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Period polynomials for Picard modular formsJul 10 2019Jul 11 2019The relations satisfied by period polynomials associated to modular forms yield a way to count dimensions of spaces of cusp forms. After showing how these relations arise from those on the mapping class group $PSL(2, \mathbb{Z})$ of the moduli space $\mathcal{M}_{0,4}$ ... More

Period polynomials for Picard modular formsJul 10 2019The relations satisfied by period polynomials associated to modular forms yield a way to count dimensions of spaces of cusp forms. After showing how these relations arise from those on the mapping class group $PSL(2, \mathbb{Z})$ of the moduli space $\mathcal{M}_{0,4}$ ... More

On a generalization of Chen's iterated integralsDec 29 2007Aug 24 2010Chen's iterated integrals may be generalized by interpolation of functions of the positive integer number of times which particular forms are iterated in integrals along specific paths, to certain complex values. These generalized iterated integrals satisfy ... 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

Pullback of parabolic bundles and covers of ${\mathbb P}^1\setminus\{0,1,\infty\}$Sep 18 2010We work over an algebraically closed ground field of characteristic zero. A $G$-cover of ${\mathbb P}^1$ ramified at three points allows one to assign to each finite dimensional representation $V$ of $G$ a vector bundle $\oplus \mathscr{O}(s_i)$ on ${\mathbb ... 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

On quadratic residue codes and hyperelliptic curvesSep 20 2006Feb 21 2008A long standing problem has been to develop "good" binary linear codes to be used for error-correction. This paper investigates in some detail an attack on this problem using a connection between quadratic residue codes and hyperelliptic curves. One question ... More

Notes on toric varietiesAug 08 2002These notes survey some basic results in toric varieties over a field with examples and applications. A computer algebra package (written by the second author) is described which deals with both affine and projective toric varieties in any number of dimensions ... More

On the variety of Borels in relative position $\vec{w}$Jan 31 2003Let $G$ be a connected semi-simple group defined over and algebraically closed field, $T$ a fixed Cartan, $B$ a fixed Borel containing $T$, $S$ a set of simple reflections associated to the simple positive roots corresponding to $(T,B)$, and let ${\cal ... More

Representations of finite groups on Riemann-Roch spacesOct 26 2002Apr 18 2004We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If $G$ is a finite subgroup of the automorphism group of a projective curve $X$ over an algebraically closed field and $D$ is a divisor on $X$ left stable ... More

Modular representations on some Riemann-Roch spaces of modular curves X(N)Feb 28 2005We compute the PSL(2,N)-module structure of the Riemann-Roch space L(D), where D is an invariant non-special divisor on the modular curve X(N), with N > 5 prime. This depends on a computation of the ramification module, which we give explicitly. These ... More

Automorphism groups of some AG codesDec 22 2004Feb 01 2005We show that in many cases, the automorphism group of a curve and the permutation automorphism group of a corresponding AG code are the same. This generalizes a result of Wesemeyer beyond the case of planar curves.

Dyson's Brownian-motion model for random matrix theory - revisited. With an Appendix by Don ZagierMar 22 2015We offer an alternative viewpoint on Dyson's original paper regarding the application of Brownian motion to random matrix theory (RMT). In particular we show how one may use the same approach in order to study the stochastic motion in the space of matrix ... More

Spectral statistics of Bernoulli matrix ensembles - a random walk approach (I)Jan 20 2015We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space of matrices ... More

On p-ary Bent Functions and Strongly Regular GraphsApr 19 2019Our main result is a generalized Dillon-type theorem, giving graph-theoretic conditions which guarantee that a $p$-ary function in an even number of variables is bent, for $p$ a prime number greater than 2. The key condition is that the component Cayley ... 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.

Bohmian Mechanics and Quantum InformationJul 14 2009Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, ... More

Bohmian Mechanics and the Quantum RevolutionDec 26 1995This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character ... 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

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

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

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.

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

The strong Bishop-Phelps-Bollobás propertyApr 06 2016In this paper we introduce the strong Bishop-Phelps-Bollob\'as property (sBPBp) for bounded linear operators between two Banach spaces $X$ and $Y$. This property is motivated by a Kim-Lee result which states, under our notation, that a Banach space $X$ ... 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.

Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefoldsAug 19 2004Aug 30 2004Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds are compared. In certain situations, the Donaldson-Thomas invariants are very easy to handle, sometimes easier than the other invariants. This point is illustrated ... More

Rational curves on Calabi-Yau threefoldsDec 16 1993Dec 30 1993This note is a survey of the enumerative geometry of rational curves on Calabi-Yau threefolds, based on a talk given by the author at the May 1991 Workshop on Mirror Symmetry at MSRI. An earlier version appeared in "Essays on Mirror Manifolds"; this version ... More

Arithmetically Cohen-Macaulay Curves cut out by QuadricsFeb 19 1992Mar 23 1992Addressing a question of M. Stillman, it had been shown by Ein, Eisenbud, and the author that in a projective space of dimension at most 5, every arithmetically Cohen-Macaulay curve which is cut out by quadrics scheme- theoretically also has its homogeneous ... More

Boltzmann's Approach to Statistical MechanicsMay 11 2001In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis, the essence ... More

Group representations on Riemann-Roch spaces of some Hurwitz curvesNov 17 2006Let q>1 denote an integer relatively prime to 2,3,7 and for which G=PSL(2,q) is a Hurwitz group for a smooth projective curve X defined over C. We compute the G-module structure of the Riemann-Roch space L(D), where D is an invariant divisor on X of positive ... 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

The probability distribution of spectral moments for the Gaussian beta-ensemblesOct 13 2015Dec 25 2015We derive the joint probability distribution of the first two spectral moments for the G$\beta$E random matrix ensembles in N dimensions for any N. This is achieved by making use of two complementary invariants of the domain in $\mathbb{R}^N$ where the ... More

Continued fractions and Parallel SQUFOFJan 11 2006In this partly expository paper, we discuss three results. (1) That the two-sided continued fraction of the normalized square root (an important part of the SQUFOF algorithm) has several very attractive properties - periodicity, a symmetry point corresponding ... More

Semiclassical approach to discrete symmetries in quantum chaosFeb 22 2012We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to irreducible ... More

GSE statistics without spinFeb 11 2013Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been one unifying ... More

A Question about Pic(X) as a G-moduleJul 02 2004Let G be a finite group acting faithfully on an irreducible non-singular projective curve defined over an algebraically closed field F. Does every G-invariant divisor class contain a G-invariant divisor? The answer depends only on G and not on the curve. ... More

Collaboration Versus CheatingDec 01 2018We outline how we detected programming plagiarism in an introductory online course for a master's of science in computer science program, how we achieved a statistically significant reduction in programming plagiarism by combining a clear explanation ... More

Automorphism Groups on Tropical Curves: Some Cohomology CalculationsJun 24 2010Oct 18 2010Let $X$ be an abstract tropical curve and let $G$ be a finite subgroup of the automorphism group of $X$. Let $D$ be a divisor on $X$ whose equivalence class is $G$-invariant. We address the following question: is there always a divisor $D'$ in the equivalence ... More

Isospectral discrete and quantum graphs with the same flip counts and nodal countsJan 16 2018The existence of non-isomorphic graphs which share the same Laplace spectrum (to be referred to as isospectral graphs) leads naturally to the following question: What additional information is required in order to resolve isospectral graphs? It was suggested ... More

Automorphism groups of generalized Reed-Solomon codesJan 25 2008We look at AG codes associated to the projective line, re-examining the problem of determining their automorphism groups (originally investigated by Duer in 1987 using combinatorial techniques) using recent methods from algebraic geometry. We (re)classify ... More

Playing with Neutrino MassesDec 25 2009Most of what is known about neutrino masses and mixings results from studies of oscillation phenomena. We focus on those neutrino properties that are not amenable to such studies: $\Sigma $, the sum of the absolute values of the neutrino masses; $m_\beta ... More

Beating the Standard ModelDec 21 1998This report, adapted from my talk at the 1998 Ettore Majorana Subnuclear School at Erice, proffers speculative explanations of the strong CP problem and the existence of cosmic rays beyond the GZK bound. It is based on works done with Sidney Coleman and ... More

Desperately Seeking SuperstringsApr 25 1986We provide a detailed analysis of the problems and prospects of superstring theory c. 1986, anticipating much of the progress of the decades to follow.

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

An Implementation of Bayesian Lensing Shear MeasurementMar 29 2014Dec 12 2014The Bayesian gravitational shear estimation algorithm developed by Bernstein and Armstrong (2014) can potentially be used to overcome multiplicative noise bias and recover shear using very low signal-to-noise ratio (S/N) galaxy images. In that work the ... More

Charm Mixing and Rare DecaysDec 07 1999Dec 09 1999There has been significant recent experimental activity on the related topics of charm mixing and rare (flavor changing neutral current) decay. For mixing, several new results from direct (wrong sign) searches and first results from lifetime difference ... 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

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

Divide and Couple: Using Monte Carlo Variational Objectives for Posterior ApproximationJun 24 2019Recent work in variational inference (VI) uses ideas from Monte Carlo estimation to tighten the lower bounds on the log-likelihood that are used as objectives. However, there is no systematic understanding of how optimizing different objectives relates ... More

Geometric Engineering of N=1 Quantum Field TheoriesNov 12 1996We construct local geometric model in terms of F- and M-theory compactification on Calabi-Yau fourfolds which lead to N=1 Yang-Mills theory in d=4 and its reduction on a circle to d=3. We compute the superpotential in d=3, as a function of radius, which ... 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

Neutrinos and Their Charged Cousins: Are They Secret Sharers?Jun 16 2011Masses and mixings of quarks and leptons differ wildly from one another. Thus it is all the more challenging to search for some hidden attribute that they may share.

A Sinister Extension of the Standard Model to SU(3)XSU(2)XSU(2)XU(1)Apr 29 2005This paper describes work done in collaboration with Andy Cohen. In our model, ordinary fermions are accompanied by an equal number `terafermions.' These particles are linked to ordinary quarks and leptons by an unconventional CP' operation, whose soft ... More

Neutrinos with Seesaw Masses and Suppressed InteractionsJan 28 2003Mixing between light and heavy neutrino states has been proposed as an explanation (or partial explanation) for the 3-sigma NuTeV anomaly and the 2-sigma departure of the $Z^0$ invisible width from its expected value. I assume herein that neutrino masses ... More

First Passage Time of Skew Brownian MotionAug 18 2010Mar 07 2011Nearly fifty years after the introduction of skew Brownian motion by It\^o and McKean (1963), the first passage time distribution remains unknown. In this paper, we generalize results of Pitman and Yor (2001) and Cs\'aki and Hu (2004) to derive formulae ... More

Compact Operators via the Berezin TransformJul 27 1998In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This result is new even ... More

Correct interpretation of trace normalized density matrices as ensemblesJun 25 1996May 03 1997A density operator, $\rho = {P}_{\alpha } |\alpha > <\alpha | + {P}_{\beta } |\beta > <\beta |$, with ${P}_{\alpha }$ and ${P}_{\beta }$ linearly independent normalized wave functions, must be traced normalized, so ${P}_{\beta } = 1 - {P}_{\alpha }$. ... More

A Neutrino Mass Matrix with Vanishing $μ$--$μ$ and $τ$--$τ$ EntriesOct 19 2007We revisit our earlier proposal for the form of the neutrino mass matrix: a two-zero ansatz wherein the CP-violating PMNS phase $\delta$ plays a surprisingly important role. We review its observable consequences and show how our ansatz follows from a ... More

Particle Physics in The United States, A Personal ViewMay 23 2013I present my views on the future of America's program in particle physics. I discuss a variety of experimental initiatives that do have the potential to make transformative impacts on our discipline and should be included in our program, as well as others ... More

Opposite Arrows of Time Can Reconcile Relativity and NonlocalityMay 09 2001Jan 15 2003We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this ... More

Fusion product of co-adjoint orbitsDec 28 1998The result contained in this paper is an application of a fixed point formula associated with Hamiltonian loop group action. We obtain a G-space which is a geometric dual of the Verlinde's fusion product. Also we obtain a proof of Verlinde formula. The ... More

Explorations of edge-weighted Cayley graphs and p-ary bent functionsJun 04 2014Let f be a function mapping an n dimensional vector space over GF(p) to GF(p). When p is 2, Bernasconi et al. have shown that there is a correspondence between certain properties of f (e.g., if it is bent) and properties of its associated Cayley graph. ... More

Deformed Quantum Cohomology and (0,2) Mirror SymmetryOct 12 2007Sep 03 2010We compute instanton corrections to correlators in the genus-zero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P1xP1, whose left-moving fermions couple to a deformation of the tangent bundle. We then deduce ... More

Diagnosing the Trouble With Quantum MechanicsApr 10 2018We discuss an article by Steven Weinberg expressing his discontent with the usual ways to understand quantum mechanics. We examine the two solutions that he considers and criticizes and propose another one, which he does not discuss, the pilot wave theory ... More

On quantum potential dynamicsDec 06 2013Nov 05 2014Non-relativistic de Broglie-Bohm theory describes particles moving under the guidance of the wave function. In de Broglie's original formulation, the particle dynamics is given by a first-order differential equation. In Bohm's reformulation, it is given ... More

Reality and the Role of the Wavefunction in Quantum TheoryJan 24 2011The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely ... More

The Berezin Transform on the Toeplitz AlgebraDec 28 2002This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.

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

Consistently Estimating Markov Chains with Noisy Aggregate DataApr 14 2016We address the problem of estimating the parameters of a time-homogeneous Markov chain given only noisy, aggregate data. This arises when a population of individuals behave independently according to a Markov chain, but individual sample paths cannot ... More

Atmospheric Neutrino Constraints on Lorentz ViolationJul 07 2004Sensitive tests of Lorentz invariance can emerge from the study of neutrino oscillations, particularly for atmospheric neutrinos where the effect is conveniently near-maximal and has been observed over a wide range of energies. We assume these oscillations ... More

A simple Solution to the Strong CP ProblemOct 14 2001We propose a minimal modification of the standard model, remarkable in its simplicity, which may solve the strong CP problem. It employs three Higgs doublets with interactions taken to be invariant under a flavor symmetry. Both CP and the flavor symmetry ... More

Strangeness Violating Dibaryon DecayJul 23 2010Non-standard physics may induce detectable flavor-changing $\Delta B=2$ interactions without inducing their flavor-conserving counterparts. Searches for $n$-$\overline n$ oscillations do not constrain such interactions, thereby motivating dedicated searches ... More

Fact and Fancy in Neutrino Physics IIJun 11 2003This brief and opinionated essay evolved from my closing talk at the Tenth International Workshop on Neutrino Telescopes, held in Venice in March 2003. Portions were inspired by several excellent presentations at the Workshop. Other scattered comments ... More

Cosmological Searches for Photon Velocity OscillationsMar 17 1998We posit a second massless photon, uncoupled to known forms of matter but undergoing Lorentz non-invariant velocity mixing with ordinary photons. Our speculation within a speculation suffers from the sin of implausibility but enjoys the virtue of verifiability. ... 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

Angular Power Spectra with Finite CountsOct 24 2014Angular anisotropy techniques for cosmic diffuse radiation maps are powerful probes, even for quite small data sets. A popular observable is the angular power spectrum; we present a detailed study applicable to any unbinned source skymap S(n) from which ... 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

Fixed point formula and loop group actionsDec 28 1998The main goal of this paper is to obtain a formula for the T-equivariant Riemann-Roch number of certain G-spaces which are the finite dimensional models of certain infinite dimensional spaces with Hamiltonian LG-actions, here T is a maximal torus of the ... More

Finite pseudo orbit expansions for spectral quantities of quantum graphsMay 18 2012Jul 06 2012We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or equal to the ... More

Toric codes over finite fieldsAug 21 2002Jul 30 2003In this note, a class of error-correcting codes is associated to a toric variety associated to a fan defined over a finite field $\fff_q$, analogous to the class of Goppa codes associated to a curve. For such a ``toric code'' satisfying certain additional ... More

Quotients of finite-dimensional operators by symmetry representationsNov 02 2017Sep 25 2018A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen representation ... More

A primer on computational group homology and cohomologyJun 04 2007Jun 10 2009These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You should know the ... More

Terrestrial Neutrino Oscillations IllustratedJul 13 1999Observations of atmospheric neutrinos offer compelling evidence that neutrinos have mass and do oscillate. Preliminary data are compatible with maximal $\nu_\mu$--$\nu_\tau$ mixing, but not with pure $\nu_\mu$--$\nu_e$ mixing. In a general three-family ... 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

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

Hamming Approximation of NP WitnessesAug 01 2012Jul 19 2013Given a satisfiable 3-SAT formula, how hard is it to find an assignment to the variables that has Hamming distance at most n/2 to a satisfying assignment? More generally, consider any polynomial-time verifier for any NP-complete language. A d(n)-Hamming-approximation ... More

A Planetary Mass and Stellar Radius Relationship for Exoplanets Orbiting Red GiantsSep 24 2018A scatter plot of exoplanet mass against red giant host star radius demonstrates an interesting positive trend: larger stars have more massive planets. This implies that the evolution of a star towards a red giant affects the masses of planets in the ... More

Computation of Superpotentials for D-BranesDec 18 2004We present a general method for the computation of tree-level superpotentials for the world-volume theory of B-type D-branes. This includes quiver gauge theories in the case that the D-brane is marginally stable. The technique involves analyzing the A-infinity ... More

Soft Superweak CP Violation and the Strong CP PuzzleJul 16 1998Feb 12 1999We discuss a class of models in which CP is violated softly in a heavy sector adjoined to the standard model. Heavy-sector loops produce the observed CP violation in kaon physics, yielding a tiny and probably undetectable value for $\epsilon^\prime$. ... More

Gorenstein Threefold Singularities with Small Resolutions via Invariant Theory for Weyl GroupsFeb 05 1992We classify simple flops on smooth threefolds, or equivalently, Gorenstein threefold singularities with irreducible small resolution. There are only six families of such singularities, distinguished by Koll{\'a}r's {\em length} invariant. The method is ... More

Cosmic Ray and Neutrino Tests of Special RelativityMar 05 1997Apr 30 1997Searches for anisotropies due to Earth's motion relative to a preferred frame -- modern versions of the Michelson-Morley experiment -- provide precise verifications of special relativity. We describe other tests, independent of this motion, that are or ... More

High-Energy Tests of Lorentz InvarianceDec 17 1998Jan 20 1999We develop a perturbative framework with which to discuss departures from exact Lorentz invariance and explore their potentially observable ramifications. Tiny non-invariant terms introduced into the standard model Lagrangian are assumed to be renormalizable ... More

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

Decays of a Leptophobic Gauge BosonJul 01 1996We discuss the theory and phenomenology of decays of a leptophobic $U(1)_\X$ gauge boson $X$, such as has been proposed to explain the alleged deviations of $R_b$ and $R_c$ from standard model predictions. If the scalars involved in the breaking of the ... More