Results for "Sarah Sheldon"

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Demonstration of Open Quantum System Optimal Control in Dynamic Nuclear PolarizationJul 09 2015Jul 20 2015Dynamic nuclear polarization (DNP) is used in nuclear magnetic resonance (NMR) to transfer polarization from electron spins to nuclear spins. The resulting nuclear polarization enhancement can, in theory, be two or three orders of magnitude depending ... More
B-branes and the Derived CategoryFeb 06 2004By a direct CFT computation, the spectrum of the topological B-model is compared to Ext groups of sheaves. A match can only be made if abstract vector bundles on holomorphic submanifolds are twisted by the canonical $\mathrm{Spin}^c$ structure of its ... More
Rational Curves on Calabi-Yau ThreefoldsFeb 05 1992By considering mirror symmetry applied to conformal field theories corresponding to strings propagating in quintic hypersurfaces in projective 4-space, Candelas, de la Ossa, Green and Parkes calculated the ``number of rational curves on the hypersurface'' ... More
Rational curves on Calabi-Yau manifolds: verifying predictions of Mirror SymmetryJan 27 1993Feb 01 1993Mirror symmetry, a phenomenon in superstring theory, has recently been used to give tentative calculations of several numbers in algebraic geometry. In this paper, the numbers of lines and conics on various hypersurfaces which satisfy certain incidence ... More
Computing with Harmonic FunctionsNov 15 2015This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral ... More
Rational Curves on Calabi-Yau ThreefoldsFeb 05 1992The point is to compare the mathematical meaning of the ``number of rational curves on a Calabi-Yau threefold'' to the meaning ascribed to the same notion by string theorists.
Verifying Multipartite Entangled GHZ States via Multiple Quantum CoherencesMay 14 2019The ability to generate and verify multipartite entanglement is an important benchmark for near-term quantum devices devices. We develop a scalable entanglement metric based on multiple quantum coherences, and demonstrate experimentally on a 20-qubit ... More
Genus zero Gopakumar-Vafa invariants of contractible curvesJan 09 2006A version of the Donaldson-Thomas invariants of a Calabi-Yau threefold is proposed as a conjectural mathematical definition of the Gopakumar-Vafa invariants. These invariants have a local version, which is verified to satisfy the required properties for ... More
Computing with Harmonic FunctionsNov 15 2015Nov 07 2016This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral ... More
A Singularity in the First-order PY Equation for a Square Well FluidJul 17 2008It is shown that a nearest nieghbor Square Well (SW) potential leads to singular behavior in first order. A solution of the first-order perturbative PY equation for an attractive nearest neighbor square well of width less than the core diameter reveals ... More
Quantum spacetime without observers: ontological clarity and the conceptual foundations of quantum gravityFeb 05 1999We explore the possibility of a Bohmian approach to the problem of finding a quantum theory incorporating gravitational phenomena. The major conceptual problems of canonical quantum gravity are the problem of time and the problem of diffeomorphism invariant ... More
Points of order 13 on elliptic curvesAug 30 2016Sep 16 2016We pick up the study of 13-torsion in elliptic curves where Mazur and Tate left off 45 years ago. We consider various questions concerning elliptic curves defined over the maximal totally real subfield of the 13th cyclotomic field (where J_1(13) acquires ... More
Effects of P-wave Annihilation on the Angular Power Spectrum of Extragalactic Gamma-rays from Dark Matter AnnihilationJun 23 2011We present a formalism for estimating the angular power spectrum of extragalactic gamma-rays produced by dark matter annihilating with any general velocity-dependent cross section. The relevant density and velocity distribution of dark matter is modeled ... More
Procedure for systematically tuning up crosstalk in the cross resonance gateMar 15 2016We present improvements in both theoretical understanding and experimental implementation of the cross resonance (CR) gate that have led to shorter two-qubit gate times and interleaved randomized benchmarking fidelities exceeding 99%. The CR gate is an ... More
Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray DataSep 16 2008We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing ... More
Torsion groups of elliptic curves over quadratic fieldsMar 30 2011Apr 14 2016We describe methods to determine all the possible torsion groups of an elliptic curve that actually appear over a fixed quadratic field. We use these methods to find, for each group that can appear over a quadratic field, the field with the smallest absolute ... More
D-branes, open string vertex operators, and Ext groupsAug 14 2002Dec 29 2003In this paper we explicitly work out the precise relationship between Ext groups and massless modes of D-branes wrapped on complex submanifolds of Calabi-Yau manifolds. Specifically, we explicitly compute the boundary vertex operators for massless Ramond ... More
Matter From GeometryJun 14 1996We provide a local geometric description of how charged matter arises in type IIA, M-theory, or F-theory compactifications on Calabi-Yau manifolds. The basic idea is to deform a higher singularity into a lower one through Cartan deformations which vary ... More
Penrose Diagram for a Transient Black HoleMay 24 2010Jun 18 2010A Penrose diagram is constructed for a spatially coherent black hole that smoothly begins an accretion, then excretes symmetrically as measured by a distant observer, with the initial and final states described by a metric of Minkowski form. Coordinate ... More
$B_s$ Mixing via $ψK^*$Sep 12 1995The decay mode $B_s\to\psi \overline{K}^*$ is suggested as a very good way to measure the $B_s$ mixing parameter $x_s$. These decays can be gathered using a $\psi\to\ell^+\ell^-$ trigger. This final state has a well resolved four track decay vertex, useful ... More
On an extension of the universal monodromy representation for $\mathbb{P}^1\backslash\{0,1,\infty\}$Aug 24 2010Aug 08 2012The Chen series map giving the universal monodromy representation of $\mathbb{P}^1\backslash\{0,1,\infty\}$ is extended to an injective 1-cocycle of $PSL(2, \mathbb{Z})$ into power series with complex coefficients in two non-commuting variables, twisted ... More
Linearly Positive Histories: Probabilities for a Robust Family of Sequences of Quantum EventsMar 29 1994Mar 03 1995Nonnegative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories. The resulting {\it linearly positive histories} avoid the highly restrictive decoherence conditions and yet give the ... More
Evading the GZK Cosmic-Ray CutoffAug 27 1998Explanations of the origin of ultra-high energy cosmic rays are severely constrained by the Greisen-Zatsepin-Kuz'min effect, which limits their propagation over cosmological distances. We argue that possible departures from strict Lorentz invariance, ... More
Measurement of Galaxy Cluster Sizes, Radial Profiles, and Luminosity Functions from SDSS Photometric DataOct 20 2004Jul 20 2005Imaging data from the Sloan Digital Sky Survey is used to measure the empirical size-richness relation for a large sample of galaxy clusters. Using population subtraction methods, we determine the radius at which the cluster galaxy number density is 200/Omega_m ... More
The Neumann Problem on EllipsoidsNov 02 2016The Neumann problem on an ellipsoid in R^n asks for a function harmonic inside the ellipsoid whose normal derivative is some specified function on the ellipsoid. We solve this problem when the specified function on the ellipsoid is a normalized polynomial ... More
Characterizing errors on qubit operations via iterative randomized benchmarkingApr 24 2015With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of 99.95% with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between unitary and ... More
Validating quantum computers using randomized model circuitsNov 30 2018We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values as high as ... More
The Galaxy Content of SDSS Clusters and GroupsOct 22 2007Imaging data from the Sloan Digital Sky Survey are used to characterize the population of galaxies in groups and clusters detected with the MaxBCG algorithm. We investigate the dependence of Brightest Cluster Galaxy (BCG) luminosity, and the distributions ... More
AAO Observer - February 2011 EditionFeb 22 2011This edition of the Australian Astronomical Observatory Observer contains articles on the detection of the baryonic acoustic oscillation signal over a wide range of redshifts by the WiggleZ dark energy survey; results and future plans for the Galaxy And ... More
Efficient Z-Gates for Quantum ComputingDec 02 2016For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. Here we show that the phase of these drives can be used to generate zero-duration arbitrary Z-gates which, combined with two $X_{\pi/2}$ gates, can generate any SU(2) ... More
Characterization of hidden modes in networks of superconducting qubitsMar 13 2017Dec 05 2017We present a method for detecting electromagnetic (EM) modes that couple to a superconducting qubit in a circuit-QED architecture. Based on measurement-induced dephasing, this technique allows the measurement of modes that have a high quality factor (Q) ... More
The structure of correlation functions in single field inflationDec 03 2008Jan 03 2010Many statistics available to constrain non-Gaussianity from inflation are simplest to use under the assumption that the curvature correlation functions are hierarchical. That is, if the n-point function is proportional to the (n-1) power of the two-point ... More
Classification of pointed rank one Hopf algebrasMar 20 2007Feb 24 2008In this paper we classify the finite-dimensional pointed rank one Hopf algebras which are generated as algebras by the first element of the coradical filtration over a field of prime characteristic.
Oracle inequalities for the Lasso in the high-dimensional Aalen multiplicative intensity modelJun 25 2012Oct 14 2013In a general counting process setting, we consider the problem of obtaining a prognostic on the survival time adjusted on covariates in high-dimension. Towards this end, we construct an estimator of the whole conditional intensity. We estimate it by the ... More
Varieties for modules of finite dimensional Hopf algebrasDec 02 2016We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples such as finite ... More
Models of Quadratic Algebras Generated by Superintegrable Systems in 2DApr 05 2011In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and nondegenerate systems. ... More
Geometric Engineering of Quantum Field TheoriesSep 30 1996Oct 08 1996Using the recent advances in our understanding of non-perturbative aspects of type II strings we show how non-trivial exact results for $N=2$ quantum field theories can be reduced to T-dualities of string theory. This is done by constructing a local geometric ... More
B Meson DecaysFeb 21 2009Dec 03 2009We discuss the most important Physics thus far extracted from studies of B meson decays. Measurements of the four CP violating angles accessible in B decay are reviewed as well as direct CP violation. A detailed discussion of the measurements of the CKM ... More
Quantum Motion on Shape Space and the Gauge Dependent Emergence of Dynamics and Probability in Absolute Space and TimeAug 21 2018Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows one to straightforwardly ... More
Is the Hypothesis About a Low Entropy Initial State of the Universe Necessary for Explaining the Arrow of Time?Feb 09 2016Jul 06 2016According to statistical mechanics, micro-states of an isolated physical system (say, a gas in a box) at time $t_0$ in a given macro-state of less-than-maximal entropy typically evolve in such a way that the entropy at time $t$ increases with $|t-t_0|$ ... More
On the Weak Measurement of Velocity in Bohmian MechanicsAug 25 2008In a recent article (New Journal of Physics 9, 165, 2007), Wiseman has proposed the use of so-called weak measurements for the determination of the velocity of a quantum particle at a given position, and has shown that according to quantum mechanics the ... More
Quantum Equilibrium and the Origin of Absolute UncertaintyAug 06 2003The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr\"odinger's ... More
Quantum Equilibrium and the Role of Operators as Observables in Quantum TheoryAug 06 2003Aug 06 2003Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear ... More
Bohmian Mechanics and the Meaning of the Wave FunctionDec 29 1995We outline how Bohmian mechanics works: how it deals with various issues in the foundations of quantum mechanics and how it is related to the usual quantum formalism. We then turn to some objections to Bohmian mechanics, for example the fact that in Bohmian ... More
Generalized quiver varieties and triangulated categoriesMay 19 2014Jun 28 2016In this paper, we introduce generalized quiver varieties which include as special cases classical and cyclic quiver varieties. The geometry of generalized quiver varieties is governed by a finitely generated algebra P: the algebra P is self-injective ... More
AAO Observer - August 2011 EditionAug 24 2011This edition of the Australian Astronomical Observatory Observer contains articles on the commissioning of the new SAMI instrument giving the first hexabundle galaxy spectra; galaxy parameter variations across and through the 6dFGS Fundamental Plane; ... More
Asymptotic Growth of Associated Primes of Certain Graph IdealsApr 15 2012Dec 05 2012We specify a class of graphs, $H_t$, and characterize the irreducible decomposition of all powers of the cover ideals. This gives insight into the structure and stabilization of the corresponding associated primes; specifically, providing an answer to ... More
Racah Polynomials and Recoupling Schemes of $\mathfrak{su}(1,1)$Apr 14 2015Jul 23 2015The connection between the recoupling scheme of four copies of $\mathfrak{su}(1,1)$, the generic superintegrable system on the 3 sphere, and bivariate Racah polynomials is identified. The Racah polynomials are presented as connection coefficients between ... More
An Explicit Construction of Type A Demazure AtomsJul 28 2007Apr 02 2009Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Sch\"{u}tzenberger into standard bases. We prove that the resulting polynomials, which we call Demazure atoms, can be obtained from a certain specialization ... More
Odd Characterizations of Almost Simple Groups (PhD Thesis 2009)Sep 25 2012In this PhD thesis we discuss methods of recognizing finite groups by the structure of normalizers of certain 3-subgroups. We explain a method for characterizing groups using character theoretic and block theoretic methods and we use these methods to ... More
Update on Hidden Sectors with Dark Forces and Dark MatterNov 21 2012Recently there has been much interest in hidden sectors, especially in the context of dark matter and dark forces, since they are a common feature of beyond standard model scenarios like string theory and SUSY and additionally exhibit interesting phenomenological ... More
Naturally Occurring Genetic Variation Influences the Severity of Drosophila Eye Degeneration Induced by Expression of a Mutant Human Insulin GeneMar 02 2013Dominant negative mutations in the insulin gene are the second most common cause of permanent neonatal diabetes. However, variation in severity and penetrance of neonatal diabetes, as in other complex genetic diseases, cannot be accounted for by known ... More
On the polynomial Szemerédi's theorem in finite fieldsFeb 06 2018Let $P_1,\dots,P_m\in\mathbb{Z}[y]$ be any linearly independent polynomials with zero constant term. We show that there exists a $\gamma>0$ such that any subset of $\mathbb{F}_q$ of size at least $q^{1-\gamma}$ contains a nontrivial polynomial progression ... More
Landau Levels, Anisotropy and HolographyJun 13 2013We analyze properties of field theories dual to extremal black branes in (4+1) dimensions with anisotropic near-horizon geometries. Such gravity solutions were recently shown to fall into nine classes which align with the Bianchi classification of real ... More
A polygonal presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$Nov 13 2009In the first section of this article, we recall Keel's well-known presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$ using irreducible boundary divisors of $\overline{\mathfrak{M}}_{0,n}$ as generators, and describe a basis for $Pic(\overline{\mathfrak{M}}_{0,n})$ ... More
How many elements of a Coxeter group have a unique reduced expression?Jan 04 2017Jan 06 2017Let $(W,R)$ be an arbitrary Coxeter system. We determine the number of elements of $W$ that have a unique reduced expression.
The Symbolic Generic Initial System of Almost Linear Point Configurations in P2Apr 29 2013Consider an ideal I in K[x,y,z] corresponding to a point configuration in P2 where all but one of the points lies on a single line. In this paper we study the symbolic generic initial system obtained by taking the reverse lexicographic generic initial ... More
Ahab's Arithmetic; or, the mathematics of Moby-DickMar 28 2019Herman Melville's novel Moby-Dick contains a surprising number of mathematical allusions. In this article we explore some of these, as well as discussing the questions that naturally follow: why did Melville choose to use so much mathematical imagery? ... More
Moduli spaces of sheaves on K3 surfaces and Galois representationsOct 15 2018We consider two K3 surfaces defined over an arbitrary field, together with a smooth proper moduli space of stable sheaves on each. When the moduli spaces have the same dimension, we prove that if the \'etale cohomology groups (with Q_ell coefficients) ... More
The a-number of hyperelliptic curvesMar 10 2017Jun 26 2017It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve ... More
The Generic Initial Ideals of Powers of a 2-Complete IntersectionJun 25 2012Sep 30 2012We compute the reverse lexicographic generic initial ideals of the powers of a 2-complete intersection ideal I. In particular, we give six algorithms to compute these generic initial ideals, the choice of which depends on the power and on the relative ... More
The Asymptotics of Symbolic Generic Initial Systems of Six Points in P2Oct 31 2012Apr 30 2013Consider the ideal I in K[x,y,z] corresponding to six points of P2. We study the limiting behaviour of the symbolic generic initial system, of I obtained by taking the reverse lexicographic generic initial ideals of the symbolic powers of I. The main ... More
The Limiting Polytope of the Generic Initial System of a Complete IntersectionFeb 06 2012Consider a complete intersection I of type (d_1,..., d_r) in a polynomial ring over a field of characteristic 0. We study the graded system of ideals {gin(I^n)}_n obtained by taking the reverse lexicographic generic initial ideals of the powers of I and ... More
A Decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth AlgorithmApr 19 2006Apr 02 2009We exhibit a weight-preserving bijection between semi-standard Young tableaux and semi-skyline augmented fillings to provide a combinatorial proof that the Schur functions decompose into nonsymmetric functions indexed by compositions. The insertion procedure ... More
Very Special RelativityJan 27 2006By Very Special Relativity (VSR) we mean descriptions of nature whose space-time symmetries are certain proper subgroups of the Poincar\'e group. These subgroups contain space-time translations together with at least a 2-parameter subgroup of the Lorentz ... More
A Lorentz-Violating Origin of Neutrino Mass?May 03 2006We explore implications for neutrino physics of Very Special Relativity (VSR), wherein the symmetry group of nature includes only a 4-parameter subgroup of the Lorentz group. VSR can provide a natural origin to lepton-number conserving neutrino masses ... More
Extragalactic and galactic gamma-rays and neutrinos from annihilating dark matterOct 30 2011Nov 16 2011We describe cosmic gamma-ray and neutrino signals of dark matter annihilation, explaining how the complementarity of these signals provides additional information that, if observable, can enlighten the particle nature of dark matter. This is discussed ... More
Effects of Velocity-Dependent Dark Matter Annihilation on the Energy Spectrum of the Extragalactic Gamma-ray BackgroundSep 18 2010We calculate the effects of velocity-dependent dark matter annihilation cross sections on the intensity of the extragalactic gamma-ray background. Our formalism does not assume a locally thermal distribution of dark matter particles in phase space, and ... More
Revised Proof of the Uniqueness Theorem for 'No Collapse' Interpretations of Quantum MechanicsOct 22 1999We show that the Bub-Clifton uniqueness theorem for 'no collapse' interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the 'weak separability' assumption.
Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspaceFeb 03 2014The fact that macroscopic systems approach thermal equilibrium may seem puzzling, for example, because it may seem to conflict with the time-reversibility of the microscopic dynamics. We here prove that in a macroscopic quantum system for a typical choice ... More
The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspaceFeb 14 2014May 16 2014We study the problem of the approach to equilibrium in a macroscopic quantum system in an abstract setting. We prove that, for a typical choice of "nonequilibrium subspace", any initial state (from the energy shell) thermalizes, and in fact does so very ... More
On the time scales in the approach to equilibrium of macroscopic quantum systemsJul 02 2013Sep 05 2013We prove two theorems concerning the time evolution in general isolated quantum systems. The theorems are relevant to the issue of the time scale in the approach to equilibrium. The first theorem shows that there can be pathological situations in which ... More
Exotics: Heavy Pentaquarks and TetraquarksJun 02 2017Jul 27 2017For many decades after the invention of the quark model in 1964 there was no evidence that hadrons are formed from anything other than the simplest pairings of quarks and antiquarks, mesons being formed of a quark-antiquark pair and baryons from three ... More
The plasmoelectric effect: optically induced electrochemical potentials in resonant metallic structuresFeb 01 2012We describe a strategy for conversion of optical power into DC electrical power using resonant absorption in plasmonic nanostructures. A thermodynamic analysis of the underlying mechanism motivates our description of the phenomenon, which we term the ... More
Winning the Caucus Race: Continuous Leader Election via Public RandomnessJan 24 2018Feb 04 2018Consensus protocols inherently rely on the notion of leader election, in which one or a subset of participants are temporarily elected to authorize and announce the network's latest state. While leader election is a well studied problem, the rise of distributed ... More
Betting on Blockchain Consensus with FantometteMay 16 2018Aug 08 2018Blockchain-based consensus protocols present the opportunity to develop new protocols, due to their novel requirements of open participation and explicit incentivization of participants. To address the first requirement, it is necessary to consider the ... More
Absence of Chaos in Bohmian DynamicsJan 06 1999The Bohm motion for a particle moving on the line in a quantum state that is a superposition of n+1 energy eigenstates is quasiperiodic with n frequencies.
Quantum Integrals from Coalgebra StructureOct 16 2014Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus confirming the ... More
Background Subtraction via Fast Robust Matrix CompletionNov 03 2017Background subtraction is the primary task of the majority of video inspection systems. The most important part of the background subtraction which is common among different algorithms is background modeling. In this regard, our paper addresses the problem ... More
On the space of non-Gaussian fields with single-clock bispectraMay 23 2016Jul 20 2016We develop a mathematical construction of non-Gaussian fields whose bispectra satisfy the single-clock inflation consistency relation. At the same order that our basis for bispectra recovers the two simplest single clock templates, we also find a third ... More
Crystalline Scaling Geometries from Vortex LatticesJun 06 2013Jun 25 2013We study magnetic geometries with Lifshitz and/or hyperscaling violation exponents (both with a hard wall cutoff in the IR and a smooth black brane horizon) which have a complex scalar field which couples to the magnetic field. The complex scalar is unstable ... More
Akashi series of Selmer groupsMay 03 2010We study the Selmer group of an elliptic curve over an admissible p-adic Lie extension of a number field F . We give a formula for the Akashi series attached to this module, in terms of the corresponding objects for the cyclotomic Zp-extension and certain ... More
Learning joint intensity-depth sparse representationsJan 03 2012Sep 18 2013This paper presents a method for learning overcomplete dictionaries composed of two modalities that describe a 3D scene: image intensity and scene depth. We propose a novel Joint Basis Pursuit (JBP) algorithm that finds related sparse features in two ... More
Twisted Graded Hecke AlgebrasJun 08 2005We generalize graded Hecke algebras to include a twisting two-cocycle for the associated finite group. We give examples where the parameter spaces of the resulting twisted graded Hecke algebras are larger than that of the graded Hecke algebras. We prove ... More
The nonequivariant coherent-constructible correspondence and tiltingFeb 14 2014Mar 06 2014The coherent-constructible correspondence is a relationship between coherent sheaves on a toric variety X, and constructible sheaves on a real torus T. This was discovered by Bondal, and explored in the equivariant setting by Fang, Liu, Treumann and Zaslow. ... More
Generalised Euler characteristics of Selmer groupsApr 23 2004May 03 2010Let E be an elliptic curve defined over a number field F, and let p be a prime >= 5. In this paper we study the structure of the Selmer group of E over p-adic Lie extensions $F_\infty$ of F. In particular, under certain global and local conditions on ... More
A Note on the Hodge Structure of the Intersection of Coloring ComplexesAug 30 2010Let $G$ be a simple graph with $n$ vertices. The coloring complex $\Delta(G)$ was defined by Steingr\'{\i}msson, and the homology of $\Delta(G)$ was shown to be nonzero only in dimension $n-3$ by Jonsson. Hanlon recently showed that the Eulerian idempotents ... More
QSym over Sym has a stable basisMar 10 2010We prove that the subset of quasisymmetric polynomials conjectured by Bergeron and Reutenauer to be a basis for the coinvariant space of quasisymmetric polynomials is indeed a basis. This provides the first constructive proof of the Garsia-Wallach result ... More
Rewriting systems in sufficiently large Artin-Tits groupsNov 09 2015Jul 16 2016A conjecture of Dehornoy claims that, given a presentation of an Artin-Tits group, every word that represents the identity can be transformed into the trivial word using the braid relations, together with certain rules (between pairs of words that are ... More
Biautomatic structures in systolic Artin groupsJul 06 2018We examine the construction of Huang and Osajda that was used in their proof of the biautomaticity of Artin groups of almost large type. We describe a slightly simpler variant of that biautomatic structure, with explicit descriptions of a few small examples, ... More
Gromov-Witten Invariants via Algebraic GeometryOct 30 1995Nov 06 1995Calculations of the number of curves on a Calabi-Yau manifold via an instanton expansion do not always agree with what one would expect naively. It is explained how to account for continuous families of instantons via deformation theory and excess intersection ... More
Quantum Philosophy: The Flight from Reason in ScienceJan 10 1996This is a talk concerning the irrationality of prominent physicists with regard to the foundations of quantum mechanics, delivered at a conference on the irrationality of the postmodern attack on science by nonscientists.
A Mathematical Theory of Quantum Sheaf CohomologyOct 17 2011Nov 02 2011The purpose of this paper is to present a mathematical theory of the half-twisted $(0,2)$ gauged linear sigma model and its correlation functions that agrees with and extends results from physics. The theory is associated to a smooth projective toric ... More
Pentaquarks and Tetraquarks at LHCbSep 14 2015Exotic resonant structures found in $\Lambda^0_b$ and $\overline{B}^0$ decays into charmonium in the LHCb experiment are discussed. Examination of the $J/\psi p$ system in $\Lambda^0_b\to J/\psi K^- p$ decays shows two states each of which must be composed ... More
Versal deformations and superpotentials for rational curves in smooth threefoldsOct 30 2000The versal deformation space of a smooth rational curve in a smooth complex threefold is explicitly computed under certain hypotheses. Under an additional hypothesis, the versal deformation space is then shown to be the variety of critical points of a ... More
On an algebraic version of the Knizhnik-Zamolodchikov equationSep 28 2010A difference equation analogue of the Knizhnik-Zamolodchikov equation is exhibited by developing a theory of the generating function $H(z)$ of Hurwitz polyzeta functions to parallel that of the polylogarithms. By emulating the role of the KZ equation ... More
Probing dark energy with cluster counts and cosmic shear power spectra: including the full covarianceMay 02 2007Sep 22 2007(Abridged) Combining cosmic shear power spectra and cluster counts is powerful to improve cosmological parameter constraints and/or test inherent systematics. However they probe the same cosmic mass density field, if the two are drawn from the same survey ... More
Feeding your Inflaton: Non-Gaussian Signatures of Interaction StructureSep 14 2011Jan 09 2012Primordial non-Gaussianity is generated by interactions of the inflaton field, either self-interactions or couplings to other sectors. These two physically different mechanisms can lead to nearly indistinguishable bispectra of the equilateral type, but ... More
A Study of Dielectric Breakdown Along Insulators Surrounding Conductors in Liquid ArgonJun 12 2015Mar 05 2016High voltage breakdown in liquid argon is an important concern in the design of liquid argon time projection chambers, which are often used as neutrino and dark matter detectors. We have made systematic measurements of breakdown voltages in liquid argon ... More
A note on filled groupsDec 16 2015Dec 17 2015Let $G$ be a finite group and $S$ a subset of $G$. Then $S$ is {\em product-free} if $S \cap SS = \emptyset$, and $S$ {\em fills} $G$ if $G^{\ast} \subseteq S \cup SS$. A product-free set is locally maximal if it is not contained in a strictly larger ... More