of the action. For each such ... More The hole probability for Gaussian random SU(2) polynomialsOct 23 2006We show that for Gaussian random SU(2)polynomials of a large degree $N$ the probability that there are no zeros in the disk of radius $r$ is less than $e^{-c_{1,r} N^2}$, and is also greater than $e^{-c_{2,r} N^2}$. Enroute to this result, we also derive ... More Quasi-arithmeticity of lattices in PO(n,1)Dec 16 2014Jun 17 2015We show that the non-arithmetic lattices in PO(n,1) of Belolipetsky and Thomson (2011), obtained as fundamental groups of closed hyperbolic manifolds with short systole, are quasi-arithmetic in the sense of Vinberg, and, by contrast, the well-known non-arithmetic ... More Kergin Approximation in Banach SpacesOct 01 2008We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges. The braid group surjects onto $G_2$ tensor spaceJul 01 2009Let V be the 7-dimensional irreducible representation of the quantum group U_q(g_2). For each n, there is a map from the braid group B_n to the endomorphism algebra of the n-th tensor power of V, given by R-matrices. We can extend this linearly to a map ... More Slow modes in Keplerian disksNov 30 2000Low-mass disks orbiting a massive body can support "slow" normal modes, in which the eigenfrequency is much less than the orbital frequency. Slow modes are lopsided, i.e., the azimuthal wavenumber m=1. We investigate the properties of slow modes, using ... More Resonant relaxation in protoplanetary disksMay 27 1998Resonant relaxation is a novel form of two-body relaxation that arises in nearly Keplerian disks such as protoplanetary disks. Resonant relaxation does not affect the semimajor axes of the particles, but enhances relaxation of particle eccentricities ... More An Eccentric Disk Model for the Nucleus of M31Feb 13 1995The nucleus of M31 may be a thick eccentric disk, composed of stars traveling on nearly Keplerian orbits around a black hole or other dark compact object. This hypothesis reproduces most of the features seen in HST photometry of the center of M31; in ... More Quantum Copy-Protection and Quantum MoneyOct 24 2011Forty years ago, Wiesner proposed using quantum states to create money that is physically impossible to counterfeit, something that cannot be done in the classical world. However, Wiesner's scheme required a central bank to verify the money, and the question ... More A Linear-Optical Proof that the Permanent is #P-HardSep 08 2011One of the crown jewels of complexity theory is Valiant's 1979 theorem that computing the permanent of an n*n matrix is #P-hard. Here we show that, by using the model of linear-optical quantum computing---and in particular, a universality theorem due ... More BQP and the Polynomial HierarchyOct 25 2009The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to topics in circuit ... More Algorithms for Boolean Function Query PropertiesJul 05 2001We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,' and an O(N) ... More Query Complexity: Worst-Case Quantum Versus Average-Case ClassicalJan 19 2000Jun 23 2000In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded error using T queries ... More Multilinear Formulas and Skepticism of Quantum ComputingNov 07 2003Jul 15 2004Several researchers, including Leonid Levin, Gerard 't Hooft, and Stephen Wolfram, have argued that quantum mechanics will break down before the factoring of large numbers becomes possible. If this is true, then there should be a natural set of quantum ... More Quantum Certificate ComplexityOct 02 2002Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) ... More The thermodynamic evolution of the cosmological event horizonSep 26 2010Aug 01 2011By manipulating the integral expression for the proper radius $R_e$ of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe, we obtain an analytical expression for the change $\dd R_e$ in response to a uniform fluctuation ... More Holographic indeterminacy and neutron starsSep 20 2008Feb 16 2009The holographic indeterminacy resulting from the quantization of spacetime leads to an inherent uncertainty (lpL)1/2 in the relative positions of two events, separated by a distance L, in a direction transverse to a null ray connecting the events, where ... More Testing MOND with VirgoHI21Mar 04 2005Jan 27 2006The 'dark galaxy' VIRGOHI21 seems to be composed of an unusually high proportion of darkmatter and is situated in a strong external gravitational field. As such it offers a rare test for theories of modified dynamics. If the system is bound then its dynamics ... More Reevaluating the Cosmological Origin of Dark MatterDec 15 2009The origin of dark matter as a thermal relic offers a compelling way in which the early universe was initially populated by dark matter. Alternative explanations typically appear exotic compared to the simplicity of thermal production. However, recent ... More Stabilizing Moduli with String CosmologySep 27 2004Oct 03 2004In this talk I will discuss the role of finite temperature quantum corrections in string cosmology and show that they can lead to a stabilization mechanism for the volume moduli. I will show that from the higher dimensional perspective this results from ... More Thermal History of the Universe After InflationOct 19 2015When did the universe thermalize? In this talk I review the status of this issue and its importance in establishing the expected properties of dark matter, the growth of large-scale structure, and the viability of inflation models when confronted with ... More Effective Field Theory for Top and Weak Boson PhysicsMay 21 2012Effective field theory is the ideal framework for discussing top and weak boson properties. We discuss the application of this framework to top physics at both tree level and one loop. We consider weak boson pair production within an effective field theory ... More top2008 Conference SummaryJul 07 2008Jul 14 2008This is a summary of the talks presented at the International Workshop on Top Quark Physics (top2008) held in Elba, Italy, May 18-24, 2008. What does it mean to have `seen' the quark-gluon plasma?Oct 01 2012Identifying the quark-gluon plasma requires convincing experimental evidence that partons move independently throughout the environment created in a heavy ion collision and with densities expected from equilibrium considerations. In lattice calculations, ... More A Co-moving Coordinate System for Relativistic HydrodynamicsDec 03 2006The equations of relativistic hydrodynamics are transformed so that steps forward in time preserves local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to co-moving observers. ... More A Formula for the Jones-Wenzl ProjectionsMar 02 2015I present a method of calculating the coefficients appearing in the Jones-Wenzl projections in the Temperley-Lieb algebras. It essentially repeats the approach of Frenkel and Khovanov published in 1997. I wrote this note mid-2002, not knowing about their ... More Four self-dual integral forms of the moonshine moduleOct 02 2017Jun 14 2018We construct four self-dual integral forms of the moonshine vertex operator algebra, each of which has symmetries given by the Fischer-Griess monster simple group. The existence of these forms resolves the last remaining open assumption in the proof of ... More Holographic Vacuum EnergyOct 18 2000Apr 10 2002Gravitational holography is argued to render the cosmological constant stable against divergent quantum corrections. This provides a technically natural solution to the cosmological constant problem. Evidence for quantum stability of the cosmological ... More $k$-differentials on curves and rigid cycles in moduli spaceMay 08 2019For $g\geq2$, $j=1,\dots,g$ and $n\geq g+j$ we exhibit infinitely many new rigid and extremal effective codimension $j$ cycles in $\overline{\mathcal{M}}_{g,n}$ from the strata of quadratic differentials and projections of these strata under forgetful ... More Seiberg-Witten invariants, orbifolds, and circle actionsJul 12 2001The main result of this paper is a formula for calculating the Seiberg-Witten invariants of 4-manifolds with fixed-point free circle actions. This is done by showing under suitable conditions the existence of a diffeomorphism between the moduli space ... More Thermodynamic Volume of Kerr-bolt-AdS SpacetimeJun 05 2014Dec 02 2014In theories of gravity where the cosmological constant defines a thermodynamic variable, the pressure, it has been shown that solutions of Einstein's equations have a corresponding thermodynamic volume. In general, the expression for the volume is not ... More The Hopf monoid on nonnesting supercharacters of pattern groupsMay 21 2014Jul 15 2015We construct supercharacter theories for a collection of unipotent matrix groups and produce a Hopf monoid from the supercharacters. These supercharacter theories are coarser than those defined by Diaconis--Isaacs for algebra groups and have supercharacters ... More Minimal faces and Schur's Lemma for embeddings into R^UAug 29 2016In the context of N. Brown's Hom(N,R^U), we establish that given \pi: N \rightarrow R^U, the dimension of the minimal face containing [\pi] is one less than the dimension of the center of the relative commutant of \pi. We also show the "convex independence" ... More Maximal harmonic group actions on finite graphsJan 15 2013Mar 27 2015This paper studies groups of maximal size acting harmonically on a finite graph. Our main result states that these maximal graph groups are exactly the finite quotients of the modular group $\Gamma=\left<x,y \ | \ x^2=y^3=1\right>$ of size at least 6. ... More Integral Subschemes of Codimension TwoApr 15 1995In this paper we study the problem of describing the integral subschemes within a fixed even linkage class $\L$ of subschemes in $\Pn$ of codimension two. In the case that $\L$ is not the class of arithmetically Cohen-Macaulay subschemes, we associate ... More On non-compact Heegaard splittingsFeb 26 2006Apr 11 2006A Heegaard splitting of an open 3-manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The ... More Limitations of Quantum Advice and One-Way CommunicationFeb 15 2004Jun 21 2018Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only limited advantages ... More Calculating n-Point Charge Correlations in Evolving SystemsAug 02 2019In dynamic systems, charge susceptibilities and local charge correlations change with time. These changes are accompanied by non-local correlations which spread diffusively with time and are constrained by local charge conservation. Assuming the local ... More The Geometry of b^k ManifoldsApr 13 2013Jul 30 2013Let $Z$ be a hypersurface of a manifold $M$. The $b$-tangent bundle of $(M, Z)$, whose sections are vector fields tangent to $Z$, is used to study pseudodifferential operators and stable Poisson structures on $M$. In this paper we introduce the $b^k$-tangent ... More Discrete Polynomial BlendingFeb 26 2016In this paper we study "discrete polynomial blending," a term used to define a certain discretized version of curve blending whereby one approximates from the "sum of tensor product polynomial spaces" over certain grids. Our strategy is to combine the ... More Cosmic GlowsDec 02 1999This is the obligatory Cosmic Microwave Background review. I discuss the current status of CMB anisotropies, together with some points on the related topic of the Far-Infrared Background. We have already learned a number of important things from CMB anisotropies. ... More MAP and Planck vs the Real UniverseOct 21 1998The Microwave Anisotropy Probe (MAP) and Planck Surveyor satellites promise to provide accurate maps of the sky at a range of frequencies and angular scales, from which it will be possible to extract estimates for cosmological parameters. But the real ... More Eulerian cube complexes and reciprocitySep 26 2013Feb 25 2014Let $G$ be the fundamental group of a compact nonpositively curved cube complex $Y$. With respect to a basepoint $x$, one obtains an integer-valued length function on $G$ by counting the number of edges in a minimal length edge-path representing each ... More Beyond Thimbles: Sign-Optimized Manifolds for Finite DensityOct 15 2018Oct 16 2018The sign problem of relativistic field theories at finite fermion chemical potential has been approached by deforming the domain of integration into complex field space. We present a method for selecting a deformed manifold of integration which is a local ... More Genus Bounds for Harmonic Group Actions on Finite GraphsJun 02 2010Dec 13 2011This paper develops graph analogues of the genus bounds for the maximal size of an automorphism group of a compact Riemann surface of genus $g\ge 2$. Inspired by the work of M. Baker and S. Norine on harmonic morphisms between finite graphs, we motivate ... More An Information Structural Approach to Spoken Language GenerationJun 10 1996Jul 03 1996This paper presents an architecture for the generation of spoken monologues with contextually appropriate intonation. A two-tiered information structure representation is used in the high-level content planning and sentence planning stages of generation ... More Convex Sets Associated to C*-AlgebrasSep 02 2015Dec 01 2015For A a separable unital C*-algebra and M a separable McDuff II_1-factor, we show that the space Hom_w(A,M) of weak approximate unitary equivalence classes of unital *-homomorphisms A \rightarrow M may be considered as a closed, bounded, convex subset ... More Sobolev extensions of Lipschitz mappings into metric spacesAug 02 2016Aug 29 2016Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ ... More Canonical elements for collision orbitsDec 12 2000I derive a set of canonical elements that are useful for collision orbits (perihelion distance approaching zero at fixed semimajor axis). The coordinates are the mean anomaly and the two spherical polar angles at aphelion. Impossibility of Succinct Quantum Proofs for Collision-FreenessJan 02 2011We show that any quantum algorithm to decide whether a function f:[n]->[n] is a permutation or far from a permutation must make Omega(n^{1/3}/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a permutation. ... More