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MiME: Multilevel Medical Embedding of Electronic Health Records for Predictive HealthcareOct 22 2018Deep learning models exhibit state-of-the-art performance for many predictive healthcare tasks using electronic health records (EHR) data, but these models typically require training data volume that exceeds the capacity of most healthcare systems. External ... More

Clinical Concept Extraction for Document-Level CodingJun 08 2019The text of clinical notes can be a valuable source of patient information and clinical assessments. Historically, the primary approach for exploiting clinical notes has been information extraction: linking spans of text to concepts in a detailed domain ... More

MorphNet: Fast & Simple Resource-Constrained Structure Learning of Deep NetworksNov 18 2017Apr 17 2018We present MorphNet, an approach to automate the design of neural network structures. MorphNet iteratively shrinks and expands a network, shrinking via a resource-weighted sparsifying regularizer on activations and expanding via a uniform multiplicative ... More

Graph Convolutional Transformer: Learning the Graphical Structure of Electronic Health RecordsJun 11 2019Effective modeling of electronic health records (EHR) is rapidly becoming an important topic in both academia and industry. A recent study showed that utilizing the graphical structure underlying EHR data (e.g. relationship between diagnoses and treatments) ... More

The Intrinsically X-ray Weak Quasar PHL 1811. I. X-ray Observations and Spectral Energy DistributionNov 10 2006This is the first of two papers reporting observations and analysis of the unusually bright (m_b=14.4), luminous (M_B=-25.5), nearby (z=0.192) narrow-line quasar PHL 1811, focusing on the X-ray properties and the spectral energy distribution. Two Chandra ... More

Multi-layer Representation Learning for Medical ConceptsFeb 17 2016Learning efficient representations for concepts has been proven to be an important basis for many applications such as machine translation or document classification. Proper representations of medical concepts such as diagnosis, medication, procedure ... More

GRAM: Graph-based Attention Model for Healthcare Representation LearningNov 21 2016Apr 01 2017Deep learning methods exhibit promising performance for predictive modeling in healthcare, but two important challenges remain: -Data insufficiency:Often in healthcare predictive modeling, the sample size is insufficient for deep learning methods to achieve ... More

Causal RegularizationFeb 08 2017Feb 23 2017In application domains such as healthcare, we want accurate predictive models that are also causally interpretable. In pursuit of such models, we propose a causal regularizer to steer predictive models towards causally-interpretable solutions and theoretically ... More

Analyzing the Role of Model Uncertainty for Electronic Health RecordsJun 10 2019In medicine, both ethical and monetary costs of incorrect predictions can be significant, and the complexity of the problems often necessitates increasingly complex models. Recent work has shown that changing just the random seed is enough for otherwise ... More

Compositional Obverter Communication Learning From Raw Visual InputApr 06 2018One of the distinguishing aspects of human language is its compositionality, which allows us to describe complex environments with limited vocabulary. Previously, it has been shown that neural network agents can learn to communicate in a highly structured, ... 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

The Josephson relation for the superfluid density in the BCS-BEC crossoverJan 29 2008Apr 23 2008The Josephson relation for the superfluid density is derived for a Fermi superfluid in the BCS-BEC crossover. This identity extends the original Josephson relation for Bose superfluids. It gives a simple exact relation between the superfluid density $\rho_s$ ... More

On Schreier unconditional sequencesMar 22 1991Let $(x_n)$ be a normalized weakly null sequence in a Banach space and let $\varep>0$. We show that there exists a subsequence $(y_n)$ with the following property: $$\hbox{ if }\ (a_i)\subseteq \IR\ \hbox{ and }\ F\subseteq \nat$$ satisfies $\min F\le ... More

The Synergy between Numerical and Perturbative Approaches to Black HolesJun 23 1998I describe approaches to the study of black hole spacetimes via numerical relativity. After a brief review of the basic formalisms and techniques used in numerical black hole simulations, I discuss a series of calculations from axisymmetry to full 3D ... More

An SYK-Like Model Without DisorderOct 31 2016Nov 03 2016Making use of known facts about "tensor models," it is possible to construct a quantum system without quenched disorder that has the same large $n$ limit for its correlation functions and thermodynamics as the SYK model. This might be useful in further ... More

Asymmetry gap in the electronic band structure of bilayer grapheneAug 09 2006Nov 02 2006A tight binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap $\Delta$ between the conduction and valence bands. In particular, a self consistent Hartree ... More

Gauge Theory and Langlands DualityJun 15 2009The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves ... More

Free field realizations in representation theory and conformal field theoryAug 18 1994Invited lecture at the International Congress of Mathematicians, Zuerich, August 3-11, 1994 (extended version), reviews free field realizations of affine Kac-Moody and W-algebras and their applications.

Lectures on the Langlands Program and Conformal Field TheoryDec 15 2005These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric reformulation, ... More

Five Lectures on Soliton EquationsNov 30 1997This is a self-contained review of a new approach to soliton equations of KdV type developed by the author together with B. Feigin and B. Enriquez.

How much of the outgoing radiation can be intercepted by Schwarzschildean black holes?Sep 11 2000The Schwarzschild spacetime is for electromagnetic waves like a nonuniform medium with a varying refraction index. A fraction of an outgoing radiation scatters off the curvature of the geometry and can be intercepted by a gravitational center. The amount ... More

Global solutions of a free boundary problem for selfgravitating scalar fieldsJun 01 1995Apr 12 1996The weak cosmic censorship hypothesis can be understood as a statement that there exists a global Cauchy evolution of a selfgravitating system outside an event horizon. The resulting Cauchy problem has a free null-like inner boundary. We study a selfgravitating ... More

A note on the Hayman-Wu theoremJul 12 2007The Hayman-Wu theorem states that the preimage of a line or circle L under a conformal mapping from the unit disc to a simply-connected domain U has total Euclidean length bounded by an absolute constant. The best possible constant is known to lie in ... More

A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group AveragingMay 15 2019Jun 09 2019In this article, we consider a second Problem of Time Facet. This started life as Wheeler's Thin Sandwich Problem, within the narrow context of 1) GR-as-Geometrodynamics, in particular its momentum constraint. 2) A Lagrangian variables level treatment. ... 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

The Chern-Ricci flow on primary Hopf surfacesMay 30 2019The Hopf surfaces provide a family of minimal non-K\"ahler surfaces of class VII on which little is known about the Chern-Ricci flow. We use a construction of Gauduchon-Ornea for locally conformally K\"ahler metrics on primary Hopf surfaces of class 1 ... 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

A partial Horn recursion in the cohomology of flag varietiesMar 15 2007Oct 09 2008Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of "smaller" flag ... More

Fifty Years in Fifteen Minutes: The Impact of the Parkes ObservatoryOct 08 2012The scientific output of Parkes over its fifty year history is briefly reviewed on a year-by-year basis, and placed in context with other national and international events of the time.

Residues in group completions and the Cech cohomology of BGMay 17 2016Let $G$ be a connected affine algebraic group over $\mathbf{C}$, let $G \to X$ be an open immersion of complex $G$-varieties, let $Z = X-G$ and let $i: Z \to X$ be the inclusion. Let $\alpha \in H^*(G,\mathbf{C})$ be primitive. We give a method to compute ... More

Process-Oriented Parallel Programming with an Application to Data-Intensive ComputingJul 21 2014We introduce process-oriented programming as a natural extension of object-oriented programming for parallel computing. It is based on the observation that every class of an object-oriented language can be instantiated as a process, accessible via a remote ... More

A Local Resolution of the Problem of Time. IX. Spacetime ConstructabilityJun 09 2019Assuming Temporal and Configurational Relationalism, GR as Geometrodynamic's DeWitt supermetric alongside local Lorentzian Relativity with its universal finite maximum propagation speed arises as one of very few options from Feeding Families through a ... More

A characterization of bipartite Leonard pairs using the notion of a tailAug 18 2013Let $V$ 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 the ... More

A Local Resolution of the Problem of Time. III. The other classical facets piecemealMay 15 2019Jun 09 2019We introduce seven further local facets of the classical Problem of Time, and underlying Background Independence aspects, the previous two articles having covered one further facet-and-aspect each for a total of nine. I.e. Constraint Closure, Assignment ... More

The Area of Polynomial Images and PreimagesFeb 17 2003Let p be a monic polynomial in one complex variable and K a measurable subset of the complex plane. In terms of the area of K, we give an upper bound on the area of the preimage of K under p and a lower bound on the area of the image of K under p, (counted ... More

Residues in group completions and the Cech cohomology of BGMay 17 2016Mar 05 2017Let $G$ be a connected affine algebraic group over $\mathbb{C}$, $G \to X$ be an open immersion of $G$-varieties, $Z = X-G$ and $i: Z \to X$ be the inclusion. Let $\alpha \in H^*(G,\mathbb{C})$ be primitive. We give a method to compute the image of $\alpha$ ... More

Topological representations of matroidsAug 22 2002Sep 18 2002There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully partitioned, Zaslavsky's enumeration of the cells of the arrangement still ... More

Update on Modular Non-Rigid Calabi-Yau ThreefoldsFeb 29 2008We review some recent results on the modularity of non-rigid Calabi-Yau threefolds.

Chaos in a continuous-time Boolean networkMay 09 2019Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range of behaviors ... 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

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

Metric contraction of the cone divisor by the conical Kähler-Ricci flowApr 02 2017We use the momentum construction of Calabi to study the conical K\"ahler-Ricci flow on Hirzebruch surfaces with cone angle along the exceptional curve, and show that either the flow Gromov-Hausdorff converges to the Riemann sphere or a single point in ... More

Category-Theoretic Quantitative Compositional Distributional Models of Natural Language SemanticsNov 06 2013This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over these contexts ... 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

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

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