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EB-GLS: An Improved Guided Local Search Based on the Big Valley StructureSep 22 2017Local search is a basic building block in memetic algorithms. Guided Local Search (GLS) can improve the efficiency of local search. By changing the guide function, GLS guides a local search to escape from locally optimal solutions and find better solutions. ... More

Sparkle Vision: Seeing the World through Random Specular MicrofacetsDec 26 2014In this paper, we study the problem of reproducing the world lighting from a single image of an object covered with random specular microfacets on the surface. We show that such reflectors can be interpreted as a randomized mapping from the lighting to ... More

Evolutionary Data Measures: Understanding the Difficulty of Text Classification TasksNov 05 2018Dec 07 2018Classification tasks are usually analysed and improved through new model architectures or hyperparameter optimisation but the underlying properties of datasets are discovered on an ad-hoc basis as errors occur. However, understanding the properties of ... More

Colliding clouds of strongly interacting spin-polarized fermionsJun 21 2011Jan 17 2012Motivated by a recent experiment at MIT, we consider the collision of two clouds of spin-polarized atomic Fermi gases close to a Feshbach resonance. We explain why two dilute gas clouds, with underlying attractive interactions between their constituents, ... More

Inequalities for the overpartition functionAug 15 2018Aug 16 2018Let $\overline{p}(n)$ denote the overpartition funtion. Engel showed that for $n\geq2$, $\overline{p}(n)$ satisfied the Tur\'{a}n inequalities, that is, $\overline{p}(n)^2-\overline{p}(n-1)\overline{p}(n+1)>0$ for $n\geq2$. In this paper, we prove several ... More

Channel Gating Neural NetworksMay 29 2018Employing deep neural networks to obtain state-of-the-art performance on computer vision tasks can consume billions of floating point operations and several Joules of energy per evaluation. Network pruning, which statically removes unnecessary features ... More

Uniform Correlation Mixture of Bivariate Normal Distributions and Hypercubically-contoured Densities That Are Marginally NormalNov 19 2015The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a uniform prior over ... More

Independent Emission and Absorption Abundances for Planetary NebulaeJan 14 2008Emission-line abundances have been uncertain for more than a decade due to unexplained discrepancies in the relative intensities of the forbidden lines and weak permitted recombination lines in planetary nebulae (PNe) and H II regions. The observed intensities ... More

Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018Jun 15 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More

Self-Supervised Siamese Learning on Stereo Image Pairs for Depth Estimation in Robotic SurgeryMay 17 2017Robotic surgery has become a powerful tool for performing minimally invasive procedures, providing advantages in dexterity, precision, and 3D vision, over traditional surgery. One popular robotic system is the da Vinci surgical platform, which allows ... More

Discrete Envy-free Division of Necklaces and MapsOct 07 2015We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divisible "cake" with a necklace of discrete, indivisible "beads." We focus ... More

Multi-Step Regression Learning for Compositional Distributional SemanticsJan 29 2013Jan 30 2013We present a model for compositional distributional semantics related to the framework of Coecke et al. (2010), and emulating formal semantics by representing functions as tensors and arguments as vectors. We introduce a new learning method for tensors, ... More

Intermodulation in Nonlinear SQUID Metamaterials: Experiment and TheoryJun 29 2016The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency ... More

Accelerated High-Resolution Photoacoustic Tomography via Compressed SensingApr 30 2016Sep 28 2016Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. ... 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

Acoustic Wave Field Reconstruction from Compressed Measurements with Application in Photoacoustic TomographySep 09 2016We present a method for the recovery of compressively sensed acoustic fields using patterned, instead of point-by-point, detection. From a limited number of such compressed measurements, we propose to reconstruct the field on the sensor plane in each ... 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

Light Rays, Singularities, and All ThatJan 13 2019This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article ... More

The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics ArenaNov 07 2011Feb 12 2013This article contains a local solution to the notorious Problem of Time in Quantum Gravity at the conceptual level and which is actually realizable for the relational triangle. The Problem of Time is that `time' in GR and `time' in ordinary quantum theory ... More

Relational Quadrilateralland Interpretation of CP^2 and QuotientsFeb 14 2011Aug 07 2013I investigate qualitatively significant regions of the configuration space for the classical and quantum mechanics of the relational quadrilateral in 2-d. This is relational in the sense that only relative ratios of separations, relative angles and relative ... More

Triangleland. I. Classical dynamics with exchange of relative angular momentumSep 06 2008Sep 23 2009In Euclidean relational particle mechanics, only relative times, relative angles and relative separations are meaningful. Barbour--Bertotti (1982) theory is of this form and can be viewed as a recovery of (a portion of) Newtonian mechanics from relational ... More

Leibniz--Mach foundations for GR and fundamental physicsMay 05 2004May 17 2004Consider the configuration space Q for some physical system, and a continuous group of transformations G whose action on the configurations is declared to be physically irrelevant. Implement G indirectly by adjoining 1 auxiliary g per independent generator ... More

Spaces of SpacesNov 30 2014May 13 2015Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I consider furthmore ... More

Where to Apply RelationalismNov 16 2014May 17 2015Relationalism -- along the lines developed by Barbour and collaborators in the past 3 decades -- can be considered an advance with 1/4 of the facets of the canonical approach's Problem of Time as identified by Isham and Kuchar. Indeed, almost all of the ... More

On Background IndependenceOct 05 2013This paper concerns what Background Independence itself is (as opposed to some particular physical theory that is background independent). The notions presented mostly arose from a layer-by-layer analysis of the facets of the Problem of Time in Quantum ... More

Machian Time Is To Be Abstracted From What Change?Sep 06 2012Apr 18 2013"It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive through the changes of things." Ernst Mach [1]. What change? Three answers to this are `any change' (Rovelli), 'all ... More

The Problem of Time in Quantum GravitySep 11 2010Jul 20 2012The problem of time in quantum gravity occurs because `time' is taken to have a different meaning in each of general relativity and ordinary quantum theory. This incompatibility creates serious problems with trying to replace these two branches of physics ... 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

Fixed Points of Maps on the Space of Rational FunctionsDec 17 2004Given integers s,t, define a function phi_{s,t} on the space of all formal series expansions by phi_{s,t} (sum a_n x^n) = sum a_{sn+t} x^n. For each function phi_{s,t}, we determine the collection of all rational functions whose Taylor expansions at zero ... 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

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

Singularities in string theoryDec 01 2002String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework for geometry ... More

Higgs portal dark matter in non-thermal cosmologiesApr 18 2018A scalar particle with a relic density set by annihilations through a Higgs portal operator is a simple and minimal possibility for dark matter. However, assuming a thermal cosmological history this model is ruled out over most of parameter space by collider ... More

A characterization of Leonard pairs using the notion of a tailOct 31 2009Let $V$ denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations $A: V\to V$ and $A^*: V\to V$ that satisfy (i) and (ii) below: (i) There exists a basis for $V$ with respect to which the matrix representing ... More

The arithmetic of solidsApr 06 2012The set of segments, each of the next is n times bigger than the first one is a simple geometric interpretation of the set $\mathbb{N}$ of natural numbers. In this paper we investigate the opposite situation. We construct an algebraic structure similar ... More

Extension of Algebraic Solutions Using The Lambert W FunctionFeb 24 2019Feb 26 2019The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented. Related techniques ... More

Value Monoids of Zero-Dimensional Valuations of Rank OneApr 13 2005Classically, Groebner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build on these ideas ... More

A scalar curvature bound along the conical Kähler-Ricci flowMay 08 2015Starting with a model conical K\"ahler metric, we prove a uniform scalar curvature bound for solutions to the conical K\"ahler-Ricci flow assuming a semi-ampleness type condition on the twisted canonical bundle. In the proof, we also establish uniform ... More

Towards a Formal Distributional Semantics: Simulating Logical Calculi with TensorsApr 22 2013Apr 28 2013The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This paper seeks to ... More

Steady state clusters and the Rath-Toth mean field forest fire modelSep 10 2018We introduce a random finite rooted tree $\mathcal{C}$, the steady state cluster, characterized by a recursive description: $\mathcal{C}$ is a singleton with probability $1/2$ and otherwise is obtained by joining by an edge the roots of two independent ... More

Superstring Perturbation Theory RevisitedSep 25 2012Nov 01 2012Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and have the expected ... More

A Note On The Chern-Simons And Kodama WavefunctionsJun 18 2003Jun 19 2003Yang-Mills theory in four dimensions formally admits an exact Chern-Simons wavefunction. It is an eigenfunction of the quantum Hamiltonian with zero energy. It is known to be unphysical for a variety of reasons, but it is still interesting to understand ... More

New Perspectives on the Quest for UnificationDec 01 1998Synthesizing older ideas about the 1/N expansion in gauge theory, the quantum mechanics of black holes, and quantum field theory in Anti de Sitter space, a new correspondence between gauge theory and quantum gravity has illuminated both subjects.

Anti De Sitter Space And HolographyFeb 20 1998Apr 06 1998Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. ... More

On S-Duality in Abelian Gauge TheoryMay 31 1995U(1) gauge theory on ${\bf R}^4$ is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of $SL(2,{\bf Z})$. In this paper, the duality is studied on a general four-manifold and it is shown ... More

On the Landau-Ginzburg Description of $N=2$ Minimal ModelsApr 07 1993Jul 09 1993The conjecture that $N=2$ minimal models in two dimensions are critical points of a super-renormalizable Landau-Ginzburg model can be tested by computing the path integral of the Landau-Ginzburg model with certain twisted boundary conditions. This leads ... More

On Black Holes In String TheoryNov 25 1991In these lecture notes from Strings `91, I briefly sketch the analogy between two dimensional black holes and the s-wave sector of four dimensional black holes, and the physical interest of the latter, particularly in the magnetically charged case.

Multi-Trace Operators, Boundary Conditions, And AdS/CFT CorrespondenceDec 31 2001Jan 04 2002We argue that multi-trace interactions in quantum field theory on the boundary of AdS space can be incorporated in the AdS/CFT correspondence by using a more general boundary condition for the bulk fields than has been considered hitherto. We illustrate ... More

The Cosmological Constant From The Viewpoint Of String TheoryFeb 29 2000Mar 01 2000The mystery of the cosmological constant is probably the most pressing obstacle to significantly improving the models of elementary particle physics derived from string theory. The problem arises because in the standard framework of low energy physics, ... More

Duality Relations Among Topological Effects In String TheoryDec 10 1999Dec 30 1999We explore two different problems in string theory in which duality relates an ordinary p-form in one theory to a self-dual (p+1)-form in another theory. One problem involves comparing D4-branes to M5-branes, and the other involves comparing the Ramond-Ramond ... More

Heterotic String Conformal Field Theory And A-D-E SingularitiesSep 30 1999Dec 10 1999We analyze the behavior of the heterotic string near an A-D-E singularity without small instantons. This problem is governed by a strongly coupled worldsheet conformal field theory, which, by a combination of O(alpha') corrections and worldsheet instantons, ... More

Small Instantons in String TheoryNov 04 1995A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra $SU(2)$ gauge symmetry appears that is supported in the core of the ... More

Geometric Langlands From Six DimensionsMay 17 2009Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as ... More

Branes, Instantons, And Taub-NUT SpacesFeb 05 2009Jun 06 2009ALE and Taub-NUT (or ALF) hyper-Kahler four-manifolds can be naturally constructed as hyper-Kahler quotients. In the ALE case, this construction has long been understood in terms of D-branes; here we give a D-brane derivation in the Taub-NUT case. Likewise, ... More

Two-Dimensional Models With (0,2) Supersymmetry: Perturbative AspectsApr 08 2005Nov 02 2006Certain perturbative aspects of two-dimensional sigma models with (0,2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of ``chiral differential operators'' is related to sigma models. In the ... More

Shor's Factoring Algorithm and Modern Cryptography. An Illustration of the Capabilities Inherent in Quantum ComputersNov 25 2004The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994, however, Peter ... More

QCD-like theories with many fermions: magnetic plasma and unusual confinementsApr 12 2012This comment-style letter represents a part of my talks on new developments in lattice QCD. While it does not contain any new results, it containes some theoretical ideas and comparisons which, I think, are not yet widely discussed in the lattice community. ... More

Shocks in Quark-Gluon PlasmasMar 29 2012May 21 2012Hydrodynamics is known to describe matter created in high energy heavy ion collisions well. Large deposition of energy by passing jets should create not only the sound waves, already discussed in literature, but also the shocks waves of finite amplitude. ... More

Deconfinement, Monopoles and New Phenomena in Heavy Ion CollisionsAug 05 2009We discuss various manifestations of the "magnetic scenario" for the quark-gluon plasma viewed as a mixture of two plasmas, of electrically (quark and gluons) as well as magnetically charged quasiparticles. Near the deconfinement phase transition, $T\approx ... More

Why does the Quark-Gluon Plasma at RHIC behave as a nearly ideal fluid ?Dec 16 2003Dec 22 2003The lecture is a brief review of the following topics: (i) collective flow phenomena in heavy ion collisions. The data from RHIC indicate robust collective flows, well described by hydrodynamics with expected Equation of State. The transport properties ... More

Characteristic Classes of Cameral CoversNov 23 2015May 17 2016We study the stack M of cameral covers for a complex reductive group G, introduced by Donagi and Gaitsgory. We compute its rational cohomology ring. In the special case G=GL(n), M is the stack of spectral covers. We also compute the cohomology ring of ... More

Prime numbers with a certain extremal type propertyAug 15 2014The convex hull of the subgraph of the prime counting function $x\rightarrow \pi(x)$ is a convex set, bounded from above by a graph of some piecewise affine function $x\rightarrow \epsilon(x)$. The vertices of this function form an infinite sequence of ... More

Is Natural SUSY Natural?Jun 06 2013Dec 02 2013We study the fine tuning associated to a `Natural Supersymmetry' spectrum with stops, after RG running, significantly lighter than the first two generation sfermions and the gluino. In particular, we emphasise that this tuning should be measured with ... More