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Disordered Locality as an Explanation for the Dark EnergyMar 30 2009Sep 04 2009We discuss a novel explanation of the dark energy as a manifestation of macroscopic non-locality coming from quantum gravity, as proposed by Markopoulou. It has been previously suggested that in a transition from an early quantum geometric phase of the ... More

Relaxion: A Landscape Without AnthropicsJul 31 2017Dec 15 2017The relaxion mechanism provides a potentially elegant solution to the hierarchy problem without resorting to anthropic or other fine-tuning arguments. This mechanism introduces an axion-like field, dubbed the relaxion, whose expectation value determines ... More

Macroscopic Objects in Theories with Energy-dependent Speeds of LightNov 12 2008Aug 06 2009Energy-dependent speeds of light have been considered an observable signature of quantum gravity effects. The two simplest dispersion relationships produce either linear or quadratic corrections, in particle energy, to the photon speed. The macroscopic ... More

Preheating after Multifield Inflation with Nonminimal Couplings, I: Covariant Formalism and Attractor BehaviorOct 29 2015We study the preheating phase for multifield models of inflation involving nonminimal couplings. The strong single-field attractor behavior during inflation in these models generically persists after the end of inflation, thereby avoiding the "de-phasing" ... More

Stellar Black Holes and the Origin of Cosmic AccelerationMay 22 2009Jul 25 2009The discovery of cosmic acceleration has presented a unique challenge for cosmologists. As observational cosmology forges ahead, theorists have struggled to make sense of a standard model that requires extreme fine tuning. This challenge is known as the ... More

Preheating after multifield inflation with nonminimal couplings, III: Dynamical spacetime resultsOct 27 2016Jan 27 2018This paper concludes our semi-analytic study of preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. Using the covariant framework of paper I in this series, we extend the rigid-spacetime results of paper ... More

Building an Inclusive AAS - The Critical Role of Diversity and Inclusion Training for AAS Council and Astronomy LeadershipOct 05 2016Diversity, equity and inclusion are the science leadership issues of our time. As our nation and the field of astronomy grow more diverse, we find ourselves in a position of enormous potential and opportunity: a multitude of studies show how groups of ... More

Preheating after multifield inflation with nonminimal couplings, III: Dynamical spacetime resultsOct 27 2016This paper concludes our semi-analytic study of preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. Using the covariant framework of Ref. [1], we extend the rigid-spacetime results of Ref. [2] by considering ... More

Preheating after multifield inflation with nonminimal couplings, II: Resonance StructureOct 27 2016Jan 27 2018This is the second in a series of papers on preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. In this paper, we work in the rigid-spacetime approximation and consider field trajectories within the single-field ... More

Preheating after Multifield Inflation with Nonminimal Couplings, I: Covariant Formalism and Attractor BehaviorOct 29 2015Jan 27 2018This is the first of a three-part series of papers, in which we study the preheating phase for multifield models of inflation involving nonminimal couplings. In this paper, we study the single-field attractor behavior that these models exhibit during ... More

Preheating after multifield inflation with nonminimal couplings, II: Resonance StructureOct 27 2016This is the second in a series of papers on preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. In this paper, we work in the rigid-spacetime approximation and consider field trajectories within the single-field ... More

Looking Under a Better Lamppost: MeV-scale Dark Matter CandidatesMar 14 2019The era of precision cosmology has revealed that about 85% of the matter in the universe is dark matter. Two well-motivated candidates are weakly interacting massive particles (WIMPs) and weakly interacting sub-eV particles (WISPs) (e.g. axions). Both ... More

Using Dark Matter Haloes to Learn about Cosmic Acceleration: A New Proposal for a Universal Mass FunctionOct 26 2010Structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit {\black or overpredict} the development of observed large-scale structures. Traditional approaches to studies of structure ... More

Probing the Fundamental Nature of Dark Matter with the Large Synoptic Survey TelescopeFeb 04 2019Apr 24 2019Astrophysical and cosmological observations currently provide the only robust, empirical measurements of dark matter. Future observations with Large Synoptic Survey Telescope (LSST) will provide necessary guidance for the experimental dark matter program. ... More

Gravitational probes of ultra-light axionsApr 18 2019The axion is a hypothetical, well-motivated dark-matter particle whose existence would explain the lack of charge-parity violation in the strong interaction. In addition to this original motivation, an `axiverse' of ultra-light axions (ULAs) with masses ... More

An Extension of the Faddeev-Jackiw Technique to Fields in Curved SpacetimesApr 01 2014Mar 20 2015The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev-Jackiw technique, which offers an alternative to that of Dirac, is a symplectic approach to calculating ... More

Dense matter with eXTPDec 10 2018In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. ... More

Q criterion for disc stability modified by external tidal fieldAug 08 2013The standard Q criterion (with Q > 1) describes the local stability of a disc supported by rotation and random motion. Most astrophysical discs, however, are under the influence of an external gravitational field which can affect their stability. A typical ... More

Jeans instability criterion modified by external tidal fieldJun 19 2013The well-known Jeans criterion describes the onset of instabilities in an infinite, homogeneous, self-gravitating medium supported by pressure. Most realistic astrophysical systems, however, are not isolated - instead they are under the influence of an ... More

Pattern Speed of Lopsidedness in Galactic DisksDec 03 2008The disks of spiral galaxies commonly show a lopsided mass distribution, with a typical fractional amplitude of 10 % for the Fourier component m=1. This is seen in both stars and gas, and the amplitude is higher by a factor of two for galaxies in a group. ... More

Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2Mar 29 2017Feb 13 2018We have studied optical metrics via null geodesics and optical-mechanical formulation of classical mechanics, and described the geometry and optics of mechanical systems with drag dependent quadratically on velocity. Then we studied null geodesics as ... More

Vertical distribution of stars and gas in a galactic diskAug 31 2005We study the vertical density distribution of stars and gas (HI and H_2) in a galactic disk which is embedded in a dark matter halo. The new feature of this work is the inclusion of gas, and the gravitational coupling between stars and gas, which has ... More

Large-Scale Asymmetry of Rotation Curves in Lopsided Spiral GalaxiesJul 02 2002Many spiral galaxies show a large-scale asymmetry with a cos\phi dependence in their rotation curves as well as in their morphology, such as M101 and NGC 628. We show that both these features can be explained by the response of a galactic disk to an imposed ... More

Delineating incoherent non-Markovian dynamics using quantum coherenceMay 21 2015We introduce a method of characterization of non-Markovianity using coherence of a system interacting with the environment. We show that under the allowed incoherent operations, monotonicity of a valid coherence measure is affected due to non-Markovian ... More

STROBE-X: X-ray Timing and Spectroscopy on Dynamical Timescales from Microseconds to YearsMar 07 2019Mar 08 2019We present the Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X), a probe-class mission concept selected for study by NASA. It combines huge collecting area, high throughput, broad energy coverage, and excellent spectral ... More

A Data-driven Approach for Human Pose Tracking Based on Spatio-temporal Pictorial StructureJul 31 2016In this paper, we present a data-driven approach for human pose tracking in video data. We formulate the human pose tracking problem as a discrete optimization problem based on spatio-temporal pictorial structure model and solve this problem in a greedy ... More

Geometrical Formulation of Relativistic MechanicsJun 06 2017Nov 24 2017The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation, and relativistic ... More

Suppression of gravitational instabilities by dominant dark matter halo in low surface brightness galaxiesJan 07 2014The low surface brightness galaxies are gas-rich and yet have a low star formation rate, this is a well-known puzzle. The spiral features in these galaxies are weak and difficult to trace, although this aspect has not been studied much. These galaxies ... More

Spiral-like Light Profiles but Elliptical-like Kinematics in Mergers of GalaxiesOct 07 2002It is commonly accepted that a merger of two spiral galaxies results in a remnant with an elliptical-like surface-brightness profile. Surprisingly, our recent study (Chitre & Jog 2002) of the 2MASS data for twenty-seven advanced mergers of galaxies has ... More

Luminosity profiles of advanced mergers of galaxies using 2MASS dataJun 06 2002A sample of 27 disturbed galaxies that show signs of interaction but have a single nucleus were selected from the Arp and the Arp-Madore catalogues. For these, the K_s band images from the Two Micron All Sky Survey (2MASS) are analysed to obtain their ... More

Effect of finite disk-thickness on swing amplification of non-axisymmetric perturbations in a sheared galactic diskJun 05 2018A typical galactic disk is observed to have a finite thickness. Here, we present the study of the physical effect of introduction of finite thickness on the generation of small-scale spiral arms by swing amplification in a differentially rotating galactic ... More

Self-consistent response of a galactic disc to vertical perturbationsJan 08 2006We study the self-consistent, linear response of a galactic disc to vertical perturbations as induced say by a tidal interaction. We calculate the self-gravitational potential corresponding to a non-axisymmetric, self-consistent density response of the ... More

On the generation of asymmetric warps in disk galaxiesOct 28 2005The warps in many spiral galaxies are now known to asymmetric. Recent sensitive observations have revealed that asymmetry of warps may be the norm rather than exception. However there exists no generic mechanism to generate these asymmetries in warps. ... More

Flaring stellar disk in low surface brightness galaxy UGC 7321May 07 2019We study the vertical structure of an edge-on low surface brightness galaxy UGC 7321 theoretically, which is one of the few well-observed LSBs. We model it as a gravitationally coupled disk system of stars and atomic hydrogen gas in the potential of the ... More

Lopsidedness and Sloshing in Centres of Advanced Mergers of GalaxiesAug 27 2007We measure the non-axisymmetry in the luminosity distribution in the central few kpc of a sample of advanced mergers of galaxies, by analyzing their 2MASS images. All mergers show a high central asymmetry: the centres of isophotes show a striking sloshing ... More

Dwarf irregular galaxies with extended HI gas disks: Suppression of small-scale spiral structure by dark matter haloMar 06 2018Dwarf irregular galaxies with extended HI disk distributions, such as DDO 154, allow measurement of rotation curves, hence deduction of dark matter halo properties to large radial distances, up to several times the optical radius. These galaxies contain ... More

Why are some galaxy disks extremely thin?Oct 31 2012Some low surface brightness galaxies are known to have extremely thin stellar disks with the vertical to planar axes ratio 0.1 or less, often referred to as superthin disks. Although their existence is known for over three decades, the physical origin ... More

Prospects for Pulsar Studies at MeV EnergiesMar 29 2019Enabled by the Fermi Large Area Telescope, we now know young and recycled pulsars fill the gamma-ray sky, and we are beginning to understand their emission mechanism and their distribution throughout the Galaxy. However, key questions remain: Is there ... More

Lopsided Spiral GalaxiesNov 07 2008The light distribution in the disks of many galaxies is non-axisymmetric or `lopsided' with a spatial extent much larger along one half of a galaxy than the other, as in M101. Recent near-IR observations show that lopsidedness is common. The stellar disks ... More

Tidally Compressed Gas in Centers of Early Type and Ultraluminous GalaxiesJul 13 1999In this paper we propose that the compressive tidal field in the centers of flat-core early type galaxies and ultraluminous galaxies compresses molecular clouds producing dense gas obseved in the centers of these galaxies. The effect of galactic tidal ... More

Progressively more prolate dark matter halo in the outer Galaxy as traced by flaring HI gasMar 30 2011A galactic disk in a spiral galaxy is generally believed to be embedded in an extended dark matter halo, which dominates its dynamics in the outer parts. However, the shape of the halo is not clearly understood. Here we show that the dark matter halo ... More

The Flattened Dark Matter Halo of M31 as Deduced from the Observed HI Scale HeightsJun 23 2008In this paper, we use the outer-galactic HI scale height data as well as the observed rotation curve as constraints to determine the halo density distribution of the Andromeda galaxy (M31). We model the galaxy as a gravitationally-coupled system of stars ... More

Angular momentum transport and evolution of lopsided galaxiesJul 12 2014The surface brightness distribution in the majority of stellar galactic discs falls off exponentially. Often what lies beyond such a stellar disc is the neutral hydrogen gas whose distribution also follows a nearly exponential profile at least for a number ... More

The origin of steep vertical stellar distribution in the Galactic diskMar 08 2007Over the past two decades observations have revealed that the vertical density distribution of stars in galaxies near the mid-plane is substantially steeper than the sech^2 function that is expected from an isothermal approximation. However, the physical ... More

Do Dark Matter Axions Form a Condensate with Long-Range Correlation?Dec 18 2014Nov 11 2015Recently there has been significant interest in the claim that dark matter axions gravitationally thermalize and form a Bose-Einstein condensate with cosmologically long-range correlation. This has potential consequences for galactic scale observations. ... More

The Mythical Snake which Swallows its Tail: Einstein's matter worldSep 25 2013Sep 26 2013In 1917 Einstein introduced into his field equations a cosmological term having the cosmological constant as a coefficient, in order that the theory should yield a static universe. Einstein desired to eliminate absolute space from physics according to ... More

Einstein the Stubborn: Correspondence between Einstein and Levi-CivitaFeb 20 2012Before developing his 1915 General Theory of Relativity, Einstein held the "Entwurf" theory. Tullio Levi-Civita from Padua, one of the founders of tensor calculus, objected to a major problematic element in this theory, which reflected its global problem: ... More

Einstein's 1912-1913 struggles with Gravitation Theory: Importance of Static Gravitational Fields TheoryFeb 13 2012In December 1911, Max Abraham published a paper on gravitation at the basis of which was Albert Einstein's 1911 June conclusion about a relationship between the velocity of light and the gravitational potential. In February 1912, Einstein published his ... More

N-Black Hole Stationary and Axially Symmetric Solutions of the Einstein-Maxwell EquationsDec 12 1994Aug 02 2004The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities phi: R^3\Sigma -> H^2_C, where Sigma is a subset of the axis of symmetry, and H^2_C is the complex hyperbolic plane. Motivated ... More

Two-body problem in general relativity: A heuristic guide for the Einstein-Rosen bridge and EPR paradoxNov 18 2015Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was ... More

The 1905 Relativity Paper and the "Light Quantum"Jul 08 2013In 1905 the well-known physicist Max Planck was coeditor of the Annalen der Physik, and he accepted Einstein's paper on light quanta for publication, even though he disliked the idea of "light quanta". Einstein's relativity paper was received by the Annalen ... More

Did Poincaré explore the inertial mass-energy equivalence?Apr 30 2012Einstein was the first to explore the inertial mass-energy equivalence. In 1905 Einstein showed that a change in energy is associated with a change in inertial mass equal to the change in energy divided by c2. In 1900 Poincar\'e considered a device creating ... More

$\text{Gal}(\overline{\mathbf{Q}}_p/\mathbf{Q}_p)$ as a geometric fundamental groupApr 28 2014Let $p$ be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that the absolute Galois group of $\mathbf{Q}_p$ is the \'etale fundamental group of a certain object $Z$ which is defined over an algebraically ... More

Information Complexity and the Quest for Interactive Compression (A Survey)Apr 26 2015Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open problems in ... More

Strange Bedfellows: Quantum Mechanics and Data MiningNov 03 2009Last year, in 2008, I gave a talk titled {\it Quantum Calisthenics}. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding ... More

Adaptive Perturbation Theory: Quantum Mechanics and Field TheoryOct 18 2005Jan 04 2006Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that ... More

Moving Mirrors, Black Holes, Hawking Radiation and All ThatNov 09 2001In this talk I show how to canonically quantize a massless scalar field in the background of a Schwarzschild black hole in Lema\^itre coordinates and then present a simplified derivation of Hawking radiation based upon this procedure. The key result of ... More

Massive Degeneracy and Goldstone Bosons: A Challenge for the Light ConeNov 09 2010Wherein it is argued that the light front formalism has problems dealing with Goldstone symmetries. It is further argued that the notion that in hadron condensates can explain Goldstone phenomena is false.

Quarks, Gluons and Frustrated AntiferromagnetsOct 01 1999The Contractor Renormalization Group method (CORE) is used to establish the equivalence of various Hamiltonian free fermion theories and a class of generalized frustrated antiferromagnets. In particular, after a detailed discussion of a simple example, ... More

Almost invariant submanifolds for compact group actionsAug 25 1999Sep 13 1999We define a C^1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C^1-close to N. The proof involves ... More

The Integration Problem for Complex Lie AlgebroidsJan 31 2006A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic ... More

Good reduction of affinoids on the Lubin-Tate towerJan 19 2010Dec 14 2010We analyze the geometry of the tower of Lubin-Tate deformation spaces, which parametrize deformations of a one-dimensional formal module of height h together with level structure. According to the conjecture of Deligne-Carayol, these spaces realize the ... More

1932 Efforts of Persuasion on the Part of Einstein to Renounce the Cosmological ConstantDec 07 2015Einstein's 1932 efforts of persuasion to renounce the cosmological constant and his possible influence on Robertson.

Einstein's Uniformly Rotating Disk and the Hole ArgumentApr 15 2015Apr 22 2015Einstein's first mention of the uniformly rotating disk in print was in 1912, in his paper dealing with the static gravitational fields. After the 1912 paper, the rotating disk problem occurred in Einstein's writings only in a 1916 review paper, "The ... More

The Einstein-Nordström TheoryMay 27 2012The Finnish physicist Gunnar Nordstr\"om developed a competing theory of gravitation to Einstein's 1912-1913 gravitation theory. The equivalence principle was valid in his theory and it also satisfied red shift of the spectral lines from the sun. However, ... More

Variation of Mass with Velocity: "Kugeltheorie" or "Relativtheorie"May 27 2012This paper deals with four topics: The first subject is Abraham's spherical electron, Lorentz's contracted electron and B\"ucherer's electron. The second topic is Einstein's 1905 relativity theory of the motion of an electron. Einstein obtained expressions ... More

Poincaré's Dynamics of the Electron - A Theory of Relativity?Apr 30 2012Before 1905, Poincar\'e stressed the importance of the method of clocks and their synchronization, but unlike Einstein, magnet and conductor (asymmetries in Lorentz's theory regarding the explanation of Faraday's induction) or chasing a light beam and ... More

Did Mileva Marić assist Einstein in writing his 1905 path breaking papers?Apr 16 2012Writers read Einstein's letter to Mari\'c from 1901 in which he wrote: "bringing our work on relative motion to a successful conclusion!" What came afterwards was boosted by a claim that Joffe had seen the original relativity paper manuscript, and that ... More

Einstein's 1916 derivation of the Field EquationsOct 24 2013In his first November 4, 1915 paper Einstein wrote the Lagrangian form of his field equations. In the fourth November 25, 1915 paper, Einstein added a trace term of the energy-momentum tensor on the right-hand side of the generally covariant field equations. ... More

Hilbert modular forms with prescribed ramificationJan 29 2008Jun 02 2009Let $K$ be a totally real field. In this article we present an asymptotic formula for the number of Hilbert modular cusp forms $f$ with given ramification at every place $v$ of $K$. When $v$ is an infinite place, this means specifying the weight of $f$ ... More

A Different Look at Dark Energy and the Time Variation of Fundamental ConstantsJan 11 2011This paper makes the simple observation that a fundamental length, or cutoff, in the context of Friedmann-Lema\^itre-Robertson-Walker (FRW) cosmology implies very different things than for a static universe. It is argued that it is reasonable to assume ... More

The Maslov GerbeDec 13 2003Let Lag(E) be the grassmannian of lagrangian subspaces of a complex symplectic vector space E. We construct a Maslov class which generates the second integral cohomology of Lag(E), and we show that its mod 2 reduction is the characteristic class of a ... More

Semistable models for modular curves of arbitrary levelOct 20 2010Feb 17 2014We produce an integral model for the modular curve $X(Np^m)$ over the ring of integers of a sufficiently ramified extension of $\mathbf{Z}_p$ whose special fiber is a {\em semistable curve} in the sense that its only singularities are normal crossings. ... More

The Multichannel Quark ModelJun 19 1996We discuss the non-relativistic multichannel quark model and describe the techniques developed to solve the resulting equations. We then investigate some simple solutions to demonstrate how the model unifies meson-meson scattering with meson spectroscopy, ... More

Categories of (co)isotropic linear relationsMar 20 2015In categories of linear relations between finite dimensional vector spaces, composition is well-behaved only at pairs of relations satisfying transversality and monicity conditions. A construction of Wehrheim and Woodward makes it possible to impose these ... More

Adaptive Perturbation Theory I: Quantum MechanicsOct 18 2005Jan 04 2006Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive perturbation theory ... More

Black Holes, Hawking Radiation and the Information ParadoxNov 21 2002This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar ... More

CORE: Frustrated Magnets, Charge Fractionalization and QCDOct 11 2004I explain how to use a simple method to extract the physics of lattice Hamiltonian systems which are not easily analyzed by exact or other numerical methods. I will then use this method to establish the relationship between QCD and a special class of ... More

A note on the Wehrheim-Woodward categoryDec 01 2010Mar 11 2011Wehrheim and Woodward have shown how to embed all the canonical relations between symplectic manifolds into a category in which the composition is the usual one when transversality and embedding assumptions are satisfied. A morphism in their category ... More

The Geometry of MomentumAug 13 2002Although the idea of the momentum map associated with a symplectic action of a group is already contained in work of Lie, the geometry of momentum maps was not studied extensively until the 1960's. Centering around the relation between symmetries and ... More

Primordial Non-GaussianityMar 11 2019Mar 14 2019Our current understanding of the Universe is established through the pristine measurements of structure in the cosmic microwave background (CMB) and the distribution and shapes of galaxies tracing the large scale structure (LSS) of the Universe. One key ... More

Dark Matter Science in the Era of LSSTMar 11 2019Astrophysical observations currently provide the only robust, empirical measurements of dark matter. In the coming decade, astrophysical observations will guide other experimental efforts, while simultaneously probing unique regions of dark matter parameter ... More

Einstein and the conservation of energy-momentum in general relativityOct 10 2013The main purpose of the present paper is to show that a correction of one mistake was crucial for Einstein's pathway to the first version of the 1915 general theory of relativity, but also might have played a role in obtaining the final version of Einstein's ... More

Einstein's Pathway to the Equivalence Principle 1905-1907Aug 25 2012Between 1905 and 1907, Einstein first tried to extend the special theory of relativity in such a way so as to explain gravitational phenomena. This was the most natural and simplest path to be taken. These investigations did not fit in with Galileo's ... More

Albert Einstein: Rebellious WunderkindMay 21 2012Childhood and Schooldays: Albert Einstein, and the family members seemed to have exaggerated the story of Albert who developed slowly, learned to talk late, and whose parents thought he was abnormal. These and other stories were adopted by biographers ... More

Albert Einstein at the Zürich Polytechnic: a rare mastery of Maxwell's electromagnetic theoryMay 19 2012Einstein at the Z\"urich Polytechnic: he skipped classes, did not attend all the lectures of his Professors, and before going to the examinations he studied instead from the notebooks of his good friend from class, Marcel Grossmann. Einstein the free-thinker ... More

Genesis of general relativity - Discovery of general relativityApr 16 2012The intermediate stage of the development of general relativity is inseparable of Marcel Grossmann's mathematical assistance. Einstein acknowledges Grossmann's help during 1912-1914 to the development of general relativity. In fact, as with special relativity ... More

Did Einstein "Nostrify" Hilbert's Final Form of the Field Equations for General Relativity?Dec 04 2014Dec 11 2014Einstein's biographer Albrecht F\"olsing explained: Einstein presented his field equations on November 25, 1915, but six days earlier, on November 20, Hilbert had derived the identical field equations for which Einstein had been searching such a long ... More

Albert Einstein and the Fizeau 1851 Water Tube ExperimentApr 16 2012In 1895 Hendrik Antoon Lorentz derived the Fresnel dragging coefficient in his theory of immobile ether and electrons. This derivation did not explicitly involve electromagnetic theory at all. According to the 1922 Kyoto lecture notes, before 1905 Einstein ... More

From the Berlin "Entwurf" Field Equations to the Einstein Tensor III: March 1916Jan 25 2012I discuss Albert Einstein's 1916 General Theory of Relativity. I show that in Einstein's 1916 review paper, "the Foundation of the General Theory of Relativity", he derived his November 25, 1915 field equations with an additional term on the right hand ... More

From the Berlin "ENTWURF" Field Equations to the Einstein Tensor I: October 1914 until Beginning of November 1915Jan 25 2012I discuss Albert Einstein's 1914 review paper, "The Formal Foundation of the General Theory of Relativity" from two points of view: the main elements in the paper that appear to have led to the downfall of the Einstein-Grossman theory; and the elements ... More

Harmonic Maps with Prescribed Singularities on Unbounded DomainsSep 19 1995The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities $\p\colon\R^3\sm\Sigma\to\H^{k+1}_\C$ into the $(k+1)$-dimensional complex hyperbolic space. In this paper, we ... More

Formal vector spaces over a local field of positive characteristicJul 26 2012Apr 02 2013Let $O$ be the ring of power series in one variable over a finite field, with $K$ its fraction field. We introduce the notion of a "formal $K$-vector space"; this is a certain kind of $K$-vector space object in the category of formal schemes. This concept ... More

Invariance of the Sprague-Grundy Function for Variants of Wythoff's GameJul 16 2015Sep 05 2015We prove three conjectures of Fraenkel and Ho regarding two classes of variants of Wythoff's game. The two classes of variants of Wythoff's game feature restrictions of the diagonal moves. Each conjecture states that the Sprague-Grundy function is invariant ... More

Explicit non-abelian Lubin-Tate theory for GL(2)Oct 06 2009Let $F$ be a non-Archimedean local field with residue field $k$ of odd characteristic, and let $B/F$ be the division algebra of rank 4. We explicitly construct a stable curve $\mathfrak{X}$ over the algebraic closure of $k$ admitting an action of $GL_2(F)\times ... More

Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical ApproximationsFeb 10 2009It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand ... More

Probing the CORE of the Haldane ConjectureSep 30 1997The COntractor REnormalization group method (CORE), originally developed for application to lattice gauge theories, is very well adapted the study of spin systems and systems with fermions. As an warmup exercise for studying Hubbard models this method ... More

Symplectic CategoriesNov 20 2009Quantization problems suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations as morphisms. These relations compose well when a transversality condition is satisfied, but the failure ... More

Simultaneous communication in noisy channelsMay 09 2010Dec 24 2011A sender wishes to broadcast a message of length $n$ over an alphabet to $r$ users, where each user $i$, $1 \leq i \leq r$ should be able to receive one of $m_i$ possible messages. The broadcast channel has noise for each of the users (possibly different ... More

Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk StoryNov 26 2014Dec 01 2014On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations. Einstein's field ... More