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Improved Online Square-into-Square PackingJan 22 2014In this paper, we show an improved bound and new algorithm for the online square-into-square packing problem. This two-dimensional packing problem involves packing an online sequence of squares into a unit square container without any two squares overlapping. ... More

Algorithms to Approximate Column-Sparse Packing ProblemsNov 07 2017Aug 05 2019Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for ... More

Vertex-weighted Online Stochastic Matching with Patience ConstraintsJul 09 2019Online Bipartite Matching is a classic problem introduced by Karp, Vazirani, and Vazirani (Proc. ACM STOC, 1990) and motivated by applications such as e-commerce, online advertising, and ride-sharing. We wish to match a set of online vertices (e.g., webpage ... More

New Algorithms, Better Bounds, and a Novel Model for Online Stochastic MatchingJun 21 2016Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/e) competitive ratio in the standard adversarial online ... More

Online Stochastic Matching: New Algorithms and BoundsJun 21 2016Nov 15 2017Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/e) competitive ratio in the standard adversarial online ... More

Online Stochastic Matching: New Algorithms and BoundsJun 21 2016Jul 23 2019Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/e) competitive ratio in the standard adversarial online ... More

Attenuate Locally, Win Globally: An Attenuation-based Framework for Online Stochastic Matching with TimeoutsApr 22 2018Online matching problems have garnered significant attention in recent years due to numerous applications in e-commerce, online advertisements, ride-sharing, etc. Many of them capture the uncertainty in the real world by including stochasticity in both ... More

Algorithms to Approximate Column-Sparse Packing ProblemsNov 07 2017Dec 11 2017Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for ... More

Attenuate Locally, Win Globally: An Attenuation-based Framework for Online Stochastic Matching with TimeoutsApr 22 2018Jun 21 2019Online matching problems have garnered significant attention in recent years due to numerous applications in e-commerce, online advertisements, ride-sharing, etc. Many of them capture the uncertainty in the real world by including stochasticity in both ... More

A Bochner Formula for Harmonic Maps into Non-Positively Curved Metric SpacesMay 26 2016We study harmonic maps from Riemannian manifolds into arbitrary non-positively curved metric spaces. First we discuss the domain variation formula with special emphasis on the error terms. Expanding higher order terms of this and other formulas in terms ... More

Shift-preserving maps on $ω^*$May 04 2016The shift map $\sigma$ on $\omega^*$ is the continuous self-map of $\omega^*$ induced by the function $n \mapsto n+1$ on $\omega$. Given a compact Hausdorff space $X$ and a continuous function $f: X \rightarrow X$, we say that $(X,f)$ is a quotient of ... More

Structure of entanglement in regulated Lorentz invariant field theoriesApr 23 2013Regulated Lorentz invariant quantum field theories satisfy an area law for the entanglement entropy $S$ of a spatial subregion in the ground state in $d>1$ spatial dimensions; nevertheless, the full density matrix contains many more than $e^{S}$ non-zero ... More

Entanglement Entropy and the Fermi SurfaceAug 12 2009Mar 11 2010Free fermions with a finite Fermi surface are known to exhibit an anomalously large entanglement entropy. The leading contribution to the entanglement entropy of a region of linear size $L$ in $d$ spatial dimensions is $S\sim L^{d-1} \log{L}$, a result ... More

Entanglement does not generally decrease under renormalizationJul 30 2013Aug 01 2013Renormalization is often described as the removal or "integrating out" of high energy degrees of freedom. In the context of quantum matter, one might suspect that quantum entanglement provides a sharp way to characterize such a loss of degrees of freedom. ... More

Experimental Summary on Hadronic Decays: A TAU98 ReviewNov 16 1998Jan 21 1999Selected results on hadronic decays of the tau lepton from the TAU98 Workshop are reviewed. A comprehensive picture emerges for strange particle branching fractions, and exploration of resonant substructure of both strange and non-strange decays is seen ... More

Update on the lattice calculation of $B \to K^* γ$Nov 30 1994We summarise our current results for calculations of the form factors for $B \to K^* \gamma$, and their extrapolation to the physical b-quark mass.

Hyperbolicity of the Cyclic Splitting ComplexDec 12 2012Dec 14 2012We define a new complex on which $Out(F_n)$ acts by simplicial automorphisms, the cyclic splitting complex of $F_n$, and show that it is hyperbolic using a method developed by Kapovich and Rafi.

Evidence on the Origin of Ergospheric Disk Field Line Topology in Simulations of Black Hole AccretionSep 19 2011This Letter investigates the origin of the asymmetric magnetic field line geometry in the ergospheric disk (and the corresponding asymmetric powerful jet) in 3-D perfect magnetohydrodynamic (MHD) numerical simulations of a rapidly rotating black hole ... More

Dynamic Boundaries of Event Horizon MagnetospheresJul 20 2007This Letter analyzes 3-dimensional simulations of Kerr black hole magnetospheres that obey the general relativistic equations of perfect magnetohydrodynamics (MHD). Particular emphasis is on the event horizon magnetosphere (EHM) which is defined as the ... More

3-D Simulations of Ergospheric Disk Driven Poynting JetsApr 05 2007This Letter reports on 3-dimensional simulations of Kerr black hole magnetospheres that obey the general relativistic equations of perfect magnetohydrodynamics (MHD). In particular, we study powerful Poynting flux dominated jets that are driven from dense ... More

Evidence of the Dynamics of Relativistic Jet Launching in QuasarsApr 01 2015Hubble Space Telescope (HST) spectra of the extreme ultraviolet (EUV), the optically thick emission from the innermost accretion flow onto the central supermassive black hole, indicate that RLQs tend to be EUV weak compared to the radio quiet quasars ... More

A Multi-Component Analysis Indicates a Positronic Major Flare in GRS 1915+105Nov 21 2011Dec 21 2011A modeling strategy that is adapted to the study of synchrotron-self absorbed plasmoids that was developed for the quasar, Mrk 231, in Reynolds et al (2009) is applied to the microquasar GRS 1915+105. The major flare from December 1993 shows spectral ... More

The Redshifted Excess in Quasar C IV Broad Emission LinesFeb 25 2010In this Letter, the Evans and Koratkar Atlas of Hubble Space Telescope Faint Object Spectrograph Spectra of Active Galactic Nuclei and Quasars is used to study the redward asymmetry in CIV broad emission lines (BELs). It is concluded that there is a highly ... More

Kinetically Dominated FRII Radio SourcesOct 02 2006The existence of FR II objects that are kinetically dominated, the jet kinetic luminosity, $Q$, is larger than the total thermal luminosity (IR to X-ray) of the accretion flow, $L_{bol}$, is of profound theoretical interest. Such objects are not expected ... More

String Theory on Calabi-Yau ManifoldsFeb 23 1997These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of string theory ... More

Asymptotic behavior of the dimension of the Chow varietySep 04 2013Jan 13 2016We analyze the asymptotics of the dimension of components of the Chow variety as degree increases. By analogy with the divisor case, the main goal is to relate the asymptotic behavior with the positivity of the corresponding cycle classes. We also compute ... More

Volume-type functions for numerical cycle classesJan 13 2016A numerical equivalence class of k-cycles is said to be big if it lies in the interior of the closed cone generated by effective classes. We construct analogues for arbitrary cycle classes of the volume function for divisors which distinguishes big classes ... More

General Properties of Quiescent NovaeJun 26 2002The observed properties of novae before and after eruption are discussed. The distribution of orbital periods of novae shows a concentration near 3.2 h, which resembles that of magnetic cataclysmic variables, and there is some evidence that many of the ... More

Rapid Oscillations in Cataclysmic VariablesDec 06 2003I give an overview of the rich phenomenology of dwarf nova oscillations (DNOs) and Quasi-periodic Oscillations (QPOs) observed in cataclysmic variable stars (CVs). The favoured interpretation of these rapid brightness modulations (3 - >1000 s time scales) ... More

Globular Cluster Distance DeterminationsAug 19 1998The present status of the distance scale to Galactic globular clusters is reviewed. Six distance determination techniques which are deemed to be most reliable are discussed in depth. These different techniques are used to calibrate the absolute magnitude ... More

The Primordial Abundance of $^6$Li and $^9$beMay 31 1994Light element ($^6$Li, $^7$Li and $^9$Be) depletion isochrones for halo stars have been calculated with standard stellar evolution models. These models include the latest available opacities and are computed through the sub-giant branch. If $^6$Li is ... More

The Age of the UniverseAug 19 1998A minimum age of the universe can be estimated directly by determining the age of the oldest objects in the our Galaxy. These objects are the metal-poor stars in the halo of the Milky Way. Recent work on nucleochronology finds that the oldest stars are ... More

Formal Verification of Monad TransformersJul 13 2012We present techniques for reasoning about constructor classes that (like the monad class) fix polymorphic operations and assert polymorphic axioms. We do not require a logic with first-class type constructors, first-class polymorphism, or type quantification; ... More

Measurement of the Top Quark Mass with a Matrix Element Method in the Lepton Plus Jets Channel at CDFMay 17 2006We present a measurement of the mass of the top quark from ppbar collisions at 1.96 TeV observed with the Collider Detector at Fermilab (CDF) at the Fermilab Tevatron Run II. The events have the decay signature of ppbar to ttbar in the lepton plus jets ... More

The Cheeger Constant, Isoperimetric Problems, and Hyperbolic SurfacesSep 30 2015Jan 06 2016We give a brief literature review of the isoperimetric problem and discuss its relationship with the Cheeger constant of Riemannian $n$-manifolds. For some non-compact, finite area 2-manifolds, we prove the existence and regularity of subsets whose isoperimetric ... More

Sub-Hermitian Geometry and the Quantitative Newlander-Nirenberg TheoremOct 26 2018Jan 04 2019Given a finite collection of $C^1$ complex vector fields on a $C^2$ manifold $M$ such that they and their complex conjugates span the complexified tangent space at every point, the classical Newlander-Nirenberg theorem gives conditions on the vector fields ... More

Deformation Formulas for Parameterizable HypersurfacesNov 29 2017We investigate one-parameter deformations of functions on affine space which define parametrizable hyper surfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the L\^e numbers of the special fiber in ... More

On the Evoution of the Light Elements I. D, He-3, and He-4Dec 08 1995The light elements D, \he3, \he4, and \li7 are produced in big bang nucleosynthesis and undergo changes in their abundances due to galactic processing. Since one may observe most of these elements only in contemporary environments, knowledge of the intervening ... More

A Note on Bounded Biclique Coverings of Complete GraphsNov 09 2015An undirected biclique $K_{a,b}$ is a graph with vertices partitioned into two sets: a set $A$ containing $a$ vertices and a set $B$ containing $b$ vertices such that every vertex in set $A$ is connected to every vertex in set $B$, and such that no two ... More

Development of a VO Registry Subject Ontology using Automated MethodsFeb 20 2015We report on our initial work to automate the generation of a domain ontology using subject fields of resources held in the Virtual Observatory registry. Preliminary results are comparable to more generalized ontology learning software currently in use. ... More

Constraints on Black Hole Jet Models Used As Diagnostic Tools of Event Horizon Telescope Observations of M87Jun 14 2019Jet models of Event Horizon Telescope (EHT) data should also conform to the observed jet profiles just downstream. This study evaluates conformance of models of black hole jets to images of the innermost jet of M87. This is a basic test that should be ... More

Seshadri constants and very ample divisors on algebraic surfacesMar 05 2001Apr 04 2001A broadly applicable geometric approach for constructing nef divisors on blow ups of algebraic surfaces at n general points is given; it works for all surfaces in all characteristics for any n. This construction is used to obtain substantial improvements ... More

Zero Spacings of Paraorthogonal Polynomials on the Unit CircleJul 02 2019We prove some new results about the spacing between neighboring zeros of paraorthogonal polynomials on the unit circle. Our methods also provide new proofs of some existing results. The main tool we will use is a formula for the phase of the appropriate ... More

Self maps of P^1 with prescribed ramification in characteristic pJul 26 2004Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of the projective line with ramification to order e_i at general points P_i, in the case that all e_i ... More

Relative dimension of morphisms and dimension for algebraic stacksMay 27 2013Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust and applies ... More

Linked Hom spacesAug 31 2010In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain to the other ... More

Which Ambient Spaces Admit Isoperimetric Inequalities for Submanifolds?Apr 24 2008Dec 16 2008We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities (for submanifolds) to hold.

Algebraic bounds on analytic multiplier idealsSep 21 2011Jun 12 2013Given a pseudo-effective divisor L we construct the diminished ideal of L, a "continuous" extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. For most pseudo-effective divisors L the multiplier ideal of the ... More

Asymptotics of linear systems, with connections to line arrangementsMay 28 2017The main focus of these notes is recent work on linear systems in which line arrangements play a role, including problems such as semi-effectivity, containment problems of symbolic powers of homogeneous ideals in their powers, bounded negativity, and ... More

Numerical triviality and pullbacksSep 20 2011Jan 12 2012Let f: X \to Z be a surjective morphism of smooth complex projective varieties with connected fibers. Suppose that L is a pseudo-effective divisor on X that is f-numerically trivial. We show that there is a divisor D on Z such that L is numerically equivalent ... More

Regularity of minimal hypersurfaces with a common free boundarySep 24 2013Let $N$ be a Riemannian manifold and consider a stationary union of three or more $C^{1,\mu}$ hypersurfaces-with-boundary $M_k$ in $N$ with a common boundary $\Gamma$. We show that if $N$ is smooth, then $\Gamma$ is smooth and each $M_k$ is smooth up ... More

Non-Rigidity of Cyclic Automorphic Orbits in Free GroupsAug 05 2011We say a subset $\Sigma \subseteq F_N$ of the free group of rank $N$ is \emph{spectrally rigid} if whenever $T_1, T_2 \in \cv_N$ are $\mathbb{R}$-trees in (unprojectivized) outer space for which $|\sigma|_{T_1} = |\sigma|_{T_2}$ for every $\sigma \in ... More

Coordinates Adapted to Vector Fields III: Real AnalyticityAug 14 2018Oct 23 2018Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are real analytic. We give necessary and ... More

One-Pass Graphic Approximation of Integer SequencesDec 14 2017Dec 18 2017A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of the sequence. ... More

A Sufficient Condition for Graphic Sequences with Given Largest and Smallest Entries, Length, and SumJul 13 2016Jun 25 2018We give a sufficient condition for a degree sequence to be graphic based on its largest and smallest elements, length, and sum. This bound generalizes a result of Zverovich and Zverovich.

Rational Homology Manifolds and Hypersurface NormalizationsApr 25 2018Aug 10 2018We prove a criterion for determining whether the normalization of a complex analytic space on which the constant sheaf is perverse is a rational homology manifold, using a perverse sheaf known as the multiple-point complex. This perverse sheaf is naturally ... More

Topology of Kähler manifolds with weakly pseudoconvex boundaryOct 20 2011Oct 10 2018We study Kahler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold $K$ has $l\ge2$ boundary components (possibly $l=\infty$), then it has first betti number at least ... More

Regularity and convergence of 4-dimensional extremal Kahler metricsApr 16 2011May 10 2011We establish a regularity result for the metric on any 4-dimensional extremal K\"ahler manifold, and a weak compactness theorem on the space of such metrics. Specifically, the sectional curvature at a point is bounded when the quantity $L^2(|\Riem|)$ ... More

Curvature Estimates for Critical 4-Manifolds with a Lower Ricci Curvature BoundSep 12 2013We draw elliptic regularity results for 4-manifolds with an elliptic system, without Sobolev constant control. Direct use of analysis is circumvented; the results come mainly through geometric and topological arguments. In contrast to our previous paper, ... More

Energy and Asymptotics of Ricci-Flat 4-Manifolds with a Killing FieldAug 22 2013Oct 10 2018Given a complete, Ricci-flat 4-manifold with a Killing field, we give an estimate on the manifold's energy in terms of a certain asymptotic quantity of the Killing field. If the Killing field has no zeros and satisfies a certain asymptotic condition, ... More

Connectedness of Brill-Noether loci via degenerationsFeb 22 2017We show that limit linear series spaces for chains of curves are reduced. Using new advances in the foundations of limit linear series, we then use degenerations to study the question of connectedness for spaces of linear series with imposed ramification ... More

Unlabeled Signed Graph ColoringNov 24 2015Feb 22 2018We extend the work of Hanlon on the chromatic polynomial of an unlabeled graph to define the unlabeled chromatic polynomial of an unlabeled signed graph. Explicit formulas are presented for labeled and unlabeled signed chromatic polynomials as summations ... More

Subsequent Singularities in Mean-Convex Mean Curvature FlowMar 08 2011Apr 07 2013We use Ilmanen's elliptic regularization to prove that for an initially smooth mean convex hypersurface in Euclidean n-space moving by mean curvature flow, the surface is very nearly convex in a spacetime neighborhood of every singularity. Previously ... More

The Maximum Principle for Minimal Varieties of Arbitrary CodimensionMay 31 2009Nov 12 2010We prove that an m-dimensional minimal variety in a Riemannian manifold cannot touch the boundary at a point where the sum of the smallest m principal curvatures is greater than 0. We also prove an analogous result for varieties with bounded mean curvature. ... More

Brill-Noether loci with fixed determinant in rank 2May 04 2010Aug 24 2011In the 1990's, Bertram, Feinberg and Mukai examined Brill-Noether loci for vector bundles of rank 2 with fixed canonical determinant, noting that the dimension was always bigger in this case than the naive expectation. We generalize their results to treat ... More

Zeros of non-Baxter paraorthogonal polynomials on the unit circleMay 27 2010Nov 03 2010We provide leading order asymptotics for the size of the gap in the zeros around 1 of paraothogonal polynomials on the unit circle whose Verblunsky coefficients satisfy a slow decay condition and are inside the interval (-1,0). We also include related ... More

Sharp Regularity for the Integrability of Elliptic StructuresOct 23 2018Jul 24 2019As part of his celebrated Complex Frobenius Theorem, Nirenberg showed that given a smooth elliptic structure (on a smooth manifold), the manifold is locally diffeomorphic to an open subset of $\mathbb{R}^r\times \mathbb{C}^n$ (for some $r$ and $n$) in ... More

Entanglement sum rules in exactly solvable modelsSep 04 2012We compute the entanglement entropy of a wide class of exactly solvable models which may be characterized as describing matter coupled to gauge fields. Our principle result is an entanglement sum rule which states that entropy of the full system is the ... More

Mutual information and the structure of entanglement in quantum field theoryOct 19 2010I study the mutual information between spatial subsystems in a variety of scale invariant quantum field theories. While it is derived from the bare entanglement entropy, the mutual information offers a more refined probe of the entanglement structure ... More

A simple model of many-body localizationJul 01 2013We study a simple and tractable model of many-body localization. The main idea is to take a renormalization group perspective in which local entanglement is removed to reach a product state. The model is built from a random local unitary which implements ... More

The movable cone via intersectionsNov 16 2011Dec 26 2012We characterize the movable cone of divisors using intersections against curves on birational models.

The Velocity Field of Quasar Broad Emission Line GasJan 25 2007In this Letter, the broad emission line (BEL) profiles of superluminal quasars with apparent jet velocities, $\beta_{a}>10$, (ultraluminal QSOs, or ULQSOs hereafter) are studied as a diagnostic of the velocity field of the BEL emitting gas in quasars. ... More

Fast Wave Polarization, Charge Horizons and the Time Evolution of Force-Free MagnetospheresJul 16 2004Numerical simulations of force-free, degenerate (ffde)pulsar and black hole magnetospheres are often based on 1-D characteristics. In particular, the plasma wave polarizations that can be propagated along the 1-D characteristics determine the time evolution ... More

The Extreme Ultraviolet Deficit and Magnetically Arrested Accretion in Radio Loud QuasarsDec 01 2014The Hubble Space Telescope composite quasar spectra presented in Telfer et al. show a significant deficit of emission in the extreme ultraviolet (EUV) for the radio loud component of the quasar population (RLQs), compared to the radio quiet component ... More

Force Free Waves and Black Hole Magnetospheric CausalityOct 03 2002The force free approximation is often useful when describing tenuous plasmas in strong cosmic magnetic fields. Time evolution of any such system is governed by the information that can be transported along the characteristics of the plasma modes allowed ... More

Energy and Asymptotics of Ricci-Flat 4-Manifolds with a Killing FieldAug 22 2013Given a complete, Ricci-flat 4-manifold with a Killing field, we give an estimate on the manifold's energy in terms of a certain asymptotic quantity of the Killing field. If the Killing field has no zeros and satisfies a certain asymptotic condition, ... More

Two Universality Results for Polynomial Reproducing KernelsMay 30 2016We prove two new universality results for polynomial reproducing kernels of compactly supported measures. The first applies to measures on the unit circle with a jump and a singularity in the weight at $1$ and the second applies to area-type measures ... More

Intermediate polars in low statesOct 09 2003Although no intermediate polar (IP) has been observed in recent years to descend into a state of low rate of mass transfer, there are candidate stars that appear to be already in intermediate and low states. V709 Cas is probably an intermediate state ... More

Forced Edges and Graph StructureOct 04 2016For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none as forbidden. We examine structure of graphs whose degree sequences contain either forced or forbidden ... More

Internal Rotation, Mixing and Lithium AbundancesMar 10 1998Lithium is an excellent tracer of mixing in stars as it is destroyed (by nuclear reactions) at a temperature around $\sim 2.5\times 10^6$ K. The lithium destruction zone is typically located in the radiative region of a star. If the radiative regions ... More

Unlabeled Signed Graph ColoringNov 24 2015We extend the work of Hanlon on the chromatic polynomial of an unlabeled graph to an unlabeled signed graph. Explicit formulas are presented for labeled and unlabeled signed chromatic polynomials as summations over distinguished order-ideals of the signed ... More

A Hall-Fusion BialgebraSep 15 2010We describe what might be called the "Hall-fusion" bialgebra constructed from a promonoidal double, and mention the corresponding face version for probicategories.

On endomorphism algebras of functors with non-compact domainApr 25 2010Aug 15 2011As a development of [2] and [3], we construct a "VN-bialgebra" in Vect_k for each k-linear split-semigroupal functor from a suitable monoidal category C to Vect_k. The main aim here is to avoid the customary compactness assumptions on generators of the ... More

Middle-Four Maps and Net CategoriesNov 27 2009We briefly relate the existence of a middle-four interchange map in a category with two monoidal structures, to the standard Cockett and Seely notion of a weakly distributive category.

Deformations and automorphisms: a framework for globalizing local tangent and obstruction spacesMay 29 2008Building on Schlessinger's work, we define a framework for studying geometric deformation problems which allows us to systematize the relationship between the local and global tangent and obstruction spaces of a deformation problem. Starting from Schlessinger's ... More

The isomorphism class of the shift mapApr 22 2019The \emph{shift map} $\sigma$ is the self-homeomorphism of $\omega^* = \beta\omega \setminus \omega$ induced by the successor function $n \mapsto n+1$ on $\omega$. We prove that the isomorphism classes of $\sigma$ and $\sigma^{-1}$ cannot be separated ... More

Infinite dimensional symmetry of corner transfer matricesDec 16 1993Dec 17 1993We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens many new possibilities, ... More

The Weight Filtration on the Constant Sheaf on a Parameterized SpaceNov 11 2018May 16 2019On an $n$-dimensional locally reduced complex analytic space $X$ on which the shifted constant sheaf $\Q_X^\bullet[n]$ is perverse, it is well-known that, locally, $\Q_X^\bullet[n]$ underlies a mixed Hodge module of weight $\leq n$ on $X$, with weight ... More

Global aspects of the geometry of surfacesJul 23 2009Jul 30 2009These notes (prepared for the author's lectures at the Cracow Summer School on Linear Systems organized by S. Mueller-Stach and T. Szemberg, held March 23-27, 2009 at the Pedagogical University of Cracow under the sponsorship of the Deutsche Forschungsgemeinschaft) ... More

A cone theorem for nef curvesJul 15 2008Mar 02 2011Following ideas of V. Batyrev, we prove an analogue of the Cone Theorem for the closed cone of nef curves: an enlargement of the cone of nef curves is the closure of the sum of a K_X-non-negative portion and countably many K_X-negative coextremal rays. ... More

The Weight Filtration on the Constant Sheaf on a Parameterized SpaceNov 11 2018Jul 12 2019On an $n$-dimensional locally reduced complex analytic space $X$ on which the shifted constant sheaf $\Q_X^\bullet[n]$ is perverse, it is well-known that, locally, $\Q_X^\bullet[n]$ underlies a mixed Hodge module of weight $\leq n$ on $X$, with weight ... More

Sub-Hermitian Geometry and the Quantitative Newlander-Nirenberg TheoremOct 26 2018Mar 15 2019Given a finite collection of $C^1$ complex vector fields on a $C^2$ manifold $M$ such that they and their complex conjugates span the complexified tangent space at every point, the classical Newlander-Nirenberg theorem gives conditions on the vector fields ... More

An Analysis of Dual-Issue Final-Offer ArbitrationOct 10 2015We discuss final-offer arbitration where two quantitative issues are in dispute and model it as a zero-sum game. Under reasonable assumptions we both derive a pure strategy pair and show that it is both a local equilibrium and furthermore that it is the ... More

Currents and Flat Chains Associated to Varifolds, with an Application to Mean Curvature FlowMay 14 2008Nov 09 2008We prove under suitable hypotheses that convergence of integral varifolds implies convergence of associated mod 2 flat chains and subsequential convergence of associated integer-multiplicity rectifiable currents. The convergence results imply restrictions ... More

On the Compactness Theorem for Embedded Minimal Surfaces in 3-manifolds with Locally Bounded Area and GenusMar 07 2015Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with multiplicity, and we analyze ... More

Controlling Area Blow-up in Minimal or Bounded Mean Curvature VarietiesJul 14 2012Jun 26 2015Consider a sequence of minimal varieties M_i in a Riemannian manifold N such that the boundary measures are uniformly bounded on compact sets. Let Z be the set of points at which the areas of the M_i blow up. We prove that Z behaves in some ways like ... More

The Completion of the Manifold of Riemannian MetricsApr 01 2009We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finite-dimensional, orientable manifold with respect to a natural metric called the $L^2$ metric. The primary motivation for studying this ... More

Note on the Fusion MapFeb 13 2009Apr 04 2011We note an inversion property of the fusion map associated to many semibialgebras.

A *-Autonomous Category of Banach Spaces--CorrectionJan 28 2009Jun 25 2009We describe a $\C$-linear additive *-autonomous category of Banach spaces. Please note that a correction has been appended to the original version 1 which is maintained here for reference. Also, a proposed example of a *-autonomous category of topological ... More

Classification of subdivision rules for geometric groups of low dimensionSep 09 2014Subdivision rules create sequences of nested cell structures on CW-complexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov ... More