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A Massive Magnetic Helium Atmosphere White Dwarf Binary in a Young Star ClusterJun 11 2019We have searched the Gaia DR2 catalogue for previously unknown hot white dwarfs in the direction of young open star clusters. The aim of this experiment was to try and extend the initial-final mass relation (IFMR) to somewhat higher masses, potentially ... More

Uncovering Multiple Populations in NGC 7099 (M 30) using Washington PhotometrySep 04 2017Over the last decade, the classical definition of Globular Clusters (GCs) as simple stellar populations was revolutionized due to the discovery of "Multiple Populations" (MPs). However, our knowledge of this phenomenon and its characteristics is still ... More

Magnetic Field Evolution During Neutron Star RecyclingApr 27 2004I describe work on two aspects of magnetic field evolution relevant for the "recycling" scenario for making millisecond radio pulsars. First, many of the theoretical ideas for bringing about accretion-induced field decay rely on dissipation of currents ... More

Detectability of Extrasolar Planets in Radial Velocity SurveysAug 25 2004Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long periods and low ... More

Multiple Populations in NGC 1851: Abundance Variations and UV Photometric Synthesis in the Washington and HST/WFC3 SystemsApr 07 2017The analysis of multiple populations (MPs) in globular clusters, both spectroscopically and photometrically, is key in understanding their formation and evolution. The relatively narrow Johnson U, F336W, and Stromgren and Sloan u filters have been crucial ... More

The delayed evolution of high-mass white dwarfs: the Q branch and double-white-dwarf mergersMay 29 2019Studying high-mass white dwarfs (WDs) can shed light on the progenitors of Type Ia supernovae. Recently, the unprecedented power of Gaia Data Release 2 (DR2) has revealed an enhancement of high-mass WDs on the H-R diagram, called the Q branch. This branch ... More

The delayed evolution of high-mass white dwarfs: the Q branch and double-white-dwarf mergersMay 29 2019Jun 07 2019Studying high-mass white dwarfs (WDs) can shed light on the progenitors of Type Ia supernovae. Recently, the unprecedented power of Gaia Data Release 2 (DR2) has revealed an enhancement of high-mass WDs on the H-R diagram, called the Q branch. This branch ... More

Improved Main Sequence Turnoff Ages of Young Open Clusters: Multicolor UBV Techniques & the Challenges of RotationJul 27 2018Main sequence turnoff ages in young open clusters are complicated by turnoffs that are sparse, have high binarity fractions, can be affected by differential reddening, and typically include a number of peculiar stars. Furthermore, stellar rotation can ... More

Exploring the nature and synchronicity of early cluster formation in the Large Magellanic Cloud IV: Evidence for Multiple Populations in Hodge 11 and NGC 2210Apr 02 2019Apr 05 2019We present a multiple population search in two old Large Magellanic Cloud (LMC) Globular Clusters, Hodge 11 and NGC 2210. This work uses data from the Advanced Camera for Surveys and Wide Field Camera 3 on the Hubble Space Telescope from programme GO-14164 ... More

On Pattern and EvolutionApr 20 2009May 10 2009A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss curvature'K'enters. ... More

Helium-rich thermonuclear bursts and the distance to the accretion-powered millisecond pulsar SAX J1808.4-3658Jul 11 2006We analysed Rossi X-ray Timing Explorer observations of the accretion-powered 401 Hz pulsar SAX J1808.4-3658, in order to precisely determine the source distance. While the fluences for the five transient outbursts observed from 1996 were constant to ... More

Uncovering Multiple Populations with Washington Photometry: I. The Globular Cluster NGC 1851Jun 02 2014The analysis of multiple populations (MPs) in globular clusters (GCs) has become a forefront area of research in astronomy. Multiple red giant branches (RGBs), subgiant branches (SGBs), and even main sequences (MSs) have now been observed photometrically ... More

Enhanced Performance of Short-Channel Carbon Nanotube Field-Effect Transistors Due to Gate-Modulated Electrical ContactsMay 01 2012We use numerical simulations to analyze recent experimental measurements of short-channel carbon nanotube field-effect transistors with palladium contacts. We show that the gate strongly modulates the contact properties, an effect that is distinct from ... More

$^3$He Transport in the Sun and the Solar Neutrino ProblemAug 20 1996Recent solar neutrino experiments have shown that both $\phi(^8$B) and the neutrino flux ratio $\phi(^7$Be)/$\phi(^8$B) are substantially below their standard solar model values, leading some to discount the possibility of an astrophysical solution to ... More

Effects of Dephasing on Spin Lifetime in Ballistic Spin-Orbit MaterialsFeb 15 2016We theoretically investigate spin dynamics in spin-orbit-coupled materials. In the ballistic limit, the spin lifetime is dictated by dephasing that arises from energy broadening plus a non-uniform spin precession. For the case of clean graphene, we find ... More

Rollercoasters and CaterpillarsJan 25 2018A rollercoaster is a sequence of real numbers for which every maximal contiguous subsequence, that is increasing or decreasing, has length at least three. By translating this sequence to a set of points in the plane, a rollercoaster can be defined as ... More

A Novel Approach to Constrain Rotational Mixing & Convective-Core Overshoot in Stars Using the Initial-Final Mass RelationJan 09 2019The semi-empirical initial-final mass relation (IFMR) connects spectroscopically analyzed white dwarfs in star clusters to the initial masses of the stars that formed them. Most current stellar evolution models, however, predict that stars will evolve ... More

WIYN Open Cluster Study. LXXV. Testing the Metallicity Dependence of Stellar Lithium Depletion Using Hyades-Aged Clusters. 1. Hyades & PraesepeFeb 13 2017WIYN/Hydra spectroscopy (at R~15,000) of the moderately metal-rich Praesepe and Hyades open clusters was used to study their main sequence (MS) iron ([Fe/H]) and lithium (A(Li)) abundances. Self-consistent [Fe/H] and Li analyses of these clusters of consistent ... More

Lithium Abundances of the Super-Metal-Rich Open Cluster NGC 6253Sep 25 2012High-resolution CTIO 4-m/HYDRA spectroscopy of the super-metal-rich open cluster NGC 6253 ([Fe/H]=+0.43+/-0.01) has been used to study the stellar lithium (Li) abundances near the cluster's turnoff. NGC 6253 greatly expands the range of [Fe/H] for clusters ... More

An Ultramassive 1.28 M$_\odot$ White Dwarf in NGC 2099Mar 01 2016With the Keck I Low-Resolution Imaging Spectrometer we have observed nine white dwarf candidates in the very rich open cluster NGC 2099 (M37). The spectroscopy shows seven to be DA white dwarfs, one to be a DB white dwarf, and one to be a DZ white dwarf. ... More

Initial-Final Mass Relation for 3 to 4 M$_\odot$ Progenitors of White Dwarfs from the Single Cluster NGC 2099May 25 2015We have expanded the sample of observed white dwarfs in the rich open cluster NGC 2099 (M37) with the Keck Low-Resolution Imaging Spectrometer. Of 20 white dwarf candidates, the spectroscopy shows 19 to be true white dwarfs with 14 of these having high ... More

Two Massive White Dwarfs from NGC 2323 and the Initial-Final Mass Relation for Progenitors of 4 to 6.5 M$_\odot$Jan 12 2016We have observed a sample of 10 white dwarf candidates in the rich open cluster NGC 2323 (M50) with the Keck Low-Resolution Imaging Spectrometer. The spectroscopy shows eight to be DA white dwarfs, with six of these having high S/N appropriate for our ... More

TESS reveals that the nearby Pisces-Eridanus stellar stream is only 120 Myr oldMay 25 2019Pisces-Eridanus (Psc-Eri), a nearby ($d$ $\simeq$ 80-226 pc) stellar stream stretching across $\approx$120 degrees of the sky, was recently discovered with Gaia data. The stream was claimed to be $\approx$1 Gyr old, which would make it an exceptional ... More

The White Dwarf Initial-Final Mass Relation for Progenitor Stars From 0.85 to 7.5 M$_\odot$Sep 05 2018We present the initial-final mass relation (IFMR) based on the self-consistent analysis of Sirius B and 79 white dwarfs from 13 star clusters. We have also acquired additional signal on eight white dwarfs previously analyzed in the NGC 2099 cluster field, ... More

Worldtube conservation laws for the null-timelike evolution problemMay 17 2011I treat the worldtube constraints which arise in the null-timelike initial-boundary value problem for the Bondi-Sachs formulation of Einstein's equations. Boundary data on a worldtube and initial data on an outgoing null hypersurface determine the exterior ... More

Deforming Representations of SL(2,R)Jan 20 2017The spherical principal series representations $\pi(\nu)$ of SL(2,$\mathbb R$) is a family of infinite dimensional representations parametrized by $\nu\in\mathbb C$. The representation $\pi(\nu)$ is irreducible unless $\nu$ is an odd integer, in which ... More

Lifting images of standard representations of symmetric groupsMar 14 2019May 02 2019We investigate closed subgroups $G \subseteq \mathrm{Sp}_{2g}(\mathbb{Z}_2)$ whose modulo-$2$ images coincide with the image $\mathfrak{S}_{2g + 1} \subseteq \mathrm{Sp}_{2g}(\mathbb{F}_2)$ of $S_{2g + 1}$ or the image $\mathfrak{S}_{2g + 2} \subseteq ... More

Some Results on Pseudo-Collar Structures on High-Dimensional ManifoldsFeb 15 2015In this paper, we recall Quillen's plus construction for high-dimensional smooth manifolds and the solution to the group extension problem. We then develop a geometric procedure due for producing a "reverse" to the plus construction, a one-sided s-cobordism ... More

Semistable models of elliptic curves over residue characteristic 2May 14 2019May 21 2019Given an elliptic curve $E$ in Legendre form $y^2 = x(x - 1)(x - \lambda)$ over the fraction field of a Henselian ring $R$ of mixed characteristic $(0, 2)$, we present an algorithm for determining a semistable model of $E$ over $R$ which depends only ... More

An equivalence between two approaches to limits of local fieldsNov 18 2015Nov 20 2015Marc Krasner proposed a theory of limits of local fields in which one relates the extensions of a local field to the extensions of a sequence of related local fields. The key ingredient in his approach was the notion of valued hyperfields, which occur ... More

Length of the continued logarithm algorithm on rational inputsJun 13 2016Jun 21 2016The continued logarithm algorithm was introduced by Gosper around 1978, and recently studied by Borwein, Calkin, Lindstrom, and Mattingly. In this note I show that the continued logarithm algorithm terminates in at most 2 log_2 p + O(1) steps on input ... More

Extension of valuations in characteristic oneMay 20 2016Aug 22 2016We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central results in the ... More

The Quantum Sabine Law for Resonances in Transmission ProblemsNov 16 2015We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering by transparent ... More

Obstruction criteria for modular deformation problemsSep 24 2014For a newform $f=\sum a_n q^n$ of weight $k \geq 3$ and a prime $\lambda$ of $\mathbf{Q}(a_n)$, the deformation problem for its associated mod $\lambda$ Galois representation is unobstructed for all primes outside some finite set. Previous results gave ... More

A concentration-collapse decomposition for $L^2$ flow singularitiesNov 05 2013We exhibit a concentration-collapse decomposition of singularities of fourth order curvature flows, including the $L^2$ curvature flow and Calabi flow, in dimensions $n \leq 4$. The proof requires the development of several new a priori estimates. First, ... More

Stark conjectures for CM curves over number fieldsAug 30 2001We present an elliptic curve analog of the Stark conjecture for the value of the $L$-function at $s=0$. Although implied by the general Beilinson conjectures, the approach here is very concrete. Several cases are proved.

An interacting particle system with geometric jump rates near a partially reflecting boundaryJan 20 2016This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the dynamics match ... More

Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank twoApr 27 2015May 22 2015We study two generalizations of the asymmetric simple exclusion process with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that ... More

On the Relative Gain Array (RGA) with Singular and Rectangular MatricesMay 25 2018Mar 04 2019In this paper we identify a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, we show that the conventional use of the Moore-Penrose pseudoinverse is ... More

Sylow 0-unipotent subgroups in groups of finite Morley rankNov 26 2007One of the central tools in the classification of simple algebraic groups is the distinction between semisimple subgroups and unipotent subgroups. It is not a priori clear how to make this distinction for torsion-free subgroups of a group of finite Morley ... More

A signalizer functor theorem for groups of finite Morley rankAug 06 2003There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik's trichotomy theorem. The "trichotomy" here is a case ... More

Does Ten Have a Friend?Jun 05 2008Jun 06 2008Any positive integer $n$ other than 10 with abundancy index 9/5 must be a square with at least 6 distinct prime factors, the smallest being 5. Further, at least one of the prime factors must be congruent to 1 modulo 3 and appear with an exponent congruent ... More

Semistable models of elliptic curves over residue characteristic 2May 14 2019Given an elliptic curve $E$ in Legendre form $y^2 = x(x - 1)(x - \lambda)$ over the fraction field of a Henselian ring $R$ of mixed characteristic $(0, 2)$, we present an algorithm for determining a semistable model of $E$ over $R$ which depends only ... More

Distinguished Cuspidal Representations over p-adic and Finite FieldsMar 26 2017May 12 2017The author's work with Murnaghan on distinguished tame supercuspidal representations is re-examined using a simplified treatment of Jiu-Kang Yu's construction of tame supercuspidal representations of $p$-adic reductive groups. This leads to a unification ... More

Elementary Deuring-Heilbronn PhenomenonJan 03 2012Jul 02 2012Adapting a technique of Pintz, we give an elementary demonstration of the Deuring phenomenon: a zero of \zeta(s) off the critical line gives a lower bound on L(1,\chi). The necessary tools are Dirichlet's 'method of the hyperbola', Euler summation, summation ... More

The stable mapping class group of simply connected 4-manifoldsOct 27 2005Apr 10 2007We consider mapping class groups \Gamma(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if M contains CP^2 (with either orientation) as a connected summand then ... More

Ideal triangulations and geometric transitionsMay 22 2013May 13 2014Thurston introduced a technique for finding and deforming three-dimensional hyperbolic structures by gluing together ideal tetrahedra. We generalize this technique to study families of geometric structures that transition from hyperbolic to anti de Sitter ... More

A Geometric Reverse To The Plus Construction And Some Examples Of Pseudo-Collars On High-Dimensional ManifoldsAug 14 2015In this paper, we develop a geometric procedure for producing a reverse to Quillen's plus construction, a construction called a 1-sided h-cobordism or semi-h-cobordism. We then use this reverse to the plus construction to produce uncountably many distinct ... More

Time dilation relation for a Dirac Hamiltonian generator on a qubit arrayDec 08 2015Dec 13 2015Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum algorithm to model ... More

Images of 2-adic representations associated to hyperelliptic JacobiansOct 10 2014Let $k$ be a subfield of $\mathbb{C}$ which contains all $2$-power roots of unity, and let $K = k(\alpha_{1}, \alpha_{2}, ... , \alpha_{2g + 1})$, where the $\alpha_{i}$'s are independent and transcendental over $k$, and $g$ is a positive integer. We ... More

Global viscosity solutions of generalized Kahler-Ricci flowOct 06 2016We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kahler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth manifold with smooth ... More

Characteristic Evolution and MatchingAug 23 2005Dec 08 2005I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations ... More

A Geometric transition from hyperbolic to anti de Sitter geometryFeb 22 2013We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe ... More

Quantum Correlations and the Measurement ProblemOct 23 2012Jan 14 2013The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. ... More

Trapping planar Brownian motion in a non circular trapOct 30 2016Nov 01 2016Brownian motion in the plane in the presence of a "trap" at which motion is stopped is shown. If the trap $T$ is a connected compact set, it is shown that the probability for planar Brownian motion to hit this set before a given time $t$ is well approximated ... More

Two constructions of Markov chains on the dual of U(n)Dec 12 2012Apr 09 2017We provide two new constructions of Markov chains which had previously arisen from the representation theory of the infinite-dimensional unitary group. The first construction uses the combinatorial rule for the Littlewood-Richardson coefficients, which ... More

Lifting images of standard representations of symmetric groupsMar 14 2019We investigate closed subgroups $G \subseteq \mathrm{Sp}_{2g}(\mathbb{Z}_2)$ whose modulo-$2$ images coincide with the image $\mathfrak{S}_{2g + 1} \subseteq \mathrm{Sp}_{2g}(\mathbb{F}_2)$ of $S_{2g + 1}$ or the image $\mathfrak{S}_{2g + 2} \subseteq ... More

A Scale-Consistent Approach for Recommender SystemsApr 30 2019In this paper we propose and develop a relatively simple and efficient approach for estimating unknown elements of a user-rating matrix in the context of a recommender system (RS). The critical theoretical property of the method is its consistency with ... More

The Bender method in groups of finite Morley rankNov 27 2007Jaligot's Lemma states that the Fitting subgroups of distinct Borel subgroups do not intersect in a tame minimal simple groups of finite Morley. Such a strong result appears hopeless without tameness. Here we use the 0-unipotence theory to build a toolkit ... More

Constructing tame supercuspidal representationsJan 26 2017Nov 28 2017A new approach to Jiu-Kang Yu's construction of tame supercuspidal representations of $p$-adic reductive groups is presented. Connections with the theory of cuspidal Deligne-Lusztig representations of finite groups of Lie type are also discussed.

On Frattini arguments in L-groups of finite Morley rankApr 20 2009We modify the Frecon-Jaligot construction of Carter subgroups to show that a degenerate type group has a Carter subgroup invariant under the Sylow 2-subgroup of a group of automorphisms; thus reducing the need to know that Carter subgroups are conjugate ... More

Notes on $\log(ζ(s))^{\prime\prime}$Nov 21 2013Dec 22 2014Motivated by the connection to the pair correlation of the Riemann zeros, we investigate the second derivative of the logarithm of the Riemann zeta function, in particular the zeros of this function. Theorem 1 gives a zero-free region. Theorem 2 gives ... More

The computational complexity of the local postage stamp problemDec 22 2001The well-studied local postage stamp problem (LPSP) is the following: given a positive integer k, a set of postive integers 1 = a1 < a2 < ... < ak and an integer h >= 1, what is the smallest positive integer which cannot be represented as a linear combination ... More

A note on 8-division fields of elliptic curvesApr 20 2017Aug 02 2017Let $K$ be a field of characteristic different from $2$ and let $E$ be an elliptic curve over $K$, defined either by an equation of the form $y^{2} = f(x)$ with degree $3$ or as the Jacobian of a curve defined by an equation of the form $y^{2} = f(x)$ ... More

Notes on Low discriminants and the generalized Newman conjectureJan 14 2013Apr 10 2013Generalizing work of Polya, de Bruijn and Newman, we allow the backward heat equation to deform the zeros of quadratic Dirichlet L-functions. There is a real constant \Lambda_Kr (generalizing the de Bruijn-Newman constant \Lambda) such that for time t>=\Lambda_Kr ... More

Galois Cohomology of Real GroupsOct 29 2013Jul 01 2014Real forms of a complex reductive group are classified in terms of Galois cohomology $H^1(\Gamma,G_{ad})$ where $G_{ad}$ is the adjoint group. Alternatively, the theory of the Cartan involution gives a description in terms of cohomology with respect to ... More

Distinguished Regular Supercuspidal Representations and Inductive Constructions of RepresentationsAug 12 2018This paper develops the theory of distinguished regular supercuspidal representations, and it highlights how the correspondence between regular characters and regular supercuspidal representations resembles induction in certain ways.

Quivers and Three-Dimensional Lie AlgebrasSep 23 2014We study a family of three-dimensional Lie algebras $L_\mu$ that depend on a continuous parameter $\mu$. We introduce certain quivers, which we denote by $Q_{m,n}$ $(m,n \in \mathbb{Z})$ and $Q_{\infty \times \infty}$, and prove that idempotented versions ... More

A Lattice-Gas with Long-Range Interactions Coupled to a Heat BathMar 18 1994Introduced is a lattice-gas with long-range 2-body interactions. An effective inter-particle force is mediated by momentum exchanges. There exists the possibility of having both attractive and repulsive interactions using finite impact parameter collisions. ... More

Homology of framed links embedded in thickened surfacesOct 30 2008We construct an infinite family of homology theories of framed links in thickened surfaces, as well as a homology theory whose graded Euler characteristic is exactly the Kauffman bracket of the link in the surface. Both theories are based on ideas coming ... More

Distinguishing topologically and smoothly doubly slice knotsJan 06 2014Nov 03 2014We construct an infinite family of smoothly slice knots that we prove are topologically doubly slice. Using the correction terms coming from Heegaard Floer homology, we show that none of these knots is smoothly doubly slice. We use these knots to show ... More

Generalized geometry, T-duality, and renormalization group flowOct 18 2013We interpret the physical $B$-field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural "Ricci flow" for generalized geometry. Next we show that the $B$-field renormalization group flow ... More

The gradient flow of the $L^2$ curvature energy on surfacesAug 25 2010We investigate the gradient flow of the $L^2$ norm of the Riemannian curvature on surfaces. We show long time existence with arbitrary initial data, and exponential convergence of the volume normalized flow to a constant scalar curvature metric when the ... More

Pluriclosed flow, Born-Infeld geometry, and rigidity results for generalized Kähler manifoldsFeb 09 2015We prove long time existence and convergence results for the pluriclosed flow, which imply geometric and topological classification theorems for generalized K\"ahler structures. Our approach centers on the reduction of pluriclosed flow to a degenerate ... More

Resonances for Thin Barriers on the CircleOct 01 2014Jan 14 2016We study high energy resonances for the operator $-\Delta_{V,\partial\Omega}:=-\Delta+\delta_{\partial\Omega}\otimes V $ when $V$ has strong frequency dependence. The operator $-\Delta_{V,\partial\Omega}$ is a Hamiltonian used to model both quantum corrals ... More

Closed-form analytical continuation of spin density interactions in spin-2 superfluidsSep 08 2016Presented is an unitary operator splitting method for handling the spin-density interaction in spinor Bose-Einstein condensates. The zero temperature behavior of a spinor BEC is given by mean field theory, where the Hamiltonian includes a nonlinear hyperfine ... More

Pluriclosed flow on manifolds with globally generated bundlesJun 13 2016We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.

Patching and Multiplicity $2^k$ for Shimura CurvesFeb 19 2019We use the Taylor--Wiles--Kisin patching method to investigate the multiplicities with which Galois representations occur in the mod $\ell$ cohomology of Shimura curves over totally real number fields. Our method relies on explicit computations of local ... More

Asymptotics of a discrete-time particle system near a reflecting boundaryMar 07 2012Dec 11 2012We examine a discrete-time Markovian particle system on the quarter-plane introduced by M. Defosseux. The vertical boundary acts as a reflecting wall. The particle system lies in the Anisotropic Kardar-Parisi-Zhang with a wall universality class. After ... More

Ramsey theory for monochromatically well-connected subsetsFeb 28 2019We define well-connectedness, an order-theoretic notion of largeness whose associated partition relations $\nu\to_{wc}(\mu)_\lambda^2$ formally weaken those of the classical Ramsey relations $\nu\to(\mu)_\lambda^2$. We show that it is consistent that ... More

Lifting images of standard representations of symmetric groupsMar 14 2019Apr 20 2019We investigate closed subgroups $G \subseteq \mathrm{Sp}_{2g}(\mathbb{Z}_2)$ whose modulo-$2$ images coincide with the image $\mathfrak{S}_{2g + 1} \subseteq \mathrm{Sp}_{2g}(\mathbb{F}_2)$ of $S_{2g + 1}$ or the image $\mathfrak{S}_{2g + 2} \subseteq ... More

Computing rank of finite algebraic structures with limited nondeterminismJun 03 2014Feb 12 2016The rank of a finite algebraic structure with a single binary operation is the minimum number of elements needed to express every other element under the closure of the operation. In the case of groups, the previous best algorithm for computing rank used ... More

A simple homotopy-theoretical proof of the Sullivan conjectureMay 19 2011We give a new proof, using comparatively simple techniques, of the Sullivan conjecture: the space of pointed maps from the classifying space of the cyclic group of order $p$ to any finite-dimensional CW complex $K$ is contractible.

Row-strict Quasisymmetric Schur Functions, Characterizations of Demazure Atoms, and Permuted Basement Nonsymmetric Macdonald PolynomialsMar 14 2013We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. We then discuss a family of polynomials called Demazure ... More

A Littlewood-Richardson Type Rule for Row-Strict Quasisymmetric Schur FunctionsFeb 07 2011We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. This expansion follows from several new properties ... More

Eigenvector localization for random band matrices with power law band widthSep 25 2008Jan 07 2009It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard ... More

Idempotent functors that preserve cofiber sequences and split suspensionsMay 10 2012Jul 23 2012We show that an $f$-localization functor $L_f$ commutes with cofiber sequences of $(N-1)$-connected finite complexes if and only if its restriction to the collection of $(N-1)$-connected finite complexes is $R$-localization for some unital subring $R\sseq\mathbb{Q}$. ... More

A Negative Answer to a Problem of Aldous on Determination of Exchangeable SequencesJul 02 2015We present results concerning when the joint distribution of an exchangeable sequence is determined by the marginal distributions of its partial sums. The question of whether or not this determination occurs was posed by David Aldous. We then consider ... More

Lehmer pairs revisitedAug 24 2015Oct 11 2015We seek to understand how the technical definition of Lehmer pair can be related to more analytic properties of the Riemann zeta function, particularly the location of the zeros of $\zeta^\prime(s)$. Because we are interested in the connection between ... More

Long Time Boundedness of Planar Jump Discontinuities for Homogeneous Hyperbolic SystemsJan 13 2019Suppose that $L(\partial_t,\partial_x)$ is a homogeneous constant coefficient strongly hyperbolic partial differential operator on ${\mathbb R}^{1+d}$ and $H$ is a characteristic hyperplane. Suppose that in a conic neighborhood of the conormal variety ... More

Markov Chains, Tensor Products, and Quantum Random WalksDec 12 2012We provide two new constructions of Markov chains which had previously arisen from the representation theory of the infinite-dimensional unitary group. The first construction uses the combinatorial rule for the Littlewood-Richardson coefficients, which ... More

Disembodied boundary data for Einstein's equationsSep 10 2009Nov 12 2009A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld conditions have been ... More

A New Way to Make WavesMar 08 2000I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other systems described ... More

The characteristic treatment of black holesNov 26 1999The characteristic initial value problem has been implemented as a robust computational algorithm (the PITT NULL CODE), with direct application to binary black holes. The event horizon can be analyzed by characteristic techniques as a stand-alone object ... More

The six-point remainder function to all loop orders in the multi-Regge limitSep 24 2012We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric N=4 Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics. In the MHV helicity configuration, our results agree with an integral ... More

The parametrized probabilistic finite-state transducer probe game player fingerprint modelJan 29 2014Fingerprinting operators generate functional signatures of game players and are useful for their automated analysis independent of representation or encoding. The theory for a fingerprinting operator which returns the length-weighted probability of a ... More

The diffeomorphism group of a K3 surface and Nielsen realizationMay 31 2007Jan 15 2009The Nielsen Realization problem asks when the group homomorphism from Diff(M) to pi_0 Diff(M) admits a section. For M a closed surface, Kerckhoff proved that a section exists over any finite subgroup, but Morita proved that if the genus is large enough ... More

Tame Supercuspidal Representations of $\GL_n$ Distinguished by Orthogonal InvolutionsAug 25 2011For a $p$-adic field $F$, the embeddings of a tame supercuspidal representation of $G= {\rm GL}_n (F)$ in the space of smooth functions on the set of symmetric matrices in $G$ are determined.

Guide to the Atlas Software: Computational Representation Theory of Real Reductive GroupsJul 19 2008This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples. See Algorithms ... More

On the theorem of Conrey and IwaniecJul 02 2013An exposition on "Spacing of zeros of Hecke L-functions and the class number problem" by Conrey and Iwaniec; any errors are my own.