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Necessary conditions for steerability of two qubits, from consideration of local operationsJun 11 2019EPR-steering refers to the ability of one observer to convince a distant observer that they share entanglement by making local measurements. Determining which states allow a demonstration of EPR-steering remains an open problem in general, even for the ... More

An adaptive fast multipole accelerated Poisson solver for complex geometriesOct 04 2016We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume ... More

Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steeringJun 27 2018Sep 12 2018Einstein-Podolsky-Rosen steering is a quantum phenomenon wherein one party influences, or steers, the state of a distant party's particle beyond what could be achieved with a separable state, by making measurements on one half of an entangled state. This ... More

The Vev Flip-Flop: Dark Matter Decay between Weak Scale Phase TransitionsAug 26 2016We propose a new alternative to the Weakly Interacting Massive Particle (WIMP) paradigm for dark matter. Rather than being determined by thermal freeze-out, the dark matter abundance in this scenario is set by dark matter decay, which is allowed for a ... More

Constraints on the pre-impact orbits of Solar System giant impactorsNov 14 2017We provide a fast method for computing constraints on impactor pre-impact orbits, applying this to the late giant impacts in the Solar System. These constraints can be used to make quick, broad comparisons of different collision scenarios, identifying ... More

Grid Diagrams and Legendrian Lens Space LinksApr 18 2008Grid diagrams encode useful geometric information about knots in S^3. In particular, they can be used to combinatorially define the knot Floer homology of a knot K in S^3, and they have a straightforward connection to Legendrian representatives of K in ... More

Robust and scalable methods for the dynamic mode decompositionDec 05 2017The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time dynamics, and a matrix ... More

Super-Isolated Elliptic Curves and Abelian Surfaces in CryptographyMay 05 2017We call a simple abelian variety over $\mathbb{F}_p$ super-isolated if its ($\mathbb{F}_p$-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about isogeny based attacks on the discrete ... More

Fano mirror periods from the Frobenius structure conjectureMar 28 2019The Fano classification program proposed by Coates-Corti-Galkin-Golyshev-Kasprzyk is based on the mirror symmetry prediction that the regularized quantum period of a Fano should be equivalent to the classical period of its mirror Landau-Ginzburg potential. ... More

Cartan's incomplete classification and an explicit ambient metric of holonomy $\mathrm{G}_2^*$Nov 26 2014Aug 22 2017In his 1910 "Five Variables" paper, Cartan solved the equivalence problem for the geometry of $(2, 3, 5)$ distributions and in doing so demonstrated an intimate link between this geometry and the exceptional simple Lie groups of type $\textrm{G}_2$. He ... More

Deformations of algebras in noncommutative geometryDec 05 2012Mar 22 2015These are significantly expanded lecture notes for the author's minicourse at MSRI in June 2012. In these notes, we give an example-motivated review of the deformation theory of associative algebras in terms of the Hochschild cochain complex as well as ... More

Are there really two different Bell's theorems?Mar 17 2015This is a polemical response to Howard Wiseman's recent paper, "The two Bell's theorems of John Bell". Wiseman argues that, in 1964, Bell established a conflict between the quantum mechanical predictions and the joint assumptions of determinism and (what ... More

Supergravity Backgrounds for Four-Dimensional Maximally Supersymmetric Yang-MillsSep 19 2016In this note, we describe supersymmetric backgrounds for the four-dimensional maximally supersymmetric Yang-Mills theory. As an extension of the method of Festuccia and Seiberg to sixteen supercharges in four dimensions, we utilize the coupling of the ... More

Equivariant slices for symplectic conesJan 14 2015The Darboux-Weinstein decomposition is a central result in the theory of Poisson (degenerate symplectic) varieties, which gives a local decomposition at a point as a product of the formal neighborhood of the symplectic leaf through the point and a formal ... More

Characterizations of Ordered Self-adjoint Operator SpacesAug 25 2015In this paper, we generalize the work of Werner and others to develop two abstract characterizations for self-adjoint operator spaces. The corresponding abstract objects can be represented as self-adjoint subspaces of $B(H)$ in such a way that both a ... More

Graphical Enumeration: A Species-Theoretic ApproachNov 21 1998An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and used to extend ... More

Rigged configurations as tropicalizations of loop Schur functionsJul 12 2016Mar 08 2017We conjecture an explicit formula for the image of a tensor product of Kirillov-Reshetikhin crystals $\bigotimes_{i=1}^m B^{1, s_i}$ under the Kirillov-Schilling-Shimozono bijection. Our conjectured formula is piecewise-linear, where the shapes are given ... More

Highly symmetric 2-plane fields on 5-manifolds and 5-dimensional Heisenberg group holonomyFeb 28 2013Dec 08 2014Nurowski showed that any generic 2-plane field $D$ on a 5-manifold $M$ determines a natural conformal structure $c_D$ on $M$; these conformal structures are exactly those (on oriented $M$) whose normal conformal holonomy is contained in the (split, real) ... More

Uniform description of the rigged configuration bijectionMar 27 2017We give a uniform description of the bijection $\Phi$ from rigged configurations to tensor products of Kirillov--Reshetikhin crystals of the form $\bigotimes_{i=1}^N B^{r_i,1}$ in dual untwisted types: simply-laced types and types $A_{2n-1}^{(2)}$, $D_{n+1}^{(2)}$, ... More

Classification of Rank 2 Cluster VarietiesJul 23 2014May 27 2019We classify rank $2$ cluster varieties (those for which the span of the rows of the exchange matrix is $2$-dimensional) according to the deformation type of a generic fiber $U$ of their ${\mathcal X}$-spaces, as defined by Fock and Goncharov [Ann. Sci. ... More

Scattering diagrams, theta functions, and refined tropical curve countsMar 20 2015Sep 27 2018Working over various monoid-graded Lie algebras and in arbitrary dimension, we express scattering diagrams and theta functions in terms of counts of tropical curves/disks, weighted by multiplicities given in terms of iterated Lie brackets. Over the tropical ... More

Kodaira-Iitaka Dimension on a Normal Prime DivisorDec 18 2008This paper was inspired by work by T. Peternell, M. Schneider and A.J. Sommese on the Kodaira dimension of subvarieties. In it I find a relation between the Kodaira-Iitaka dimension of a divisor on a normal variety and that of related divisors on an irreducible ... More

Homogeneous Real (2,3,5) Distributions with IsotropyJul 08 2018Feb 04 2019We classify multiply transitive homogeneous real (2,3,5) distributions up to local diffeomorphism equivalence.

Theta bases and log Gromov-Witten invariants of cluster varietiesMar 07 2019Using heuristics from mirror symmetry, combinations of Gross, Hacking, Keel, Kontsevich, and Siebert have given combinatorial constructions of canonical bases of "theta functions" on the coordinate rings of various log Calabi-Yau spaces, including cluster ... More

Rigged configurations as tropicalizations of loop Schur functionsJul 12 2016We conjecture an explicit formula for the image of a tensor product of Kirillov--Reshetikhin crystals $\bigotimes_{i=1}^m B^{1, s_i}$ under the Kirillov--Schilling--Shimozono bijection. Our conjectured formula is piecewise-linear, where the shapes are ... More

The Observer Class HypothesisJan 11 2011The discovery of a small cosmological constant has stimulated interest in the measure problem. One should expect to be a typical observer, but defining such a thing is difficult in the vastness of an eternally inflating universe. We propose that a crucial ... More

A Simple, Direct Finite Differencing of the Einstein EquationsFeb 04 2009We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a source for these ... More

Multilevel rejection sampling for approximate Bayesian computationFeb 10 2017Feb 28 2018Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate Bayesian computation ... More

The COBE DIRBE Point Source CatalogJun 07 2004We present the COBE DIRBE Point Source Catalog, an all-sky catalog containing infrared photometry in 10 bands from 1.25 microns to 240 microns for 11,788 of the brightest near and mid-infrared point sources in the sky. Since DIRBE had excellent temporal ... More

High-pT Signatures in Vector-Leptoquark ModelsJan 29 2019Apr 16 2019We present a detailed analysis of the collider signatures of TeV-scale massive vector bosons motivated by the hints of lepton flavour non-universality observed in $B$-meson decays. We analyse three representations that necessarily appear together in a ... More

On the Uncertainties of Results Derived from HI Spectral Line Stacking ExperimentsApr 29 2019We present the results of a set of mock experiments aimed at quantifying the accuracy of results derived from HI spectral line stacking experiments. We focus on the effects of spatial and spectral aperture sizes and redshift uncertainties on co-added ... More

Realistic On-The-Fly Outcomes of Planetary Collisions: Machine Learning Applied to Simulations of Giant ImpactsMar 11 2019Planet formation simulations are capable of directly integrating the evolution of hundreds to thousands of planetary embryos and planetesimals, as they accrete pairwise to become planets. In principle such investigations allow us to better understand ... More

Assembling Omnitigs using Hidden-Order de Bruijn GraphsMay 14 2018De novo DNA assembly is a fundamental task in Bioinformatics, and finding Eulerian paths on de Bruijn graphs is one of the dominant approaches to it. In most of the cases, there may be no one order for the de Bruijn graph that works well for assembling ... More

Exploring limits to prediction in complex social systemsFeb 02 2016How predictable is success in complex social systems? In spite of a recent profusion of prediction studies that exploit online social and information network data, this question remains unanswered, in part because it has not been adequately specified. ... More

A Unified Framework for Sparse Relaxed Regularized Regression: SR3Jul 14 2018Nov 08 2018Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, variable selection, ... More

Embedding Complexity In the Data Representation Instead of In the Model: A Case Study Using Heterogeneous Medical DataFeb 12 2018Electronic Health Records have become popular sources of data for secondary research, but their use is hampered by the amount of effort it takes to overcome the sparsity, irregularity, and noise that they contain. Modern learning architectures can remove ... More

A theorem of Bombieri-Vinogradov type with few exceptional moduliMay 29 2019If a set S of pairwise coprime moduli q, less than x^(9/40), is considered, one obtains the expected behavior for primes up to x in arithmetic progressions mod q, except for a subset of S whose cardinality is bounded by a power of log x.

On universal and periodic $β$-expansions, and the Hausdorff dimension of the set of all expansionsDec 06 2012May 28 2013In this paper we study the topology of a set naturally arising from the study of $\beta$-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and sufficient conditions ... More

On the homology of regular quotientsMay 09 2013We construct a free resolution of $R/I^s$ over $R$ where $I\ideal R$ is generated by a (finite or infinite) regular sequence. This generalizes the Koszul complex for the case $s=1$. For $s>1$, we easily deduce that the algebra structure of $\Tor^R_*(R/I,R/I^s)$ ... More

Invariants of Hamiltonian flow on locally complete intersectionsJan 20 2014Jun 24 2016We consider the Hamiltonian flow on complex complete intersection surfaces with isolated singularities, equipped with the Jacobian Poisson structure. More generally we consider complete intersections of arbitrary dimension equipped with Hamiltonian flow ... More

The 2-Calabi-Yau property for multiplicative preprojective algebrasMay 28 2019We prove that multiplicative preprojective algebras, defined by Crawley-Boevey and Shaw, are 2-Calabi-Yau algebras for quivers containing an unoriented cycle. We also prove that the dg versions of these algebras (arising in Fukaya categories of certain ... More

Approximation properties of $β$-expansions IIJun 25 2015Given $\beta\in(1,2)$ and $x\in[0,\frac{1}{\beta-1}]$, a sequence $(\epsilon_{i})_{i=1}^{\infty}\in\{0,1\}^{\mathbb{N}}$ is called a $\beta$-expansion for $x$ if $$x=\sum_{i=1}^{\infty}\frac{\epsilon_{i}}{\beta^{i}}.$$ In a recent article the author studied ... More

A flexible and computationally tractable discrete distribution derived from a stationary renewal processFeb 28 2018A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be carried out and ... More

Characteristics for $E_\infty$ ring spectraMay 14 2014Jun 01 2017We introduce a notion of characteristic for connective $p$-local $E_\infty$ ring spectra and study some basic properties. Apart from examples already pointed out by Markus Szymik, we investigate some examples built from Hopf invariant $1$ elements in ... More

Digit frequencies and self-affine sets with non-empty interiorJan 24 2017In this paper we study digit frequencies in the setting of expansions in non-integer bases, and self-affine sets with non-empty interior. Within expansions in non-integer bases we show that if $\beta\in(1,1.787\ldots)$ then every $x\in(0,\frac{1}{\beta-1})$ ... More

Quantum Chemistry as a Benchmark for Near-Term Quantum ComputersMay 04 2019We present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. ... More

The growth rate and dimension theory of beta-expansionsAug 30 2012Oct 15 2012In a recent paper of Feng and Sidorov they show that for $\beta\in(1,\frac{1+\sqrt{5}}{2})$ the set of $\beta$-expansions grows exponentially for every $x\in(0,\frac{1}{\beta-1})$. In this paper we study this growth rate further. We also consider the ... More

Exceptional digit frequencies and expansions in non-integer basesNov 28 2017In this paper we study the set of digit frequencies that are realised by elements of the set of $\beta$-expansions. The main result of this paper demonstrates that as $\beta$ approaches $1,$ the set of digit frequencies that occur amongst the set of $\beta$-expansions ... More

Power operations in $K$-theory completed at a primeJun 21 2014Aug 13 2018We describe the action of power operations on the $p$-completed cooperation algebras $K^\vee_0 K = K_0(K)\sphat_p$ for $K$-theory at a prime~$p$, and $K^\vee_0 KO = K_0(KO)\sphat_2$.

Creating new distributions using integration and summation by partsApr 03 2019Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the resulting pdfs ... More

A multifractal zeta function for cookie cutter setsAug 13 2012Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions ... More

Kostka polynomials from nilpotent cones and Springer fiber cohomologySep 08 2015We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This can be viewed as a bigrading ... More

Characterizations of ordered operator spacesAug 02 2016We demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operators whose real part is positive). Defining the gauge of an operator $T \in ... More

Existence of Kirillov--Reshetikhin crystals for multiplicity free nodesFeb 02 2019We show that the Kirillov--Reshetikhin crystal $B^{r,s}$ exists when $r$ is a node such that the Kirillov--Reshetikhin module $W^{r,s}$ has a multiplicity free classical decomposition.

A new linear quotient of C^4 admitting a symplectic resolutionSep 14 2011We show that the quotient C^4/G admits a symplectic resolution for G = (Q_8 x D_8)/(Z/2) < Sp(4,C). Here Q_8 is the quaternionic group of order eight and D_8 is the dihedral group of order eight, and G is the quotient of their direct product which identifies ... More

A uniform approach to soliton cellular automata using rigged configurationsJun 08 2017Feb 11 2019For soliton cellular automata, we give a uniform description and proofs of the solitons, the scattering rule of two solitons, and the phase shift using rigged configurations in a number of special cases. In particular, we prove these properties for the ... More

Rigged configurations and the $\ast$-involution for generalized Kac--Moody algebrasDec 19 2018We construct a uniform model for highest weight crystals and $B(\infty)$ for generalized Kac--Moody algebras using rigged configurations. We also show an explicit description of the $\ast$-involution on rigged configurations for $B(\infty)$: that the ... More

Rigged configurations for all symmetrizable typesSep 25 2015Feb 17 2017In an earlier work, the authors developed a rigged configuration model for the crystal $B(\infty)$ (which also descends to a model for irreducible highest weight crystals via a cutting procedure). However, the result obtained was only valid in finite ... More

An Eulerian permutation statistic and generalizationsAug 15 2012Recently, the second author studied an Eulerian statistic (called cover) in the context of convex polytopes, and proved an equal joint distribution of (cover,des) with (des,exc). In this paper, we present several direct bijective proofs that cover is ... More

Strong Jumps and Lagrangians of Non-Uniform HypergraphsMar 05 2014The hypergraph jump problem and the study of Lagrangians of uniform hypergraphs are two classical areas of study in the extremal graph theory. In this paper, we refine the concept of jumps to strong jumps and consider the analogous problems over non-uniform ... More

Crystal structure on rigged configurations and the filling mapSep 09 2014Apr 18 2015In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the bijection between ... More

A proof of the parabolic Schauder estimates using Trudinger's method and the mean value property of the heat equationApr 04 2012One method available to prove the Schauder estimates is Neil Trudinger's method of mollification. In the case of second order elliptic equations, the method requires little more than mollification and the solid mean value inequality for subharmonic functions. ... More

$\mathcal{E}_\infty$ ring spectra and elements of Hopf invariant $1$Mar 19 2015Apr 16 2017The $2$-primary Hopf invariant $1$ elements in the stable homotopy groups of spheres form the most accessible family of elements. In this paper we explore some properties of the $\mathcal{E}_\infty$ ring spectra obtained from certain iterated mapping ... More

Equidistribution and the shrinking target problem for sequences of polynomialsMay 31 2019Jun 06 2019Let $(f_n)_{n=1}^{\infty}$ be a sequence of polynomials and $\alpha>1$. In this paper we study the distribution of the sequence $(f_n(\alpha))_{n=1}^{\infty}$ modulo one. We give sufficient conditions for a sequence $(f_n)_{n=1}^{\infty}$ to ensure that ... More

Approximation properties of $β$-expansionsSep 09 2014Let $\beta\in(1,2)$ and $x\in [0,\frac{1}{\beta-1}]$. We call a sequence $(\epsilon_{i})_{i=1}^\infty\in\{0,1\}^{\mathbb{N}}$ a $\beta$-expansion for $x$ if $x=\sum_{i=1}^{\infty}\epsilon_{i}\beta^{-i}$. We call a finite sequence $(\epsilon_{i})_{i=1}^{n}\in\{0,1\}^{n}$ ... More

Calculating with topological André-Quillen theory, I: Homotopical properties of universal derivations and free commutative $S$-algebrasAug 09 2012Mar 29 2017We adopt the viewpoint that topological And\'e-Quillen theory for commutative $S$-algebras should provide usable (co)homology theories for doing calculations in the sense traditional within Algebraic Topology. Our main emphasis is on homotopical properties ... More

Badly approximable numbers for sequences of ballsMay 22 2014May 29 2014It is a classical result from Diophantine approximation that the set of badly approximable numbers has Lebesgue measure zero. In this paper we generalise this result to more general sequences of balls. Given a countable set of closed $d$-dimensional Euclidean ... More

On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measureFeb 28 2014May 28 2014Let $\lambda_{1},\ldots,\lambda_{n}$ be real numbers in $(0,1)$ and $p_{1},\ldots,p_{n}$ be points in $\mathbb{R}^{d}$. Consider the collection of maps $f_{j}:\mathbb{R}^{d}\to\mathbb{R}^{d} $ given by $$f_{j}(x)=\lambda_{j} x +(1-\lambda_{j})p_{j}.$$ ... More

An analogue of Khintchine's theorem for self-conformal setsSep 15 2016Khintchine's theorem is a classical result from metric number theory which relates the Lebesgue measure of certain limsup sets with the convergence/divergence of naturally occurring volume sums. In this paper we ask whether an analogous result holds for ... More

Precise Infrared Radial Velocities from Keck/NIRSPEC and the Search for Young PlanetsFeb 01 2012We present a high-precision infrared radial velocity study of late-type stars using spectra obtained with NIRSPEC at the W. M. Keck Observatory. Radial velocity precisions of 50 m/s are achieved for old field mid-M dwarfs using telluric features for precise ... More

Kirillov-Reshetikhin crystals $B^{1,s}$ using Nakajima monomials for $\widehat{\mathfrak{sl}}_n$Oct 28 2016Dec 06 2016We give a realization of the Kirillov-Reshetikhin crystal $B^{1,s}$ using Nakajima monomials for $\widehat{\mathfrak{sl}}_n$ using the crystal structure given by Kashiwara. We then describe the tensor product in terms of a shift of indices, allowing us ... More

Connecting marginally large tableaux and rigged configurations via crystalsMay 26 2015We show that the bijection from rigged configurations to tensor products of Kirillov-Reshetikhin crystals extends to a crystal isomorphism between the $B(\infty)$ models given by rigged configurations and marginally large tableaux.

Coinvariants of Lie algebras of vector fields on algebraic varietiesNov 08 2012We prove that the space of coinvariants of functions on an affine variety by a Lie algebra of vector fields whose flow generates finitely many leaves is finite-dimensional. Cases of the theorem include Poisson (or more generally Jacobi) varieties with ... More

The Geometry of Almost Einstein (2,3,5) DistributionsJun 03 2016Jan 19 2017We analyze the classic problem of existence of Einstein metrics in a given conformal structure for the class of conformal structures inducedf Nurowski's construction by (oriented) (2,3,5) distributions. We characterize in two ways such conformal structures ... More

Geometry of the set of synchronous quantum correlationsMay 15 2019We provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario. We show that these correlations form a closed set. Moreover, every correlation in this set can be realized using ... More

Turan Problems on Non-uniform HypergraphsJan 09 2013A non-uniform hypergraph $H=(V,E)$ consists of a vertex set $V$ and an edge set $E\subseteq 2^V$; the edges in $E$ are not required to all have the same cardinality. The set of all cardinalities of edges in $H$ is denoted by $R(H)$, the set of edge types. ... More

Gradient corrections to the exchange-correlation free energyAug 06 2014We develop the first order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite temperature density functional calculations. Based on this we propose and implement a simple temperature dependent ... More

Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimesJul 25 2014We have developed and implemented a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density ... More

Ionic and electronic transport properties in dense plasmas by orbital-free density functional theoryOct 02 2015We validate the application of our recent orbital-free density functional theory (DFT) approach, [Phys. Rev. Lett. 113, 155006 (2014)], for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion ... More

On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform modelsSep 09 2018We show that a tensor product of nonexceptional type Kirillov--Reshetikhin (KR) crystals is isomorphic to a direct sum of Demazure crystals; we do this in the mixed level case and without the perfectness assumption, thus generalizing a result of Naoi. ... More

Virtual Crystals and Nakajima MonomialsJul 30 2017Sep 26 2018An explicit description of the virtualization map for the (modified) Nakajima monomial model for crystals is given. We give an explicit description of the Lusztig data for modified Nakajima monomials in type $A_n$.

Rigged configurations and the $*$-involutionJan 22 2016Mar 02 2016We give an explicit description of the $*$-involution on the rigged configuration model for $B(\infty)$.

Symplectic resolutions of quiver varieties and character varietiesJan 30 2016Dec 13 2018In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover ... More

Filtrations on Springer fiber cohomology and Kostka polynomialsSep 08 2015Sep 25 2017We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct ... More

Poisson-de Rham homology of hypertoric varieties and nilpotent conesMay 04 2014We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this ... More

Ramified Satake Isomorphisms for strongly parabolic charactersOct 03 2012For certain characters of the compact torus of a reductive $p$-adic group, which we call strongly parabolic characters, we prove Satake-type isomorphisms. Our results generalize those of Satake, Howe, Bushnell and Kutzko, and Roche.

Integral equation formulation of the biharmonic Dirichlet problemMay 26 2017We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation can be used. ... More

Virtualization map for the Littelmann path modelSep 27 2015Oct 31 2017We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type independent proof that certain Kirillov--Reshetikhin ... More

Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curvesFeb 19 2019We define a symmetric monoidal category Trop which, roughly, has degrees of tropical curves as its objects and types of tropical curves as its morphisms. A symmetric monoidal functor with domain Trop is what we call a (2D) tropical quantum field theory ... More

K-theoretic crystals for set-valued tableaux of rectangular shapesApr 21 2019Jun 03 2019In earlier work with C. Monical (2018), we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured that such a K-crystal structure existed on the set of semistandard ... More

Image Ellipticity from Atmospheric AberrationsMar 06 2007We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors ... More

What is odd about binary Parseval frames?Jul 24 2015This paper examines the construction and properties of binary Parseval frames. We address two questions: When does a binary Parseval frame have a complementary Parseval frame? Which binary symmetric idempotent matrices are Gram matrices of binary Parseval ... More

Interferometric CO(3-2) Observations toward the Central Region of NGC 1068Dec 01 2011We present CO(3-2) interferometric observations of the central region of the Seyfert 2 galaxy NGC 1068 using the Submillimeter Array, together with CO(1-0) data taken with the Owens Valley Radio Observatory Millimeter Array. Both the CO(3-2) and CO(1-0) ... More

Making root cause analysis feasible for large code bases: a solution approach for a climate modelOct 31 2018Feb 11 2019For large-scale simulation codes with huge and complex code bases, where bit-for-bit comparisons are too restrictive, finding the source of statistically significant discrepancies (e.g., from a previous version, alternative hardware or supporting software ... More

MuSR and neutron diffraction studies on the tuning of spin-glass phase in partially ordered double perovskite SrMn$_{1-x}$W$_x$O$_3$Oct 16 2018Tunability of the partially ordered double perovskite (PODP) and coexisting spin-glass phase in SrMn1-xWxO3 (x=0.20 to 0.40) have been studied using neutron powder diffraction (NPD), muon spin relaxation (MuSR), and magnetic susceptibility (X) measurements. ... More

Propagation Modeling Through Foliage in a Coniferous Forest at 28 GHzFeb 18 2019The goal of this article is to investigate the propagation behavior of 28-GHz millimeter wave in coniferous forests and model its basic transmission loss. Field measurements were conducted with a custom-designed sliding correlator sounder. Relevant foliage ... More

Structure, antiferromagnetism and superconductivity of the layered iron arsenide NaFeAsOct 17 2008Mar 05 2009A new layered iron arsenide NaFeAs isostructural with the superconducting lithium analogue, displays evidence for the coexistence of superconductivity and magnetic ordering.

Improved Quantum Hard-Sphere Ground-State Equations of StateMay 09 2007Oct 26 2007The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a sphere-of-influence picture, and generalized to fermion hard-sphere systems ... More

Study of Conduction Cooling Effects in Long Aspect Ratio Penning-Malmberg Micro-TrapsJul 12 2013A first order perturbation with respect to velocity has been employed to find the frictional damping force imposed on a single moving charge due to a perturbative electric field, inside a long circular cylindrical trap. We find that the electric field ... More

Prompt Electromagnetic Transients from Binary Black Hole MergersOct 05 2017Jan 16 2018Binary black hole (BBH) mergers provide a prime source for current and future interferometric GW observatories. Massive BBH mergers may often take place in plasma-rich environments, leading to the exciting possibility of a concurrent electromagnetic (EM) ... More