total 4667took 0.10s

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

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

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

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

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 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

Dyadic torsion of 2-dimensional hyperelliptic JacobiansOct 29 2014Let $k$ be a field of characteristic $0$, and let $\alpha_{1}$, $\alpha_{2}$, ..., $\alpha_{5}$ be algebraically independent and transcendental over $k$. Let $K$ be the transcendental extension of $k$ obtained by adjoining the elementary symmetric functions ... 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

An abelian subfield of the dyadic division field of a hyperelliptic JacobianFeb 28 2018Feb 13 2019Given a field $k$ of characteristic different from $2$ and an integer $d \geq 3$, let $J$ be the Jacobian of the "generic" hyperelliptic curve given by $y^2 = \prod_{i = 1}^d (x - \alpha_i)$, where the $\alpha_i$'s are transcendental and independent over ... More

Prime-to-$p$ étale fundamental groups of punctured projective lines over strictly Henselian fieldsJul 03 2017Jul 20 2017Let $K$ be the fraction field of a strictly Henselian DVR of characteristic $p \geq 0$ with algebraic closure $\bar{K}$, and let $\alpha_{1}, ..., \alpha_{d} \in \mathbb{P}_{K}^{1}(K)$. In this paper, we give explicit generators and relations for the ... More

Dyadic Torsion of Elliptic CurvesOct 24 2013Nov 11 2014Let $k$ be a field of characteristic $0$, and let $\alpha_{1}$, $\alpha_{2}$, and $\alpha_{3}$ be algebraically independent and transcendental over $k$. Let $K$ be the transcendental extension of $k$ obtained by adjoining the elementary symmetric functions ... 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

Boundary Conditions for the Gravitational FieldMar 09 2012Apr 24 2012A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation ... More

Geometrization of metric boundary data for Einstein's equationsApr 02 2009The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new formulation of ... More

Characteristic Evolution and MatchingOct 10 2008Jan 12 2012I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that ... 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

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

The K-level crossings of a random algebraic polynomial with dependent coefficientsDec 21 2009For a random polynomial with standard normal coefficients, two cases of the K-level crossings have been considered by Farahmand. When the coefficients are independent, Farahmand was able to derive an asymptotic value for the expected number of level crossings, ... More

The real zeros of a random algebraic polynomial with dependent coefficientsJun 10 2009Jul 18 2010Mark Kac gave one of the first results analyzing random polynomial zeros. He considered the case of independent standard normal coefficients and was able to show that the expected number of real zeros for a degree n polynomial is on the order of (2/pi)log(n), ... 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.

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

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

Stability of Critical p-Improper Interval GraphsMar 15 2019A $p$-improper interval graph is an interval graph that has an interval representation in which no interval contains more than $p$ other intervals. A critical $p$-improper interval graph is $p-1$ improper when any vertex is removed. In this paper we investigate ... More

Gromov-- Witten Invariants of Toric FibrationsJan 09 2009We prove a conjecture of Artur Elezi in a generalized form suggested by Givental. Namely, our main result relates genus-0 Gromov--Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric manifold. When the ... 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

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

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

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 $L^2$ Behavior of Eigenfunctions Near the Glancing SetApr 06 2016Let $M$ be a compact manifold with or without boundary and $H\subset M$ be a smooth, interior hypersurface. We study the restriction of Laplace eigenfunctions solving $(-h^2\Delta_g-1)u=0$ to $H$. In particular, we study the degeneration of $u|_H$ as ... More

Generalized Kähler-Ricci flow and the classification of nondegenerate generalized Kähler surfacesJan 12 2016We study the generalized K\"ahler-Ricci flow on complex surfaces with nondegenerate Poisson structure, proving long time existence and convergence of the flow to a weak hyperK\"ahler structure.

Modular forms of arbitrary even weight with no exceptional primesJan 12 2016Apr 01 2016A result of Dieulefait-Wiese proves the existence of modular eigenforms of weight 2 for which the image of every associated residual Galois representation is as large as possible. We generalize this result to eigenforms of general even weight k $\geq$ ... More

NPCs Vote! Changing Voter Reactions Over Time Using the Extreme AI Personality EngineSep 17 2016Can non-player characters have human-realistic personalities, changing over time depending on input from those around them? And can they have different reactions and thoughts about different people? Using Extreme AI, a psychology-based personality engine ... More

Quantum lattice gas algorithmic representation of gauge field theorySep 07 2016Sep 14 2016Presented is a quantum lattice gas algorithm to efficiently model a system of Dirac particles interacting through an intermediary gauge field. The algorithm uses a fixed qubit array to represent both the spacetime and the particles contained in the spacetime. ... More

Rank parity for congruent supersingular elliptic curvesMay 26 2016Oct 06 2016A recent paper of Shekhar compares the ranks of elliptic curves $E_1$ and $E_2$ for which there is an isomorphism $E_1[p] \simeq E_2[p]$ as $\mathrm{Gal}(\bar{\mathbf{Q}}/\mathbf{Q})$-modules, where $p$ is a prime of good ordinary reduction for both curves. ... More

A note on cabled slice knots and reducible surgeriesJul 16 2015We consider the question of when a slice knot admits a reducible Dehn surgery. By analyzing the correction terms associated to such a surgery, we show that slice knots cannot admit surgeries with more than two summands. We also give a necessary Heegaard ... More

Pluriclosed flow on generalized Kähler manifolds with split tangent bundleMay 04 2014Jun 02 2015We show that the pluriclosed flow preserves generalized K\"ahler structures with the extra condition $[J_+,J_-] = 0$, a condition referred to as "split tangent bundle." Moreover, we show that in this in this case the flow reduces to a nonconvex fully ... 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

Optimal Scaling and Shaping of Random Walk Metropolis via Diffusion Limits of Block-I.I.D. TargetsFeb 18 2019This work extends Roberts et al. (1997) by considering limits of Random Walk Metropolis (RWM) applied to block IID target distributions, with corresponding block-independent proposals. The extension verifies the robustness of the optimal scaling heuristic, ... More

A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groupsJan 18 2016This paper introduces a (2+1)-dimensional Gaussian field which has the Gaussian free field on the upper half-plane with zero boundary conditions as certain two-dimensional sections. Along these sections, called space-like paths, it matches the Gaussian ... More

The Gaussian free field in interlacing particle systemsSep 20 2011Aug 23 2014We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the fluctuations of ... More

An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerationsJan 16 2017Jan 31 2017A recent paper \cite{KMMO} introduced the stochastic U_q(A_n^{(1)}) vertex model. The stochastic S-matrix is related to the R-matrix of the quantum group U_q(A_n^{(1)}) by a gauge transformation. We will show that a certain function D^+_{\mu} intertwines ... More

Finite-dimensional spaces in resolving classesMay 03 2012Using the theory of resolving classes, we show that if $X$ is a CW complex of finite type such that $\map_*(X, S^{2n+1})\sim *$ for all sufficiently large $n$, then $\map_*(X, K) \sim *$ for every simply-connected finite-dimensional CW complex $K$; and ... More

Signalizers and balance in groups of finite Morley rankNov 27 2007Nov 28 2008We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has Prufer 2-rank at most two. This article covers the signalizer functor theory and identifies the groups of Lie rank at least ... More

Strong Homology, Derived Limits, and Set TheorySep 30 2015We consider the question of the additivity of strong homology. This entails isolating the set-theoretic content of the higher derived limits of an inverse system indexed by the functions from $\mathbb{N}$ to $\mathbb{N}$. We show that this system governs, ... More

On the Rank of the Elliptic Curve y^2=x(x-p)(x-2)Sep 09 2009An elliptic curve E defined over \Q is an algebraic variety which forms a finitely generated abelian group, and the structure theorem then implies that E = \Z^r + \Z_{tors} for some r \geq 0; this value r is called the rank of E. It is a classical problem ... More

Miller Spaces and Spherical Resolvability of Finite ComplexesNov 13 2001We show that if $K$ is a nilpotent finite complex, then $\Omega K$ can be built from spheres using fibrations and homotopy (inverse) limits. This is applied to show that if ${\mathrm {map}}_*(X,S^n)$ is weakly contractible for all $n$, then ${\mathrm ... More

Josephine: Using JavaScript to safely manage the lifetimes of Rust dataJun 29 2018This paper is about the interface between languages which use a garbage collector and those which use fancy types for safe manual memory management. Garbage collection is the traditional memory management scheme for functional languages, whereas type ... More

Hamming Distance for ConjugatesOct 05 2007Aug 15 2008Let x, y be strings of equal length. The Hamming distance h(x,y) between x and y is the number of positions in which x and y differ. If x is a cyclic shift of y, we say x and y are conjugates. We consider f(x,y), the Hamming distance between the conjugates ... More

Simultaneous avoidance of large squares and fractional powers in infinite binary wordsApr 29 2003In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with y >= 4 nor cubes xxx. We show that `cube' can be replaced by any fractional power > 5/2. We also consider the analogous problem where `4' is replaced ... More

Optimal Focusing for Monochromatic Scalar and Electromagnetic WavesAug 20 2010For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation, the electric ... 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

How large is large? Estimating the critical disorder for the Anderson modelMay 30 2013Oct 17 2014Complete localization is shown to hold for the $d$-dimensional Anderson model with uniformly distributed random potentials provided the disorder strength $\lambda >\lambda_{And}$ where $\lambda_{\text{And}}$ satisfies $\lambda_{\text{And}}=\mu_d e \ln ... More

A Correction Note: Attractive Nearest Neighbor Spin Systems on the IntegersSep 19 2014In this note, we discuss a proof in T. Liggett's work on attractive translation invariant nearest neighbor spin systems on the integers. A correction to a wrong estimate is provided.

Extended TQFT's and Quantum GravitySep 29 2007This paper gives a definition of an extended topological quantum field theory (TQFT) as a weak 2-functor Z: nCob_2 -> 2Vect, by analogy with the description of a TQFT as a functor Z: nCob -> Vect. We also show how to obtain such a theory from any finite ... More

Repulsive behavior in an exceptional familyAug 31 2011Mar 05 2012The existence of a Landau-Siegel zero leads to the Deuring-Heilbronn phenomenon, here appearing in the 1-level density in a family of quadratic twists of a fixed genus character L-function. We obtain explicit lower order terms describing the vertical ... More

On Zagier's conjecture for $L(E,2)$: a number field exampleMar 15 2012We work out an example, for a CM elliptic curve E defined over a real quadratic field F, of Zagier's conjecture. This relates L(E,2) to values of the elliptic dilogarithm function at a divisor in the Jacobian of E which arises from K-theory.

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.

Computing $L$-functions with large conductorJun 05 2003May 05 2006An algorithm is given to efficiently compute $L$-functions with large conductor in a restricted range of the critical strip. Examples are included for about 21000 dihedral Galois representations with conductor near $10^7$. The data shows good agreement ... More

Unit Consistency, Generalized Inverses, and Effective System Design MethodsApr 24 2016This paper examines the potential role of unit consistency as a system design principle. Unit-consistent generalized matrix inverses and unit-invariant matrix decompositions are derived in support of this principle. Applications of the methods described ... More

A Quantitative Vainberg Method for Black Box ScatteringNov 18 2015Mar 04 2016We give a quantitative version of Vainberg's method relating pole free regions to propagation of singularities for black box scatterers. In particular, we show that there is a logarithmic resonance free region near the real axis of size $\tau$ with polynomial ... 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

Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroupsJan 08 2018We write explicit contour integral formulas for probability distributions of the multi-species q-TAZRP and the multi-species ASEP starting with q-exchangeable initial conditions. The formulas are equal to the corresponding explicit contour integral formulas ... More

Three-dimensional Gaussian fluctuations of non-commutative random surfaces along time-like pathsJan 23 2014Jul 31 2014We construct a continuous-time non-commutative random walk on $U(\mathfrak{gl}_N)$ with dilation maps $U(\mathfrak{gl}_N)\rightarrow L^2(U(N))^{\otimes\infty}$. This is an analog of a continuous-time non-commutative random walk on the group von Neumann ... More

A Multi-species ASEP(q,j) and q-TAZRP with Stochastic DualityMay 02 2016This paper introduces a multi-species version of a process called ASEP(q,j). In this process, up to 2j particles are allowed to occupy a lattice site, the particles drift to the right with asymmetry 0<q^{2j}<1, and there are n-1 species of particles in ... More

Finite Extensions of $\mathbb{Z}_\mathrm{max}$Jun 04 2014Aug 22 2016We classify the semifields and division semirings containing the max-plus semifield $\mathbb{Z}_\mathrm{max}$, which are finitely generated as $\mathbb{Z}_\mathrm{max}$-semimodules.

Cremona transformations, surface automorphisms and plane cubicsNov 19 2008Jul 26 2010We give a method for constructing many examples of automorphisms with positive entropy on rational complex surfaces. The general idea is to begin with a quadratic Cremona transformation that fixes a reduced cubic curve and then use the group structure ... More

The Real Chevalley InvolutionMar 08 2012Feb 13 2014We consider the Chevalley involution in the context of real reductive groups. We show that if G(R) is the real points of a connected reductive group, there is an involution, unique up to conjugacy by G(R), taking any semisimple element to a conjugate ... More

The framed little 2-discs operad and diffeomorphisms of handlebodiesAug 19 2010Aug 21 2010The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (i.e., the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to the modular ... More

Small Seifert fibered surgery on hyperbolic pretzel knotsOct 29 2012Jul 23 2013We complete the classification of hyperbolic pretzel knots admitting Seifert fibered surgeries. This is the final step in understanding all exceptional surgeries on hyperbolic pretzel knots. We also present results toward similar classifications for non-pretzel ... 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

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

More Examples of Pseudo-Collars on High-Dimensional ManifoldsApr 07 2018In a previous paper, we developed general techniques for constructing a variety of pseudo-collars, as defined by Guilbault and Tinsley, with roots in earlier work by Chapman and Siebenmann. As an application of our techniques, we exhibited an uncountable ... 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

A hybrid OpenMP and MPI implementation of a conservative spectral method for the Boltzmann equationJan 17 2013We demonstrate the implementation of a hybrid OpenMP and MPI parallelization of a conservative spectral method for the Boltzmann equation originally developed by Gamba and Tharkabhushaman. We perform a scaling analysis to demonstrate that the problem ... More

N derivatives are necessary for order N+1 convergence in quadrature: a converse resultJan 28 2014Results on the error bounds of quadrature methods are well known - most state that if the method has degree N, and the integrand has N derivatives, then the error is order N+1. We prove here a converse: that if the integrand fails to have N derivatives, ... More

The diffeomorphism group of a K3 surface and Nielsen realizationMay 31 2007Nov 12 2017The 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

A Review of Charmed Baryon Experimental DataJun 26 2002A review of the experimental results on charmed baryons, with an accent on those reported most recently. Talk given at FPCP conference, U. Penn, May 2002.

The long time behavior of fourth-order curvature flowsMar 21 2011Nov 10 2011We show precompactness results for solutions to parabolic fourth order geometric evolution equations. As part of the proof we obtain smoothing estimates for these flows in the presence of a curvature bound, an improvement on prior results which also require ... More

Asymptotic Curvature Decay and Removal of Singularities of Bach-Flat MetricsAug 07 2007We prove a removal of singularities result for Bach-flat metrics in dimension 4 under the assumption of bounded L^2 norm of curvature, bounded Sobolev constant and a volume growth bound. This result extends the removal of singularities result for special ... 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

Text Data Mining: Theory and MethodsJul 16 2008This paper provides the reader with a very brief introduction to some of the theory and methods of text data mining. The intent of this article is to introduce the reader to some of the current methodologies that are employed within this discipline area ... 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

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

On the shock wave spectrum for isentropic gas dynamics with capillarityJun 15 2008We consider the stability problem for shock layers in Slemrod's model of an isentropic gas with capillarity. We show that these traveling waves are monotone in the weak capillarity case, and become highly oscillatory as the capillarity strength increases. ... More

Minimally intersecting filling pairs on the punctured surface of genus twoJul 19 2018In this short note, we construct a minimally intersecting pair of simple closed curves that fill a genus 2 surface with an odd, greater than 3, number of punctures. This finishes the determination of minimally intersecting filling pairs for all surfaces ... More