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Cross sections of Borel flows with restrictions on the distance setApr 08 2016Given a set of positive reals, we provide a necessary and sufficient condition for a free Borel flow to admit a cross section with all distances between adjacent points coming from this set.

On time change equivalence of Borel flowsSep 19 2016This paper addresses the notion of time change equivalence for Borel multidimensional flows. We show that all free flows are time change equivalent up to a compressible set. An appropriate version of this result for non-free flows is also given.

Micrometeoroid Events in LISA PathfinderMay 07 2019The zodiacal dust complex, a population of dust and small particles that pervades the Solar System, provides important insight into the formation and dynamics of planets, comets, asteroids, and other bodies. Here we present a new set of data obtained ... More

Gravitational-wave parameter estimation with gaps in LISA: a Bayesian data augmentation methodJul 10 2019By listening to gravity in the low frequency band, between 0.1 mHz and 1 Hz, the future space-based gravitational-wave observatory LISA will be able to detect tens of thousands of astrophysical sources from cosmic dawn to the present. The detection and ... More

Topological classification of time-asymmetry in unitary quantum processesMar 07 2017Effective gauge fields have allowed the emulation of matter under strong magnetic fields leading to the realization of Harper-Hofstadter, Haldane models, and led to demonstrations of one-way waveguides and topologically protected edge states. Central ... More

Where are the Intermediate Mass Black Holes?Mar 19 2019Observational evidence has been mounting for the existence of intermediate mass black holes (IMBHs, 10^2-10^5 Msun), but observing them at all, much less constraining their masses, is very challenging. In one theorized formation channel, IMBHs are the ... More

Regular cross sections of Borel flowsJul 08 2015Jul 15 2015Any free Borel flow is shown to admit a cross section with only two possible distances between adjacent points. Non smooth flows are proved to be Lebesgue orbit equivalent if and only if they admit the same number of invariant ergodic probability measures. ... More

Graev ultrametrics and free products of Polish groupsDec 12 2012Oct 10 2013We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two Polish groups ... More

Apex Exponents for Polymer--Probe InteractionsSep 02 2004We consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents $\gamma_1$ and $\gamma_2$, characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, vary continuously ... More

Automatic continuity for homomorphisms into free productsDec 07 2012Jun 11 2013A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In particular, any completely ... More

Providing better confidentiality and authentication on the Internet using Namecoin and MinimaLTJul 24 2014In this paper, we introduce a duo of improvements for the Internet that would lead to better security. The authentication model on the Internet is broken and TLS connections have a considerable overhead. We try to address those issues with changes in ... More

Graph-Guided Banding of the Covariance MatrixJun 01 2016Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix ... More

A comment on the integration of Leibniz algebrasNov 26 2010Jan 20 2011In this note we point out that the definition of the universal enveloping dialgebra for a Leibniz algebra is consistent with the interpretation of a Leibniz algebra as a generalization not of a Lie algebra, but of the adjoint representation of a Lie algebra. ... More

Intermediate asymptotics for critical and supercritical aggregation equations and Patlak-Keller-Segel modelsSep 30 2010Mar 27 2011We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose of this work is to identify when solutions decay to the self-similar ... More

A proof of the Andre-Oort conjecture for A_gJun 04 2015Dec 01 2015We give a proof of the Andr\'e-Oort conjecture for $\mathcal{A}_g$ - the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven `averaged' version of the Colmez conjecture yields lower bounds for Galois ... More

Symmetries in LDDMM with higher order momentum distributionsJun 14 2013Jul 17 2013In some implementations of the Large Deformation Diffeomorphic Metric Mapping formulation for image registration we consider the motion of particles which locally translate image data. We then lift the motion of the particles to obtain a motion on the ... More

Extended AIGER Format for SynthesisMay 22 2014May 26 2014We extend the AIGER format, as used in HWMCC, to a format that is suitable to define synthesis problems with safety specifications. We recap the original format and define one format for posing synthesis problems and one for solutions of synthesis problems ... More

gadfly: A pandas-based Framework for Analyzing GADGET Simulation DataMar 16 2016We present the first public release (v0.1) of the open-source GADGET Dataframe Library: gadfly. The aim of this package is to leverage the capabilities of the broader python scientific computing ecosystem by providing tools for analyzing simulation data ... More

Ultra-high field enhancing in Split Ring Resonators by azimuthally polarized excitationNov 25 2011We study the field enhancement and resonance frequencies in split-ring resonators (SRR) illuminated by azimuthally polarized light. We find that compared to linearly polarized illumination, the azimuthally polarized illumination increase the intensity ... More

Hessenberg decomposition of matrix fields and bounded operator fieldsJun 14 2009Hessenberg decomposition is the basic tool used in computational linear algebra to approximate the eigenvalues of a matrix. In this article, we generalize Hessenberg decomposition to continuous matrix fields over topological spaces. This works in great ... More

Ikehara-type theorem involving boundednessJul 03 2008Consider any Dirichlet series sum a_n/n^z with nonnegative coefficients a_n and finite sum function f(z)=f(x+iy) when x is greater than 1. Denoting the partial sum a_1+...+a_N by s_N, the paper gives the following necessary and sufficient condition in ... More

Orthomodular lattices, Foulis Semigroups and Dagger Kernel CategoriesDec 04 2009Jun 18 2010This paper is a sequel to arXiv:0902.2355 and continues the study of quantum logic via dagger kernel categories. It develops the relation between these categories and both orthomodular lattices and Foulis semigroups. The relation between the latter two ... More

On Finite Memory Universal Data Compression and Classification of Individual SequencesDec 04 2006Jan 24 2013Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a-priori information about X is available at the encoder, ... More

Simulating many-body lattice systems on a single nano-mechanical resonatorSep 12 2012We show that lattice systems, such as the Bose-Hubbard model, can be simulated on a single nano- or micro-mechanical resonator, by exploiting its many modes. The on-site Hamiltonians are engineered by coupling the mechanical modes to the modes of a pair ... More

Applications of Feedback Control in Quantum SystemsMay 02 2006We give an introduction to feedback control in quantum systems, as well as an overview of the variety of applications which have been explored to date. This introductory review is aimed primarily at control theorists unfamiliar with quantum mechanics, ... More

A simple formula for pooling knowledge about a quantum systemMar 24 2005When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the states-of-knowledge of the respective observers. Here we derive ... More

The Topology of Mobility-Gapped InsulatorsNov 19 2018Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall ... More

The pure cactus group is residually nilpotentApr 24 2018We show that the pure cactus group $\Gamma_{n+1}$ is residually nilpotent and exhibit a surjective homomorphism $\Gamma_{n+1} \to (\mathbb{Z}/2\mathbb{Z})^{2^n-n(n+1)/2-1}$ whose kernel is residually torsion-free nilpotent.

Climbing the Kaggle Leaderboard by Exploiting the Log-Loss OracleJul 06 2017In the context of data-mining competitions (e.g., Kaggle, KDDCup, ILSVRC Challenge), we show how access to an oracle that reports a contestant's log-loss score on the test set can be exploited to deduce the ground-truth of some of the test examples. By ... More

Unsupervised Learning for Lexicon-Based ClassificationNov 21 2016In lexicon-based classification, documents are assigned labels by comparing the number of words that appear from two opposed lexicons, such as positive and negative sentiment. Creating such words lists is often easier than labeling instances, and they ... More

Ordered Factorizations with $k$ FactorsOct 16 2016We give an overview of combinatoric properties of the number of ordered $k$-factorizations $f_k(n,l)$ of an integer, where every factor is greater or equal to $l$. We show that for a large number $k$ of factors, the value of the cumulative sum $F_k(x,l)=\sum\nolimits_{n\leq ... More

Fully Convolutional Networks for Text ClassificationFeb 14 2019In this work I propose a new way of using fully convolutional networks for classification while allowing for input of any size. I additionally propose two modifications on the idea of attention and the benefits and detriments of using the modifications. ... More

Stable Higgs bundles and Hermitian-Einstein metrics on non-Kähler manifoldsOct 17 2011Oct 27 2014Let $X$ be a compact Gauduchon manifold, and let $E$ and $V_0$ be holomorphic vector bundles over $X$. Suppose that $E$ is stable when considering all subsheaves preserved by a Higgs field $\theta\in H^0($End$(E)\otimes V_0)$. Then a modified version ... More

Existence of approximate Hermitian-Einstein structures on semi-stable bundlesDec 08 2010Aug 26 2013The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is bounded from below. This implies that E admits an approximate ... More

Assessment of electrical and infrastructure recovery in Puerto Rico following hurricane Maria using a multisource time series of satellite imageryJul 16 2018Puerto Rico suffered severe damage from the category 5 hurricane (Maria) in September 2017. Total monetary damages are estimated to be ~92 billion USD, the third most costly tropical cyclone in US history. The response to this damage has been tempered ... More

Algorithms for computing linear invariants if directed graphsMar 11 2005Call two pairs $(M,N)$ and $(M',N')$ of $m\times n$ matrices over a field $K$, \emph{simultaneously K-equivalent} if there exist square invertible matrices $S,T$ over K, with $M'=SMT$ and $N'=SNT$. Kronecker \cite{Kronecker} has given a complete set of ... More

Schooling Choice, Labour Market Matching, and WagesMar 24 2018Jul 04 2018This paper develops an empirical two-sided matching model with endogenous pre-investment. The model can be used to measure the impact of frictions in labour markets using a single cross-section of matched employer-employee data. The observed matching ... More

Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More

Spaces of rational maps and the Stone-Weierstrass TheoremJul 08 2003Sep 30 2004It is shown that Segal's theorem on the spaces of rational maps from CP^1 to CP^n can be extended to the spaces of continuous rational maps from CP^m to CP^n for any m less than or equal to n. The tools are the Stone-Weierstrass Theorem and Vassiliev's ... More

Short Ropes and Long KnotsOct 06 1998Dec 10 2000A rope is a non-singular embedding of a closed interval into R^3, which sends the ends of the interval to some fixed points A and B such that |AB|=1. A rope is short if its length is less than 3. The main result of the paper is that the fundamental group ... More

Some Singular Limit Laminations of Embedded Minimal Planar DomainsJul 19 2011In this paper we give two examples of sequences of embedded minimal planar domains in $\mathbb{R}^3$ which converge to singular laminations of $\mathbb{R}^3$. In contrast with the situation for embedded minimal disks, these examples do not arise from ... More

Floer homology of surgeries on two-bridge knotsApr 04 2002Nov 02 2002We compute the Ozsvath-Szabo Floer homologies HF^{+-} and HF-hat for three-manifolds obtained by integer surgery on a two-bridge knot.

Floer homology and knot complementsJun 26 2003We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CF_r. It carries information about the Floer homology of large integral ... More

Schooling Choice, Labour Market Matching, and WagesMar 24 2018Jul 02 2019We develop inference for a two-sided matching model where the characteristics of agents on one side of the market are endogenous due to pre-matching investments. The model can be used to measure the impact of frictions in labour markets using a single ... More

Derived Algebraic Geometry III: Commutative AlgebraMar 07 2007May 04 2009This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.

Near-group categoriesSep 07 2002Aug 27 2003We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules, and an explicit ... More

Quivers with relations arising from Koszul algebras of $\mathfrak g$-invariantsOct 08 2008Let $\mathfrak g$ be a complex simple Lie algebra and let $\Psi$ be an extremal set of positive roots. One associates with $\Psi$ an infinite dimensional Koszul algebra $\bold S_\Psi^{\lie g}$ which is a graded subalgebra of the locally finite part of ... More

Simplicity of finitely-aligned k-graph C*-algebrasOct 25 2008It is shown that no local periodicity is equivalent to the aperiodicity condition for arbitrary finitely-aligned k-graphs. This allows us to conclude that C*(\Lambda) is simple if and only if \Lambda is cofinal and has no local periodicity.

Conditional least squares estimation in nonstationary nonlinear stochastic regression modelsJan 13 2010Let $\{Z_n\}$ be a real nonstationary stochastic process such that $E(Z_n|{\mathcaligr F}_{n-1})\stackrel{\mathrm{a.s.}}{<}\infty$ and $E(Z^2_n|{\mathcaligr F}_{n-1})\stackrel{\mathrm{a.s.}}{<}\infty$, where $\{{\mathcaligr F}_n\}$ is an increasing sequence ... More

Partial monoids and Dold-Thom functorsDec 20 2007Feb 06 2013Dold-Thom functors are generalizations of infinite symmetric products, where integer multiplicities of points are replaced by composable elements of a partial abelian monoid. It is well-known that for any connective homology theory, the machinery of $\Gamma$-spaces ... More

Unordered Factorizations with $k$ PartsJul 17 2019We derive new formulas for the number of unordered (distinct) factorizations with $k$ parts of a positive integer $n$ as sums over the partitions of $k$ and an auxiliary function, the number of partitions of the prime exponents of $n$, where the parts ... More

From Hierarchical to Relative HyperbolicityMay 29 2019Jul 15 2019We provide a simple, combinatorial criteria for a hierarchically hyperbolic space to be relatively hyperbolic by proving a new formulation of relative hyperbolicity in terms of hierarchy structures. In the case of clean hierarchically hyperbolic groups, ... More

Bost-Connes type systems for function fieldsFeb 24 2006May 01 2012We describe a construction which associates to any function field $k$ and any place $\infty$ of $k$ a $C^*$-dynamical system $(C_{k,\infty},\sigma_t)$ that is analogous to the Bost-Connes system associated to $\QQ$ and its archimedian place. Our construction ... More

Test Sensitivity in the Computer-Aided Detection of Breast Cancer from Clinical Mammographic Screening: a Meta-analysisFeb 06 2013Objectives: To assess evaluative methodologies for comparative measurements of test sensitivity in clinical mammographic screening trials of computer-aided detection (CAD) technologies. Materials and Methods: This meta-analysis was performed by analytically ... More

A Statistical Significance Simulation Study for the General ScientistSep 29 2011When a scientist performs an experiment they normally acquire a set of measurements and are expected to demonstrate that their results are "statistically significant" thus confirming whatever hypothesis they are testing. The main method for establishing ... More

Semiclassical resolvent bounds in dimension twoApr 13 2016In this note we give an elementary proof of weighted resolvent bounds for semiclassical Schr\"odinger operators in dimension two. We require mild decay conditions on the potential. The resolvent norm grows exponentially in the inverse semiclassical parameter, ... More

Morse Matchings on a HypersimplexNov 07 2012We present a family of complete acyclic Morse matchings on the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. In a future paper we will utilize these matchings to ... More

Derived Algebraic Geometry V: Structured SpacesMay 04 2009In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.

Stanley-Wilf limits are typically exponentialOct 31 2013For a permutation $\pi$, let $S_{n}(\pi)$ be the number of permutations on $n$ letters avoiding $\pi$. Marcus and Tardos proved the celebrated Stanley-Wilf conjecture that $L(\pi)= \lim_{n \to \infty} S_n(\pi)^{1/n}$ exists and is finite. Backed by numerical ... More

A bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurementsDec 01 2004Jan 24 2006The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the Holevo bound ... More

Topics in Quantum Measurement and Quantum NoiseOct 05 1998Oct 06 1998In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be described ... More

Lower Bounds for non-Archimedean Lyapunov ExponentsOct 08 2015Oct 18 2016Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\textbf{P}^1$ denote the Berkovich projective line over $K$. The Lyapunov exponent for a rational map $\phi\in K(z)$ of degree $d\geq 2$ measures the exponential rate ... More

An Equidistribution Result For Dynamical Systems on the Berkovich Projective LineSep 16 2014Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\phi\in K(z)$ with $\textrm{deg}(\phi) \geq 2$. In this paper we consider the functions $\textrm{ordRes}_{\phi^n}(x)$ that measure the resultant of $\phi$ at points in ... More

Feedback Control Using Only Quantum Back-ActionApr 24 2009The traditional approach to feedback control is to apply forces to a system by modifying the Hamiltonian. Here we show that quantum systems can be controlled without any Hamiltonian feedback, purely by exploiting the random quantum back-action of a continuous ... More

Feedback control for communication with non-orthogonal statesJan 24 2006Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this measurement ... More

Some properties of the Higgs sector of the Next-to Minimal SuperSymmetric ModelJun 16 2011The problems of the standard model are briefly reviewed and the motivations for introducing supersymmetry are discussed. Two realistic supersymmetric models; the Minimal SuperSymmetric Model, MSSM, and its proposed extension NMSSM are introduced briefly ... More

A Bound on the Norm of Shortest Vectors in Lattices Arising from CM Number FieldsOct 29 2012This paper partially addresses the problem of characterizing the lengths of vectors in a family of Euclidean lattices that arise from any CM number field. We define a modified quadratic form on these lattices, the weighted norm, that contains the standard ... More

Understanding ACT-R - an Outsider's PerspectiveJun 01 2013The ACT-R theory of cognition developed by John Anderson and colleagues endeavors to explain how humans recall chunks of information and how they solve problems. ACT-R also serves as a theoretical basis for "cognitive tutors", i.e., automatic tutoring ... More

Holography Inspired Stringy HadronsFeb 01 2016Jun 30 2016Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons and glueballs as strings in four dimensional space time. The models are based on a "map" from stringy hadrons of holographic confining backgrounds. In ... More

Langevin process reflected on a partially elastic boundary IApr 12 2010Jul 22 2011Consider a Langevin process, that is an integrated Brownian motion, constrained to stay on the nonnegative half-line by a partially elastic boundary at 0. If the elasticity coefficient of the boundary is greater than or equal to a critical value (0.16), ... More

Jets in Nuclear Collisions: Status and PerspectiveMar 29 2005Apr 06 2005I review the status and future directions of jet-related measurements in high energy nuclear collisions and their application as a probe of QCD matter.

Measurements of High Density Matter at RHICNov 11 2002Nov 13 2002QCD predicts a phase transition between hadronic matter and a Quark Gluon Plasma at high energy density. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is a new facility dedicated to the experimental study of matter under ... More

Projective Connections and the Algebra of DensitiesAug 20 2008Projective connections first appeared in Cartan's papers in the 1920's. Since then they have resurfaced periodically in, for example, integrable systems and perhaps most recently in the context of so called projectively equivariant quantisation. We recall ... More

Multiple elliptic gamma functions associated to conesSep 08 2016We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, associated to good rational cones. We explain how good cones are related to collections of $SL_r(\mathbb{Z})$-elements and prove that the generalized multiple ... More

Automatic Classifiers as Scientific Instruments: One Step Further Away from Ground-TruthDec 19 2018Automatic detectors of facial expression, gesture, affect, etc., can serve as scientific instruments to measure many behavioral and social phenomena (e.g., emotion, empathy, stress, engagement, etc.), and this has great potential to advance basic science. ... More

Renormalization of single-ion magnetic anisotropy in the absence of Kondo effectDec 04 2017Feb 21 2018Inelastic spin flip excitations associated with single-ion magnetic anisotropy of quantum spins, can be strongly renormalized by Kondo exchange coupling to the conduction electrons in the substrate, as shown recently for the case of Co adatoms on CuN$_2$ ... More

Local energy decay for Lipschitz wavespeedsJul 20 2017May 06 2018We prove a logarithmic local energy decay rate for the wave equation with a wavespeed that is a compactly supported Lipschitz perturbation of unity. The key is to establish suitable resolvent estimates at high and low energy for the meromorphic continuation ... More

Suppression of plasma echoes and Landau damping in Sobolev spaces by weak collisions in a Vlasov-Fokker-Planck equationApr 03 2017In this paper, we study Landau damping in the weakly collisional limit of a Vlasov-Fokker-Planck equation with nonlinear collisions in the phase-space $(x,v) \in \mathbb T_x^n \times \mathbb R^n_v$. The goal is four-fold: (A) to understand how collisions ... More

Aerial UAV-IoT Sensing for Ubiquitous Immersive Communication and Virtual Human TeleportationMar 12 2017Jul 21 2017We consider UAV IoT aerial sensing that delivers multiple VR/AR immersive communication sessions to remote users. The UAV swarm is spatially distributed over a wide area of interest, and each UAV captures a viewpoint of the scene below it. The remote ... More

Another Enumeration of Caterpillar TreesOct 28 2018A caterpillar tree is a connected, acyclic, graph in which all vertices are either a member of a central path, or joined to that central path by a single edge. In other words, caterpillar trees are the class of trees which become path graphs after removing ... More

Semiclassical resolvent bound for compactly supported $L^\infty$ potentialsFeb 25 2018May 06 2018We give an elementary proof of a weighted resolvent estimate for semiclassical Schr\"odinger operators in dimension $n \ge 1$. We require the potential belong to $L^\infty(\mathbb{R}^n)$ and have compact support, but do not require that it have derivatives ... More

Measuring Compositionality in Representation LearningFeb 19 2019Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this compositional ... More

The Calculus of Democratization and DevelopmentDec 12 2017In accordance with "Democracy's Effect on Development: More Questions than Answers", we seek to carry out a study in following the description in the 'Questions for Further Study.' To that end, we studied 33 countries in the Sub-Saharan Africa region, ... More

Duality for ConvexityNov 19 2009This paper studies convex sets categorically, namely as algebras of a distribution monad. It is shown that convex sets occur in two dual adjunctions, namely one with preframes via the Boolean truth values {0,1} as dualising object, and one with effect ... More

Lower bound for the remainder in the prime-pair conjectureJun 25 2008For any positive integer r, let pi_{2r}(x) denote the number of prime pairs (p, p+2r) with p not exceeding (large) x. According to the prime-pair conjecture of Hardy and Littlewood, pi_{2r}(x) should be asymptotic to 2C_{2r}li_2(x) with an explicit positive ... More

Higher Topos TheoryAug 02 2006Jul 31 2008This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck topoi. A few ... More

The topological pigeonhole principle for ordinalsOct 09 2014Jul 12 2016Given a cardinal $\kappa$ and a sequence $\left(\alpha_i\right)_{i\in\kappa}$ of ordinals, we determine the least ordinal $\beta$ (when one exists) such that the topological partition relation \[\beta\rightarrow\left(top\,\alpha_i\right)^1_{i\in\kappa}\] ... More

(Infinity,2)-Categories and the Goodwillie Calculus IMay 04 2009May 08 2009The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is also considered). Our ... More

Quasisymmetric Functions from Combinatorial Hopf Monoids and Ehrhart TheoryMar 31 2016We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class ... More

The Hopf monoid of coloring problemsNov 13 2016We study coloring problems, which are induced subposets P of a Boolean lattice, paired with an order ideal I from the poset of intervals, ordered by inclusion. We study a quasisymmetric function associated to coloring problems, called the chromatic quasisymmetric ... More

Tensors Masquerading as Matchgates: Relaxing Planarity Restrictions on Pfaffian CircuitsOct 06 2015Oct 30 2015Holographic algorithms, alternatively known as Pfaffian circuits, have received a great deal of attention for giving polynomial-time algorithms of $\#\mathsf{P}$-hard problems. Much work has been done to determine the extent of what this machinery can ... More

Langevin process reflected on a partially elastic boundary IIMar 15 2011A particle subject to a white noise external forcing moves like a Langevin process. Consider now that the particle is reflected at a boundary which restores a portion c of the incoming speed at each bounce. For c strictly smaller than the critical value ... More

Regarding a uniqueness property of singly-periodic Scherk surfacesMar 18 2013May 13 2013Inspired by an argument of Ros [15] -- we use the L\'{o}pez-Ros deformation to give another proof of the fact -- due to Meeks and Wolf [13] -- that the only smooth, connected, singly-periodic minimal surfaces in $\Real^3$ with the area growth of two planes ... More

Lens space surgeries and a conjecture of Goda and TeragaitoMay 06 2004Mar 30 2005Using work of Ozsvath and Szabo, we show that if a nontrivial knot in S^3 admits a lens space surgery with slope p, then p <= 4g+3, where g is the genus of the knot. This is a close approximation to a bound conjectured by Goda and Teragaito.

Stable Infinity CategoriesAug 09 2006May 08 2009This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a variety of constructions. ... More

An elementary proof of the Briancon-Skoda theoremJul 01 2008Mar 26 2012We give a new elementary proof of the Brian\c{c}on-Skoda theorem, which states that for an $m$-generated ideal $\mathfrak{a}$ in the ring of germs of analytic functions at $0\in \C^n$, the $\nu$:th power of its integral closure is contained in $\mathfrak{a}$, ... More

The homology of moduli stacks of complexesJul 07 2019We compute the $E$-homology of the moduli stack $\mathcal{M}$ of objects in the derived category of a smooth complex projective variety $X$, where $E$ is a complex-oriented homology theory with rational coefficient ring. For curves, surfaces, and some ... More

Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019Jul 03 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More

The Existence of an Abelian Variety over the Algebraic Numbers isogenous to no JacobianOct 11 2010We prove the existence of an Abelian variety $A$ of dimension $g$ over $\Qa$ which is not isogenous to any Jacobian, subject to the necessary condition $g>3$. Recently, C.Chai and F.Oort gave such a proof assuming the Andr\'e-Oort conjecture. We modify ... More

Derived Algebraic Geometry II: Noncommutative AlgebraFeb 11 2007Sep 19 2007In this paper, we present an infinity-categorical version of the theory of monoidal categories. We show that the infinity category of spectra admits an essentially unique monoidal structure (such that the tensor product preserves colimits in each variable), ... More