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Mirkovic-Vilonen polytopes and Khovanov-Lauda-Rouquier algebrasOct 25 2012Jun 24 2015We describe how Mirkovic-Vilonen polytopes arise naturally from the categorification of Lie algebras using Khovanov-Lauda-Rouquier algebras. This gives an explicit description of the unique crystal isomorphism between simple representations of the KLR ... More

Decay estimates for Rivière's equation, with applications to regularity and compactnessFeb 03 2011Apr 01 2011We derive a selection of energy estimates for a generalisation of a critical equation on the unit disc in $\mathbb{R}^2$ introduced by Rivi\`ere. Applications include sharp regularity results and compactness theorems which generalise a large amount of ... More

Equilibration of isolated many-body quantum systems with respect to general distinguishability measuresMar 09 2016Jul 21 2016We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are unimaginably ... More

Typical Relaxation of Isolated Many-Body Systems Which Do Not ThermalizeMay 19 2017We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical ... More

The diameter of the set of boundary slopes of a knotDec 07 2004Apr 21 2009Let K be a tame knot with irreducible exterior M(K) in a closed, connected, orientable 3--manifold Sigma such that pi_1(Sigma) is cyclic. If infinity is not a strict boundary slope, then the diameter of the set of strict boundary slopes of K, denoted ... More

Combinatorial descriptions of the crystal structure on certain PBW bases (extended abstract)Mar 30 2016Lusztig's theory of PBW bases gives a way to realize the infinity crystal for any simple complex Lie algebra where the underlying set consists of Kostant partitions. In fact, there are many different such realizations, one for each reduced expression ... More

Computing in matrix groups without memoryOct 22 2013Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve updates of ... More

Towards nonaxisymmetry; initial results using the Flux Coordinate Independent method in BOUT++Sep 21 2016Fluid simulation of stellarator edge transport is difficult due to the complexities of mesh generation; the stochastic edge and strong nonaxisymmetry inhibit the use of field aligned coordinate systems. The recent implementation of the Flux Coordinate ... More

Quasi-Antichain Chermak-Delgado Lattices of Finite GroupsJul 23 2014The Chermak-Delgado lattice of a finite group is a dual, modular sublattice of the subgroup lattice of the group. This paper considers groups with a quasi-antichain interval in the Chermak-Delgado lattice, ultimately proving that if there is a quasi-antichain ... More

Groups Whose Chermak-Delgado Lattice is a ChainMay 10 2013For a finite group G with subgroup H the Chermak-Delgado measure of H in G refer to the product of the order of H with the order of its centralizer, C_G(H). The set of all subgroups with maximal Chermak-Delgado measure form a sublattice, CD(G), within ... More

PBW bases and marginally large tableaux in types B and CAug 14 2017We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara's infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from ... More

Accurate emulators for large-scale computer experimentsMar 12 2012Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the procedure shows ... More

Combinatorial descriptions of the crystal structure on certain PBW basesJun 06 2016Using the theory of PBW bases, one can realize the crystal $B(\infty)$ for any semisimple Lie algebra over $\mathbf{C}$ using Kostant partitions as the underlying set. In fact there are many such realizations, one for each reduced expression for the longest ... More

Spectroscopic analysis of cool giants and supergiantsMar 12 2014Cool red giants and supergiants are among the most complex and fascinating stars in the Universe. They are bright and large, and thus can be observed to enormous distances allowing us to study the properties of their host galaxies, such as dynamics and ... More

Quantum Computing in a Macroscopic Dark PeriodSep 03 2001Nov 02 2001Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via ... More

Interactive Exploration of the Employment Situation Report: From Fixed Tables to Dynamic DiscoveryAug 11 2016The monthly Bureau of Labor Statistics Employment Situation Report is widely anticipated by economists, journalists, and politicians as it is used to forecast the economic condition of the United States. The report has broad impact on public and corporate ... More

Massively Multilingual Neural Grapheme-to-Phoneme ConversionAug 04 2017Grapheme-to-phoneme conversion (g2p) is necessary for text-to-speech and automatic speech recognition systems. Most g2p systems are monolingual: they require language-specific data or handcrafting of rules. Such systems are difficult to extend to low ... More

PBW bases and marginally large tableaux in type DJun 08 2016We give an explicit description of the unique crystal isomorphism between two realizations of $B(\infty)$ in type $D$: that using marginally large tableaux and that using PBW monomials with respect to one particularly nice reduced expression of the longest ... More

Computing in permutation groups without memoryOct 22 2013Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since they typically involve updates ... More

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent methodAug 08 2016We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference ... More

The effects of non-uniform drive on plasma filamentsOct 10 2018Wendelstein 7-X core fueling is primarily achieved through pellet injection. The trajectory of plasmoids from an ablating pellet is an ongoing research question, which is complicated by the complex magnetic geometry of W7-X; curvature drive varies significantly ... More

Highest weights for truncated shifted Yangians and product monomial crystalsNov 30 2015Truncated shifted Yangians are a family of algebras which are natural quantizations of slices in the affine Grassmannian. We study the highest weight representations of these algebras. In particular, we conjecture that the possible highest weights for ... More

Ranking and Tradeoffs in Sponsored Search AuctionsApr 29 2013In a sponsored search auction, decisions about how to rank ads impose tradeoffs between objectives such as revenue and welfare. In this paper, we examine how these tradeoffs should be made. We begin by arguing that the most natural solution concept to ... More

Sparse Sequence-to-Sequence ModelsMay 14 2019Sequence-to-sequence models are a powerful workhorse of NLP. Most variants employ a softmax transformation in both their attention mechanism and output layer, leading to dense alignments and strictly positive output probabilities. This density is wasteful, ... More

WIYN Open Cluster Study LXII: Comparison of Isochrone Systems using Deep Multi-Band Photometry of M35Aug 07 2014Aug 08 2014Current generation stellar isochrone models exhibit non-negligible discrepancies due to variations in the input physics. The success of each model is determined by how well it fits the observations, and this paper aims to disentangle contributions from ... More

Sparse Sequence-to-Sequence ModelsMay 14 2019Jun 12 2019Sequence-to-sequence models are a powerful workhorse of NLP. Most variants employ a softmax transformation in both their attention mechanism and output layer, leading to dense alignments and strictly positive output probabilities. This density is wasteful, ... More

The potential of Red Supergiants as extra-galactic abundance probes at low spectral resolutionMay 06 2010Red Supergiants (RSGs) are among the brightest stars in the local universe, making them ideal candidates with which to probe the properties of their host galaxies. However, current quantitative spectroscopic techniques require spectral resolutions of ... More

On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor productsJun 20 2018Nov 26 2018Truncated shifted Yangians are a family of algebras which naturally quantize slices in the affine Grassmannian. These algebras depend on a choice of two weights $\lambda$ and $\mu$ for a Lie algebra $\mathfrak{g}$, which we will assume is simply-laced. ... More

Towards Vision-Based Deep Reinforcement Learning for Robotic Motion ControlNov 12 2015Nov 13 2015This paper introduces a machine learning based system for controlling a robotic manipulator with visual perception only. The capability to autonomously learn robot controllers solely from raw-pixel images and without any prior knowledge of configuration ... More

Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR modelApr 22 2010This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated ... More

Consequences and Limits of Nonlocal StrategiesApr 12 2004Jan 11 2010This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible ... More

Assessing The Factual Accuracy of Generated TextMay 30 2019We propose a model-based metric to estimate the factual accuracy of generated text that is complementary to typical scoring schemes like ROUGE (Recall-Oriented Understudy for Gisting Evaluation) and BLEU (Bilingual Evaluation Understudy). We introduce ... More

Place Categorization and Semantic Mapping on a Mobile RobotJul 09 2015In this paper we focus on the challenging problem of place categorization and semantic mapping on a robot without environment-specific training. Motivated by their ongoing success in various visual recognition tasks, we build our system upon a state-of-the-art ... More

Quantum quincunx in cavity quantum electrodynamicsJul 04 2002Apr 13 2003We introduce the quantum quincunx, which physically demonstrates the quantum walk and is analogous to Galton's quincunx for demonstrating the random walk. In contradistinction to the theoretical studies of quantum walks over orthogonal lattice states, ... More

Resonant Cascaded Down-ConversionDec 27 2008We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO present two \chi^2 level oscillation thresholds that are ... More

Generating Wikipedia by Summarizing Long SequencesJan 30 2018We show that generating English Wikipedia articles can be approached as a multi- document summarization of source documents. We use extractive summarization to coarsely identify salient information and a neural abstractive model to generate the article. ... More

The progenitor mass of the magnetar SGR1900+14Oct 26 2009Magnetars are young neutron stars with extreme magnetic fields (B > 10^{14}-10^{15}G). How these fields relate to the properties of their progenitor stars is not yet clearly established. However, from the few objects associated with young clusters it ... More

Perfectoid covers of abelian varietiesApr 12 2018For an abelian variety $A$ over an algebraically closed non-archimedean field of residue characteristic $p$, we show that there exists a perfectoid space which is the tilde-limit of $\varprojlim_{[p]}A$.

Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian ComputationAug 01 2010We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are ... More

A Modular Benchmarking Infrastructure for High-Performance and Reproducible Deep LearningJan 29 2019Jun 13 2019We introduce Deep500: the first customizable benchmarking infrastructure that enables fair comparison of the plethora of deep learning frameworks, algorithms, libraries, and techniques. The key idea behind Deep500 is its modular design, where deep learning ... More

Verifying Atom Entanglement Schemes by Testing Bell's InequalityFeb 16 2001Recent experiments to test Bell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests ... More

Wetting Phase Transition at the Surface of Liquid Ga-Bi alloys: An X-ray Reflectivity StudyJul 11 2004X-ray reflectivity measurements of the binary liquid Ga-Bi alloy reveal a dramatically different surface structure above and below the monotectic temperature $T_{mono}=222^{\circ}$ C. A Gibbs-adsorbed Bi monolayer resides at the surface at both regimes. ... More

X-ray study of the liquid potassium surface: structure and capillary wave excitationsJun 24 2004We present x-ray reflectivity and diffuse scattering measurements from the liquid surface of pure potassium. They strongly suggest the existence of atomic layering at the free surface of a pure liquid metal with low surface tension. Prior to this study, ... More

Surface Structure of Liquid Metals and the Effect of Capillary Waves: X-ray Studies on Liquid IndiumJun 24 2004We report x-ray reflectivity (XR) and small angle off-specular diffuse scattering (DS) measurements from the surface of liquid Indium close to its melting point of $156^\circ$C. From the XR measurements we extract the surface structure factor convolved ... More

Red Supergiant Stars as Cosmic Abundance Probes. III. NLTE effects in J-band Magnesium linesDec 19 2014Feb 26 2015Non-LTE calculations for Mg I in red supergiant stellar atmospheres are presented to investigate the importance of non-LTE for the formation of Mg I lines in the NIR J-band. Recent work using medium resolution spectroscopy of atomic lines in the J-band ... More

Red Supergiant Stars as Cosmic Abundance Probes: NLTE Effects in J-band Iron and Titanium LinesApr 02 2012Detailed non-LTE calculations for red supergiant stars are presented to investigate the influence of NLTE on the formation of atomic iron and titanium lines in the J-band. With their enormous brightness at J-band red supergiant stars are ideal probes ... More

A massive cluster of Red Supergiants at the base of the Scutum-Crux armAug 06 2007Sep 25 2007We report on the unprecedented Red Supergiant (RSG) population of a massive young cluster, located at the base of the Scutum-Crux Galactic arm. We identify candidate cluster RSGs based on {\it 2MASS} photometry and medium resolution spectroscopy. With ... More

Regression Monte Carlo for Microgrid ManagementFeb 28 2018We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production ... More

Incorporating Hierarchical Structure Into Dynamic Systems: An Application Of Estimating HIV Epidemics At Sub-National And Sub-Population LevelFeb 18 2016Dynamic models have been successfully used in producing estimates of HIV epidemics at national level, due to their epidemiological nature and their ability to simultaneously estimate prevalence, incidence, and mortality rates. Recently, HIV interventions ... More

The Effelsberg-Bonn HI Survey (EBHIS)Apr 06 2011The Effelsberg-Bonn HI survey (EBHIS) comprises an all-sky survey north of Dec = -5 degrees of the Milky Way and the local volume out to a red-shift of z ~ 0.07. Using state of the art Field Programmable Gate Array (FPGA) spectrometers it is feasible ... More

Surface layering of liquids: The role of surface tensionJun 24 2004Recent measurements show that the free surfaces of liquid metals and alloys are always layered, regardless of composition and surface tension; a result supported by three decades of simulations and theory. Recent theoretical work claims, however, that ... More

Verification of BOUT++ by the Method of Manufactured SolutionsFeb 22 2016BOUT++ is a software package designed for solving plasma fluid models. It has been used to simulate a wide range of plasma phenomena ranging from linear stability analysis to 3D plasma turbulence, and is capable of simulating a wide range of drift-reduced ... More

Deep Reinforcement Learning with Attention for Slate Markov Decision Processes with High-Dimensional States and ActionsDec 03 2015Dec 16 2015Many real-world problems come with action spaces represented as feature vectors. Although high-dimensional control is a largely unsolved problem, there has recently been progress for modest dimensionalities. Here we report on a successful attempt at addressing ... More

A Modular Benchmarking Infrastructure for High-Performance and Reproducible Deep LearningJan 29 2019We introduce Deep500: the first customizable benchmarking infrastructure that enables fair comparison of the plethora of deep learning frameworks, algorithms, libraries, and techniques. The key idea behind Deep500 is its modular design, where deep learning ... More

Fine-Grained Classification via Mixture of Deep Convolutional Neural NetworksNov 30 2015We present a novel deep convolutional neural network (DCNN) system for fine-grained image classification, called a mixture of DCNNs (MixDCNN). The fine-grained image classification problem is characterised by large intra-class variations and small inter-class ... More

Red Supergiants as Cosmic Abundance Probes: The Magellanic CloudsApr 14 2015Red Supergiants (RSGs) are cool (~4000K), highly luminous stars (L - 10^5 Lsun), and are among the brightest near-infrared (NIR) sources in star-forming galaxies. This makes them powerful probes of the properties of their host galaxies, such as kinematics ... More

Red Supergiant Stars as Cosmic Abundance Probes: II. NLTE Effects in J-band Silicon LinesDec 11 2012Medium resolution J-band spectroscopy of individual red supergiant stars is a promising tool to investigate the chemical composition of the young stellar population in star forming galaxies. As a continuation of recent work on iron and titanium, detailed ... More

Betti Tables of Reducible Algebraic CurvesOct 10 2012We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti table for line arrangements that satisfy certain hypotheses. We also give ... More

Wetting behavior at the free surface of a liquid gallium-bismuth alloy: An X-ray reflectivity study close to the bulk monotectic pointJun 26 2004We present x-ray reflectivity measurements from the free surface of a liquid gallium-bismuth alloy (Ga-Bi) in the temperature range close to the bulk monotectic temperature $T_{mono} = 222$C. Our measurements indicate a continuous formation of a thick ... More

Microscopic View on Short-Range Wetting at the Free Surface of the Binary Metallic Liquid Gallium-Bismuth: An X-ray Reflectivity and Square Gradient Theory StudyJun 26 2004We present an x-ray reflectivity study of wetting at the free surface of the binary liquid metal gallium-bismuth (Ga-Bi) in the region where the bulk phase separates into Bi-rich and Ga-rich liquid phases. The measurements reveal the evolution of the ... More

Observational signatures of a kink-unstable coronal flux rope using Hinode/EISMay 15 2017The signatures of energy release and energy transport for a kink-unstable coronal flux rope are investigated via forward modelling. Synthetic intensity and Doppler maps are generated from a 3D numerical simulation. The CHIANTI database is used to compute ... More

Conformal dynamics problem listJan 18 1990This is a list of unsolved problems given at the Conformal Dynamics Conference which was held at SUNY Stony Brook in November 1989. Problems were contributed by the editor and the other authors.

The chemical abundances in the Galactic Centre from the atmospheres of Red SupergiantsNov 19 2008The Galactic Centre (GC) has experienced a high degree of recent star-forming activity, as evidenced by the large number of massive stars currently residing there. The relative abundances of chemical elements in the GC may provide insights into the origins ... More

SCRAM: Spatially Coherent Randomized Attention MapsMay 24 2019Attention mechanisms and non-local mean operations in general are key ingredients in many state-of-the-art deep learning techniques. In particular, the Transformer model based on multi-head self-attention has recently achieved great success in natural ... More

Plasma Panel Detectors for MIP Detection for the SLHC and a Test Chamber DesignJul 03 2010Performance demands for high and super-high luminosity at the LHC (up to 10^35 cm^(-2) sec^(-1) after the 2017 shutdown) and at future colliders demand high resolution tracking detectors with very fast time response and excellent temporal and spatial ... More

The cool supergiant population of the massive young star cluster RSGC1Nov 29 2007We present new high-resolution near-IR spectroscopy and OH maser observations to investigate the population of cool luminous stars of the young massive Galactic cluster RSGC1. Using the 2.293\micron CO-bandhead feature, we make high-precision radial velocity ... More

A model for sequential evolution of ligands by exponential enrichment (SELEX) dataMay 08 2012Sep 27 2012A Systematic Evolution of Ligands by EXponential enrichment (SELEX) experiment begins in round one with a random pool of oligonucleotides in equilibrium solution with a target. Over a few rounds, oligonucleotides having a high affinity for the target ... More

Energy absorption in the laser-QED regimeJan 23 2019Jan 28 2019A theoretical and numerical investigation of non-ponderomotive absorption at laser intensities relevant to quantum electrodynamics is presented. It is predicted that there is a regime change in the dependence of fast electron energy on incident laser ... More

Red Supergiants as Cosmic Abundance Probes: massive star clusters in M83, and the mass-metallicity relation of nearby galaxiesAug 29 2017We present an abundance analysis of seven super-star clusters in the disk of M83. The near-infrared spectra of these clusters are dominated by Red Supergiants, and the spectral similarity in the J-band of such stars at uniform metallicity means that the ... More

Unusual structures inherent in point pattern data predict colon cancer patient survivalMay 16 2017Cancer patient diagnosis and prognosis is informed by assessment of morphological properties observed in patient tissue. Pathologists normally carry out this assessment, yet advances in computational image analysis provide opportunities for quantitative ... More

Chemical abundance patterns in the inner Galaxy: the Scutum Red Supergiant ClustersFeb 13 2009The location of the Scutum Red-Supergiant (RSG) clusters at the end of the Galactic Bar makes them an excellent probe of the Galaxy's secular evolution; while the clusters themselves are ideal testbeds in which to study the predictions of stellar evolutionary ... More

What if the LHC does not find supersymmetry in the sqrt(s)=7 TeV run?Feb 23 2011We investigate the implications for supersymmetry from an assumed absence of any signal in the first period of LHC data taking at 7 TeV center-of-mass energy and with 1 to 7 fb^(-1) of integrated luminosity. We consider the zero-lepton plus four jets ... More

The temperatures of Red SupergiantsFeb 12 2013We present a re-appraisal of the temperatures of Red Supergiants (RSGs) using their optical and near-infrared spectral energy distributions (SEDs). We have obtained data of a sample of RSGs in the Magellanic Clouds using VLT+XSHOOTER, and we fit MARCS ... More

Baryon Content of Massive Galaxy Clusters at z=0-0.6Dec 07 2011We study the relationship between two major baryonic components in galaxy clusters, namely the stars in galaxies, and the ionized gas in the intracluster medium (ICM), using 94 clusters that span the redshift range 0-0.6. Accurately measured total and ... More

Novel approaches to dark-matter detection using space-time separated clocksFeb 19 2019We discuss the theoretical analysis and interpretation of space-time separated clock experiments in the context of a space-time varying scalar field that is non-universally coupled to the standard model fields. If massive, such a field is a candidate ... More

A new presentation of the cyclotomic Cherednik algebraSep 18 2016We give an alternate presentation of the cyclotomic rational Cherednik algebra. This presentation has a diagrammatic flavor, and it provides a simple explanation of several surprising facts about this algebra. It allows direct proof of the connection ... More

Big Bang Models in String TheoryMay 19 2006Dec 20 2006These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a ... More

Dimension-free Maximal Inequalities for Spherical Means in the HypercubeSep 17 2013Dec 08 2014We extend the main result of \cite{HKS} -- the existence of dimension-free $L^2$-bounds for the spherical maximal function in the hypercube -- to all $L^p, p > 1$. Our approach is motivated by the spectral technique developed in \cite{S} and \cite{NS} ... More

Improved mixing time bounds for the Thorp shuffle and L-reversal chainFeb 04 2008We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying a condition that involves only pairs of cards, then we use it to obtain improved bounds for two previously studied models. E. Thorp introduced the following card shuffling ... More

Singularity formation in the Yang-Mills flowOct 08 2002May 31 2003This paper studies rapidly forming singularities in the Yang-Mills flow. It is shown that a sequence of blow-ups near the singular point converges, modulo the gauge group, to a homothetically shrinking soliton with non-zero curvature. The proof uses Hamilton's ... More

Renormalization Group and Black Hole Production in Large Extra DimensionsJul 31 2007Aug 22 2007It has been suggested that the existence of a non-Gaussian fixed point in general relativity might cure the ultraviolet problems of this theory. Such a fixed point is connected to an effective running of the gravitational coupling. We calculate the effect ... More

Construction of Maximal Hypersurfaces with Boundary ConditionsAug 22 2014Oct 07 2016We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of ... More

The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundaryJan 07 2014Feb 25 2014I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism is a chart independent ... More

Relative entropy and the Pinsker product formula for sofic groupsMay 05 2016We continue our study of the outer Pinsker factor for probability measure-preserving actions of sofic groups. Using the notion of doubly quenched convergence developed by Austin, we prove that in many cases the outer Pinsker factor of a product action ... More

Infinite-dimensional $\ell^1$ minimization and function approximation from pointwise dataMar 09 2015Jun 23 2016We consider the problem of approximating a smooth function from finitely-many pointwise samples using $\ell^1$ minimization techniques. In the first part of this paper, we introduce an infinite-dimensional approach to this problem. Three advantages of ... More

Subelliptic Resolvent Estimates for Non-self-adjoint Semiclassical Schrodinger OperatorsSep 02 2016Oct 01 2016In this paper we prove a subelliptic resolvent estimate for a class of semiclassical non-self-adjoint Schr\"odinger operators with purely imaginary potentials when the spectral parameter is in a parabolic neighborhood of the imaginary axis.

A new infinite family of non-abelian strongly real Beauville $p$-groups for every odd prime $p$Aug 02 2016We prove that there exist infinitely many a non-abelian strongly real Beauville $p$-group for every prime $p$. Previously only finitely many in the case $p=2$ have been constructed.

The Deligne-Mostow list and special families of surfacesJul 14 2016We study whether there exist infinitely many surfaces with given discrete invariants for which the H^2 is of CM type. This is a surface analogue of a conjecture of Coleman about curves. We construct a large number of examples of families of surfaces with ... More

Strongly Real Beauville GroupsMay 29 2014A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We ... More

Sarkozy's theorem in function fieldsMay 24 2016Jun 02 2016S\'ark\"ozy proved that dense sets of integers contain two elements differing by a $k$th power. The bounds in quantitative versions of this theorem are rather weak compared to what is expected. We prove a version of S\'ark\"ozy's theorem for polynomials ... More

Sparse 3D convolutional neural networksMay 12 2015Aug 25 2015We have implemented a convolutional neural network designed for processing sparse three-dimensional input data. The world we live in is three dimensional so there are a large number of potential applications including 3D object recognition and analysis ... More

A Data Science Course for Undergraduates: Thinking with DataMar 18 2015Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the increasingly sophisticated ... More

The critical CoHA of a quiver with potentialNov 27 2013Oct 27 2016Pursuing the similarity between the Kontsevich--Soibelman construction of the cohomological Hall algebra of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the inetgrality conjecture ... More

Invariance of orientation data for ind-constructible Calabi-Yau $A_{\infty}$ categories under derived equivalenceJun 28 2010Oct 25 2011We study orientation data, as introduced by Kontsevich and Soibelman in order to define well-behaved integration maps from the motivic Hall algebra of 3-dimensional Calabi-Yau categories to rings of motives. We start with an example that demonstrates ... More

Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropyFeb 18 2019We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an algebraic action of $G$ on $X,$ there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly ... More

Long arithmetic progressions of primesAug 02 2005This is an article for a general mathematical audience on the author's work, joint with Terence Tao, establishing that there are arbitrarily long arithmetic progressions of primes. It is based on several one hour lectures, chiefly given at British universities. ... More

Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and SarnakNov 17 2009Nov 18 2009This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer science. We ... More

Sum-product phenomena in F_p: a brief introductionApr 14 2009These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains ... More

Independence Tuples and Deninger's ProblemFeb 12 2015Apr 27 2016Motivated by our results in "Polish Models and Sofic Entropy," we define modified version of the independence tuples for sofic entropy developed by Kerr and Li. These modified version essentially require that the independence sequences give rise to representations ... More

Polish Models and Sofic EntropyNov 06 2014Dec 31 2015For actions of a sofic group on probability spaces, the entropy has been defined by Bowen, with an extension by Kerr-Li. In particular, when the action is by homeomorphisms of a compact space preserving a given measure, Kerr-Li show one can compute the ... More