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Small Bodies Science with TwinkleMar 23 2019Twinkle is an upcoming 0.45m space-based telescope equipped with a visible and two near-infrared spectrometers over the spectral range 0.4 - 4.5$\mu$m with a resolving power R $\sim$ 250 ($\lambda$\textless 2.42$\mu$m) and R $\sim$ 60 ($\lambda$\textgreater ... More

Remote-sensing Characterisation of Major Solar System Bodies with the Twinkle Space TelescopeMar 23 2019Remote-sensing observations of Solar System objects with a space telescope offer a key method of understanding celestial bodies and contributing to planetary formation and evolution theories. The capabilities of Twinkle, a space telescope in a low Earth ... More

Towards a more complex description of chemical profiles in exoplanets retrievals: A 2-layer parameterisationMar 26 2019State of the art spectral retrieval models of exoplanet atmospheres assume constant chemical profiles with altitude. This assumption is justified by the information content of current datasets which do not allow, in most cases, for the molecular abundances ... More

Pushing the Limits of Exoplanet Discovery via Direct Imaging with Deep LearningApr 12 2019Further advances in exoplanet detection and characterisation require sampling a diverse population of extrasolar planets. One technique to detect these distant worlds is through the direct detection of their thermal emission. The so-called direct imaging ... More

Exoplanet Spectroscopy and Photometry with the Twinkle Space TelescopeNov 20 2018Dec 22 2018The Twinkle space telescope has been designed for the characterisation of exoplanets and Solar System objects. Operating in a low Earth, Sun-synchronous orbit, Twinkle is equipped with a 45 cm telescope and visible (0.4 - 1um) and infrared (1.3 - 4.5um) ... More

Geometric Endoscopy and Mirror SymmetryOct 31 2007Apr 05 2008The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces to T-duality on the generic Hitchin fibers, which are smooth tori. In this ... More

Navier-Stokes Hamiltonian for the Similarity Renormalization GroupJul 03 2014Jul 07 2015The Navier-Stokes Hamiltonian is derived from first principles. Its Hamilton equations are shown to be equivalent to the continuity, Navier-Stokes, and energy conservation equations of a compressible viscous fluid. The derivations of the Euler and Navier-Stokes ... More

Singlet-Triplet Splitting of Positronium in Light-Front QEDMar 14 1997We study the QED bound-state problem in a light-front hamiltonian approach. It is important to establish the equivalence (or not) of equal-time and light-front approaches in the well-understood arena of Quantum Electrodynamics. Along these lines, the ... More

Observing exoplanets in the near-infrared from a high altitude balloon platformMar 22 2019Although there exists a large sample of known exoplanets, little spectroscopic data exists that can be used to study their global atmospheric properties. This deficiency can be addressed by performing phase-resolved spectroscopy -- continuous spectroscopic ... More

Analytic physical model of anisotropic anomalous diffusionJun 12 2013Jun 26 2013The temporal Fokker-Planck equation is analytically integrated in an arbitrary number of spatial dimensions but with the 2D and 3D results highlighted. It is shown that a temporal power-law ansatz for the anisotropic diffusion coefficients leads naturally ... More

On the risk of convex-constrained least squares estimators under misspecificationJun 13 2017We consider the problem of estimating the mean of a noisy vector. When the mean lies in a convex constraint set, the least squares projection of the random vector onto the set is a natural estimator. Properties of the risk of this estimator, such as its ... More

Scales of a fluidSep 29 2014The flow of a viscous fluid is perturbed by its internal friction which generates heat and leads to a small temperature change. This does not occur for an ideal fluid. We would like to resolve this picture as a function of the dynamical macroscopic scales ... More

Light-Front Hamiltonian Approach to the Bound-State Problem in Quantum ElectrodynamicsSep 25 1997Sep 26 1997This dissertation presents the first theoretical investigation of the Lamb shift in a light-front hamiltonian approach: the dominant part of the splitting between the 2S(1/2) and 2P(1/2) energy levels in hydrogen is calculated. Also presented for the ... More

Comments on the CMS discovery of the "Ridge" in High Multiplicity pp collisions at LHCSep 23 2010A very recent paper by the CMS collaboration \cite{cms_ridge} has created large discussion in the media, which call it important but did not explain why, in some places even calling it "unundestandable". While it is of course too soon to know what causes ... More

Quark-Gluon Plasma - New FrontiersApr 08 2008As implied by organizers, this talk is not a conference summary but rather an outline of progress/challenges/``frontiers'' of the theory. Some fundamental questions addressed are: Why is sQGP such a good liquid? Do we understand (de)confinement and what ... More

Emerging Theory of Strongly Coupled Quark-Gluon PlasmaMar 19 2007RHIC data have shown robust collective flows, including recent spectacular ``conical flow'' from quenched jets: that confirms that QGP above the critical line is in a strongly coupled regime. One way to study Non-Abelian classical strongly coupled plasmas ... More

Physics of Strongly coupled Quark-Gluon PlasmaJul 18 2008Sep 15 2008This review cover our current understanding of strongly coupled Quark-Gluon Plasma (sQGP), especially theoretical progress in (i) explaining the RHIC data by hydrodynamics, (ii) describing lattice data using electric-magnetic duality; (iii) understanding ... More

The conical flow from quenched jets in sQGPSep 05 2006Starting with a reminder of what is strongly coupled Quark-Gluon Plasma (sQGP), we proceed to recent advances in jet quenching and heavy quark diffusion, with a brief summary of various results based on AdS/CFT correspondence. The conical flow is a hydrodynamical ... More

A Cosmological Constant from Gauge Field Instantons?Jul 21 2004Although all interactions in the Standard Model generate nonzero shifts of the vacuum energy and pressure, gravity does not interact with them. Assuming (i) that the reason why it is so breaks down at some scale $M_g$ and that (ii) the instanton-induced ... More

Analytic Continuation Of Chern-Simons TheoryJan 18 2010Aug 28 2010The title of this article refers to analytic continuation of three-dimensional Chern-Simons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the volume conjecture, or analytic continuation of three-dimensional ... More

Geometric Langlands And The Equations Of Nahm And BogomolnyMay 29 2009Nov 06 2009Geometric Langlands duality relates a representation of a simple Lie group $G^\vee$ to the cohomology of a certain moduli space associated with the dual group $G$. In this correspondence, a principal $SL_2$ subgroup of $G^\vee$ makes an unexpected appearance. ... More

Mirror Symmetry, Hitchin's Equations, And Langlands DualityFeb 07 2008Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking a complex structure ... More

Chiral Ring Of Sp(N) And SO(N) Supersymmetric Gauge Theory In Four DimensionsFeb 25 2003Jul 17 2003The chiral ring of classical supersymmetric Yang-Mills theory with gauge group $Sp(N)$ or SO(N) is computed, extending previous work (of Cachazo, Douglas, Seiberg, and the author) for SU(N). The result is that, as has been conjectured, the ring is generated ... More

Quest For UnificationJul 09 2002The GUT-based approach to physics has been attractive since it was first put forward close to thirty years ago; it has been enriched by new ideas, notably supersymmetry and strings; and there are real hints that it is on the right track, notably from ... More

Deconstruction, G_2 Holonomy, and Doublet-Triplet SplittingJan 04 2002Jan 15 2002We describe a mechanism for using discrete symmetries to solve the doublet-triplet splitting problem of four-dimensional supersymmetric GUT's. We present two versions of the mechanism, one via ``deconstruction,'' and one in terms of M-theory compactification ... More

World-Sheet Corrections Via D-InstantonsJul 07 1999We use a D-instanton or physical gauge approach to re-derive the heterotic string worldsheet instanton contribution to the superpotential in Calabi-Yau compactification. We derive an analogous formula for worldsheet instanton corrections to the moduli ... More

Theta Dependence In The Large N Limit Of Four-Dimensional Gauge TheoriesJul 15 1998The theta dependent of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every theta, there are infinitely many vacua that ... More

New ``Gauge'' Theories In Six DimensionsOct 07 1997Dec 08 1997More general constructions are given of six-dimensional theories that look at low energy like six-dimensional super Yang-Mills theory. The constructions start with either parallel fivebranes in Type IIB, or M-theory on $(\C^2\times\S^1)/\Gamma$ for $\Gamma$ ... More

Branes And The Dynamics Of QCDJun 13 1997Jun 30 1997A brane configuration is described that is relevant to understanding the dynamics of N=1 supersymmetric Yang-Mills theory. Confinement and spontaneous breaking of a discrete chiral symmetry can be understood as consequences of the topology of the brane. ... More

Solutions Of Four-Dimensional Field Theories Via M TheoryMar 24 1997N=2 supersymmetric gauge theories in four dimensions are studied by formulating them as the quantum field theories derived from configurations of fourbranes, fivebranes, and sixbranes in Type IIA superstrings, and then reinterpreting those configurations ... More

Is Supersymmetry Really Broken?Sep 19 1994In 2 + 1 dimensions, in the presence of gravity, supersymmetry can ensure the vanishing of the cosmological constant without requiring the equality of bose and fermi masses.

Ground Ring Of Two Dimensional String TheoryAug 16 1991String theories with two dimensional space-time target spaces are characterized by the existence of a ``ground ring'' of operators of spin $(0,0)$. By understanding this ring, one can understand the symmetries of the theory and illuminate the relation ... More

Conformal Field Theory In Four And Six DimensionsDec 02 2007Feb 07 2008The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.

Supersymmetric Index Of Three-Dimensional Gauge TheoryFeb 27 1999Apr 11 1999In N=1 super Yang-Mills theory in three spacetime dimensions, with a simple gauge group $G$ and a Chern-Simons interaction of level $k$, the supersymmetric index $\Tr (-1)^F$ can be computed by making a relation to a pure Chern-Simons theory or microscopically ... More

Physical Interpretation Of Certain Strong Coupling SingularitiesSep 18 1996We interpret certain strong coupling singularities of the $E_8\times E_8$ heterotic string on K3 in terms of exotic six-dimensional theories in which $E_8$ is a gauge symmetry. These theories are closely related to theories obtained at small instanton ... More

Non-Perturbative Superpotentials In String TheoryApr 05 1996May 07 1996The non-perturbative superpotential can be effectively calculated in $M$-theory compactification to three dimensions on a Calabi-Yau four-fold $X$. For certain $X$, the superpotential is identically zero, while for other $X$, a non-perturbative superpotential ... More

Five-branes And $M$-Theory On An OrbifoldDec 29 1995Feb 08 1996We relate Type IIB superstrings compactified to six dimensions on K3 to an eleven-dimensional theory compactified on $({\bf S}^1)^5/{\bf Z}_2$. Eleven-dimensional five-branes enter the story in an interesting way.

Sigma Models And The ADHM Construction Of InstantonsOct 07 1994This paper is devoted to the construction of a family of linear sigma models with $(0,4)$ supersymmetry which should flow in the infrared to the stringy version of Yang-Mills instantons on ${\bf R}^4$. The family depends on the full set of expected parameters ... More

More On Gauge Theory And Geometric LanglandsJun 13 2015The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an $A$-brane of ... More

Billiards with BombsJun 01 2015In this paper, we define a variant of billiards in which the ball bounces around a square grid erasing walls as it goes. We prove that there exist periodic tunnels with arbitrarily large period from any possible starting point, that there exist non-periodic ... More

The "Parity" Anomaly On An Unorientable ManifoldMay 08 2016Sep 06 2016The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. This anomaly has traditionally been ... More

A Dynamical Mechanism for the Big Bang and Non-Regularizability for $w=1$Nov 14 2014We consider a contracting universe and its transition to expansion through the big bang singularity with a time varying equation of state $w$, where $w$ approaches $1$ as the universe contracts to the big bang. We show that this singularity is non-regularizable. ... More

Network Models in Epidemiology: Considering Discrete and Continuous DynamicsOct 19 2015Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series of articles, ... More

Notes On Holomorphic String And Superstring Theory Measures Of Low GenusJun 16 2013Dec 03 2013It has long been known that in principle, the genus g vacuum amplitude for bosonic strings or superstrings in 26 or 10 dimensions can be entirely determined from conditions of holomorphy. Moreover, this has been done in practice for bosonic strings of ... More

On quotients of Banach spaces having shrinking unconditional basesNov 16 1990It is proved that if a Banach space $Y$ is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in $Y$ has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's ... More

Winds and Accretion in Young StarsSep 21 2008Establishing the origin of accretion powered winds from forming stars is critical for understanding angular momentum evolution in the star-disk interaction region. Here, the high velocity component of accretion powered winds is launched and accreting ... More

Recent Advances in the Langlands ProgramMar 06 2003Sep 30 2003These are the notes for the lecture given by the author at the "Current Events" Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for GL(n) in the function field case and its proof ... More

Vertex Algebras and Algebraic CurvesJul 10 2000Sep 07 2001This is the text of the Bourbaki seminar that I gave on June 24, 2000.

On the rate of equidistribution of expanding horospheres in finite-volume quotients of $\mathrm{SL}(2,\mathbb{C})$Dec 08 2015Let $\Gamma$ be a lattice in $G=\mathrm{SL}(2,\mathbb{C})$. We give an effective equidistribution result with precise error terms for expanding translates of pieces of horospherical orbits in $\Gamma\backslash G$. Our method of proof relies on the theory ... More

Bohm theory for abstruse measurements: application to layer depth profiling by Auger spectroscopyOct 17 2016Modified Bohm formalism is applied to solve a problem of abstruse layer depth profiles measured by the Auger electron spectroscopy technique in real physical systems, i.e., the desorbed carbon/passive layer on NiTi substrate and the adsorbed oxygen/surface ... More

A modular quintic Calabi-Yau threefold of level 55Mar 06 2009In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold which is modular, in the sense that the L-function of its middle-dimensional cohomology is associated to a classical modular form of weight ... More

Non-perturbative reheating and NnaturalnessAug 22 2017We study models in which reheating happens only through non-perturbative processes. The energy transferred can be exponentially suppressed unless the inflaton is coupled to a particle with a parametrically small mass. Additionally, in some models a light ... More

Heavy superpartners with less tuning from hidden sector renormalisationNov 12 2013In supersymmetric extensions of the Standard Model, superpartner masses consistent with collider bounds typically introduce significant tuning of the electroweak scale. We show that hidden sector renormalisation can greatly reduce such a tuning if the ... More

How to recognize a Leonard pairJan 30 2019Let $V$ denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations $A: V\rightarrow V$ and $A^{*}: V\rightarrow V$ that satisfy (i) and (ii) below. (i) There exists a basis for $V$ with respect to which ... More

Expected observing efficiency of the Maunakea Spectroscopic Explorer (MSE)Jul 20 2018The Maunakea Spectroscopic Explorer (MSE) will obtain millions of spectra each year in the optical to near-infrared, at low (R ~ 3,000) to high (R ~ 40,000) spectral resolution by observing >4,000 spectra per pointing via a highly multiplexed fiber-fed ... More

Electronic properties of monolayer and bilayer grapheneMay 22 2012The tight-binding model of electrons in graphene is reviewed. We derive low-energy Hamiltonians supporting massless Dirac-like chiral fermions and massive chiral fermions in monolayer and bilayer graphene, respectively, and we describe how their chirality ... More

Mathematics, Love, and TattoosNov 14 2012Reflections on the film "Rites of Love and Math" (directed by Reine Graves and the author) and its "formula of love".

Langlands Program, Trace Formulas, and their GeometrizationFeb 09 2012Nov 06 2014The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction ... More

Affine Algebras, Langlands Duality and Bethe AnsatzJun 05 1995Sep 23 1999We review various aspects of representation theory of affine algebras at the critical level, geometric Langlands correspondence, and Bethe ansatz in the Gaudin models. Geometric Langlands correspondence relates D-modules on the moduli space of G-bundles ... More

Ramifications of the geometric Langlands ProgramNov 09 2006Nov 24 2006The global geometric Langlands correspondence relates Hecke eigensheaves on the moduli stack of G-bundles on a smooth projective algebraic curve X and holomorphic G'-bundles with connection on X, where G' is the Langlands dual group of G. This correspondence ... More

Object-Oriented Parallel ProgrammingApr 17 2014We introduce an object-oriented framework for parallel programming, which is based on the observation that programming objects can be naturally interpreted as processes. A parallel program consists of a collection of persistent processes that communicate ... More

Fluid accretion onto a spherical black hole: relativistic description versus Bondi modelJul 07 1999We describe general-relativistically a spherically symmetric stationary fluid accretion onto a black hole. Relativistic effects enhance mass accretion, in comparison to the Bondi model predictions, in the case when backreaction is neglected. That enhancement ... More

Event horizons and apparent horizons in spherically symmetric geometriesJan 06 1993Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, must propagate outward with a velocity equal to the velocity of radially outgoing photons. That proves, within ... More

Schwarzschild horizon and the gravitational redshift formulaOct 16 2001Dec 27 2001The gravitational redshift formula is usually derived in the geometric optics approximation. In this note we consider an exact formulation of the problem in the Schwarzschild space-time, with the intention to clarify under what conditions this redshift ... More

Selfgravitating nonlinear scalar fieldsJun 16 2000We investigate the Cauchy problem for the Einstein - scalar field equations in asymptotically flat spherically symmetric spacetimes, in the standard 1+3 formulation. We prove the local existence and uniqueness of solutions for initial data given on a ... More

Why do surface tensions of most of organic liquids demonstrate close values?Jun 02 2010Values of surface tension of most of organic liquids are of the same order of magnitude. The natural explanation for this lies in the fact that surface tension is governed by London dispersion forces, which are independent of the permanent dipole moment ... More

Information-based models for finance and insuranceOct 05 2010In financial markets, the information that traders have about an asset is reflected in its price. The arrival of new information then leads to price changes. The `information-based framework' of Brody, Hughston and Macrina (BHM) isolates the emergence ... More

Microarrays for Amino Acid Analysis and Protein SequencingAug 10 1999A method is described where the aminoacyl-tRNA synthetase system is used to create very small devices for quantitative analysis of the amino acids that occur in proteins. The basis of the method is that each of the 20 synthetases and/or a tRNA specific ... More

A "Domain Wall" Scenario for the AdS/QCDOct 31 2007Dec 28 2007We propose a scenario for bottom-up gravity dual picture of QCD-like theories, which consists of two near-AdS$_5$ domains separated by the ``domain wall'' at which the effective coupling relatively rapidly switches from small perturbative value at its ... More

Some thoughts on critical and tricritical points and deconfinementSep 05 2006We start with a discussion of a phase diagram and three special collision energies: (i) the first touching of the mixed phase; (ii) the softest point; (iii) the critical point. We then proceed to more details about the role a massless critical mode should ... More

Lower Bound on Entanglement of Formation for the Qubit-Qudit SystemJan 06 2003Wootters [PRL 80, 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed form expression for the EOF of an arbitrary mixed state in any system more ... More

Perturbative Gauge Theory As A String Theory In Twistor SpaceDec 15 2003Oct 06 2004Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space ... More

Anomaly Cancellation On Manifolds Of G_2 HolonomyAug 22 2001Smooth manifolds of G_2 holonomy, used to compactify M-theory to four dimensions, give only abelian gauge groups without charged matter multiplets. But singular G_2-manifolds can give abelian or nonabelian gauge groups with chiral fermions. We describe ... More

Lepton Number And Neutrino MassesJun 28 2000I briefly review the arguments which in the 1970's convinced many theoretical physicists to anticipate lepton number violation, and to guess a range of neutrino masses.

Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge TheoriesMar 16 1998Apr 07 1998The correspondence between supergravity (and string theory) on $AdS$ space and boundary conformal field theory relates the thermodynamics of ${\cal N}=4$ super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in ... More

On The Conformal Field Theory Of The Higgs BranchJul 11 1997Jul 22 1997We study 1+1-dimensional theories of vector and hypermultiplets with (4,4) supersymmetry. Despite strong infrared fluctuations, these theories flow in general to distinct conformal field theories on the Coulomb and Higgs branches. In some cases there ... More

On Flux Quantization In M-Theory And The Effective ActionSep 16 1996Oct 18 1996The quantization law for the antisymmetric tensor field of $M$-theory contains a gravitational contribution not known previously. When it is included, the low energy effective action of $M$-theory, including one-loop and Chern-Simons contributions, is ... More

Bound States Of Strings And $p$-BranesOct 18 1995Oct 23 1995The recent discovery of an explicit conformal field theory description of Type II $p$-branes makes it possible to investigate the existence of bound states of such objects. In particular, it is possible with reasonable precision to verify the prediction ... More

A New Look At The Path Integral Of Quantum MechanicsSep 30 2010The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct explanation ... More

Three-Dimensional Gravity RevisitedJun 22 2007We consider the problem of identifying the CFT's that may be dual to pure gravity in three dimensions with negative cosmological constant. The c-theorem indicates that three-dimensional pure gravity is consistent only at certain values of the coupling ... More

Quantum Gravity In De Sitter SpaceJun 13 2001We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is embedded in a ... More

Toroidal Compactification Without Vector StructureDec 03 1997Many important ideas about string duality that appear in conventional $\T^2$ compactification have analogs for $\T^2$ compactification without vector structure. We analyze some of these issues and show, in particular, how orientifold planes associated ... More

String Theory Dynamics In Various DimensionsMar 20 1995Mar 24 1995The strong coupling dynamics of string theories in dimension $d\geq 4$ are studied. It is argued, among other things, that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring, and that a recently conjectured ... More

Chern-Simons Gauge Theory As A String TheoryJul 28 1992Dec 22 2003Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time interpretations. ... More

Two Dimensional String Theory And Black HolesJun 17 1992This lecture surveys a few loosely related topics, ranging from the scarcity of quantum field theories -- and the role that this has played, and still plays, in physics -- to paradoxes involving black holes in soluble two dimensional string theory and ... More

Miniclusters in the AxiverseSep 01 2016If dark matter is an axion-like-particle a significant fraction of the present day relic abundance could be concentrated in compact gravitationally bound miniclusters. We study the minicluster masses compatible with the dark matter relic density constraint. ... More

The Super Period Matrix With Ramond PuncturesJan 11 2015We generalize the super period matrix of a super Riemann surface to the case that Ramond punctures are present. For a super Riemann surface of genus g with 2r Ramond punctures, we define, modulo certain choices that generalize those in the classical theory ... More

A multiplicative formula for structure constants in the cohomology of flag varietiesDec 10 2008Nov 03 2010Let G be a complex semi-simple Lie group and let P,Q be a pair of parabolic subgroups of G such that Q contains P. Consider the flag varieties G/P, G/Q and Q/P. We show that certain structure constants in H^*(G/P) with respect to the Schubert basis can ... More

Recent progress in understanding deconfinement and chiral restoration phase transitionsOct 26 2016Paradigme shift in gauge topology, from instantons to their constituents -- instanton-dyons -- has recently lead to very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at sufficiently high density explains ... More

Configuration Spaces in Fundamental PhysicsMar 05 2015Apr 19 2016I consider configuration spaces for $N$-body problems, gauge theories and for GR in both geometrodynamical and Ashtekar variables forms, including minisuperspace and inhomogeneous perturbations thereabout in the former case. These examples include many ... More

Quantum Cosmology will need to become a Numerical SubjectJun 24 2013Jun 26 2013The inhomogeneous fluctuations that underlie structure formation - galaxies and CMB hotspots - might have been seeded by quantum cosmological fluctuations, as magnified by some inflationary mechanism. The Halliwell-Hawking model for these, as a lower-energy ... More

Relational Quadrilateralland. I. The Classical TheoryFeb 19 2012Nov 25 2013Relational particle mechanics models bolster the relational side of the absolute versus relational motion debate, and are additionally toy models for the dynamical formulation of General Relativity and its Problem of Time. They cover two aspects that ... More

Shape Space Methods for Quantum Cosmological TrianglelandSep 13 2009Oct 18 2010With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so by importing ... More

Does relationalism alone control geometrodynamics with sources?Nov 02 2007This paper concerns relational first principles from which the Dirac procedure exhaustively picks out the geometrodynamics corresponding to general relativity as one of a handful of consistent theories. This was accompanied by a number of results and ... More

Records TheorySep 12 2007Sep 23 2009In quantum gravity, one seeks to combine quantum mechanics and general relativity. In such attempts, one comes across the `problem of time' impasse: the notion of time is conceptually different in each of these theories. In this paper, I consider the ... More

Emergent Semiclassical Time in Quantum Gravity. I. Mechanical ModelsNov 01 2006Nov 04 2007Strategies intended to resolve the problem of time in quantum gravity by means of emergent or hidden timefunctions are considered in the arena of relational particle toy models. In situations with `heavy' and `light' degrees of freedom, two notions of ... More

Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets CompletedJun 11 2015Temporal Relationalism (TR) is that there is no time for the universe as a whole at the primary level. Time emerges rather at a secondary level; one compelling idea for this is Mach's `time is to be abstracted from change'. TR leads to, and better explains, ... More

Problem of Time in Quantum GravityJun 11 2012Aug 16 2012The Problem of Time occurs because the `time' of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions ... More

Relational Quadrilateralland. Analogues of Isospin and HyperchargeFeb 19 2012Aug 07 2013I consider the momenta and conserved quantities for CP^2 interpreted as the space of quadrilaterals. This builds on seminar I and II's kinematics via making use of MacFarlane's work considering the SU(3)-like (and thus particle physics-like) conserved ... More

Foundations of Relational Particle DynamicsJun 26 2007Nov 08 2009Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as discussion of conceptual ... More