arXiv subjects

David Wright

Publications and source records attributed to David Wright.

36 records · Page 2Linked to original sources

arXiv2018

The Structure of the Three-Dimensional Special Linear Group over a Local Field

For K a local field, it is shown that SL3(K) acts on a simply connected two dimensional simplicial complex in which a single face serves as a fundamental domain. From this it follows that SL3(K) is the generalized amalgamated product of three subgroups. Specifically if K is the field of fractions of the discrete valuation ring O, then SL3(K) is the amalgamation of three subgroups isomorphic to SL3(O) along pairwise intersections. This generalizes a theorem of Ihara, which gives the structure of SL2(K) as the amalgamated product of two groups in analogous fashion.

math.GR↗

arXiv2015

The Mid-Infrared Instrument for the James Webb Space Telescope, VI: The Medium Resolution Spectrometer

We describe the design and performance of the Medium Resolution Spectrometer (MRS) for the JWST-MIRI instrument. The MRS incorporates four coaxial spectral channels in a compact opto-mechanical layout that generates spectral images over fields of view up to 7.7 X 7.7 arcseconds in extent and at spectral resolving powers ranging from 1,300 to 3,700. Each channel includes an all-reflective integral field unit (IFU): an 'image slicer' that reformats the input field for presentation to a grating spectrometer. Two 1024 X 1024 focal plane arrays record the output spectral images with an instantaneous spectral coverage of approximately one third of the full wavelength range of each channel. The full 5 to 28.5 micron spectrum is then obtained by making three exposures using gratings and pass-band-determining filters that are selected using just two three-position mechanisms. The expected on-orbit optical performance is presented, based on testing of the MIRI Flight Model and including spectral and spatial coverage and resolution. The point spread function of the reconstructed images is shown to be diffraction limited and the optical transmission is shown to be consistent with the design expectations.

astro-ph.IM↗

arXiv2015

The Mid-Infrared Instrument for JWST, II: Design and Build

The Mid-InfraRed Instrument (MIRI) on the James Webb Space Telescope (JWST) provides measurements over the wavelength range 5 to 28.5 microns. MIRI has, within a single 'package', four key scientific functions: photometric imaging, coronagraphy, single-source low-spectral resolving power (R ~ 100) spectroscopy, and medium-resolving power (R ~ 1500 to 3500) integral field spectroscopy. An associated cooler system maintains MIRI at its operating temperature of < 6.7 K. This paper describes the driving principles behind the design of MIRI, the primary design parameters, and their realization in terms of the 'as-built' instrument. It also describes the test program that led to delivery of the tested and calibrated Flight Model to NASA in 2012, and the confirmation after delivery of the key interface requirements.

astro-ph.IM↗

arXiv2014

Simply connected open 3-manifolds with rigid genus one ends

We construct uncountably many simply connected open 3-manifolds with genus one ends homeomorphic to the Cantor set. Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds are complements of rigid generalized Bing-Whitehead (BW) Cantor sets. Previous examples of rigid Cantor sets with simply connected complement in $R^{3}$ had infinite genus and it was an open question as to whether finite genus examples existed. The examples here exhibit the minimum possible genus, genus one. These rigid generalized BW Cantor sets are constructed using variable numbers of Bing and Whitehead links. Our previous result with Željko determining when BW Cantor sets are equivalently embedded in $R^{3}$ extends to the generalized construction. This characterization is used to prove rigidity and to distinguish the uncountably many examples.

math.GT↗

arXiv2013

The Amalgamated Product Structure of the Tame Automorphism Group in Dimension Three

It is shown the the tame subgroup $\text{TA}_3(\mathbb C)$ of the group $\text{GA}_3(\mathbb C)$ of polynomials automorphisms of ${\mathbb C}^3$ can be realized as the product of three subgroups, amalgamated along pairwise intersections, in a manner that generalizes the well-known amalgamated free product structure of $\text{TA}_2(\mathbb C)$ (which coincides with $\text{GA}_2(\mathbb C)$ by Jung's Theorem). The result follows from defining relations for $\text{TA}_3(\mathbb C)$ given by U. U. Umirbaev.

math.AG↗

arXiv2012

Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring

In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. In the case R is a Dedekind Q-algebra, some stronger results are obtained. A key element in the proof is a theorem which yields the following corollary: Over an Artinian ring A all two-dimensional polynomial automorphisms having Jacobian determinant one are stably tame, and are tame if A is a Q-algebra. Another crucial ingredient, of interest in itself, is that stable tameness is a local property: If an automorphism is locally tame, then it is stably tame.

math.AC↗

arXiv2010

Images of Locally Finite Derivations of Polynomial Algebras in Two Variables

In this paper we show that the image of any locally finite $k$-derivation of the polynomial algebra $k[x, y]$ in two variables over a field $k$ of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image $Im D$ of every $k$-derivation $D$ of $k[x, y]$ such that $1\in Im D$ and $div D=0$ is a Mathieu subspace of $k[x, y]$.

math.AC↗

arXiv2010

On the Image Conjecture

The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of the Image Conjecture and show how it leads to another fascinating and elusive assertion that we here dub the Factorial Conjecture. Various cases of the Factorial Conjecture are proved.

math.RA↗

arXiv2009

Distinguishing Bing-Whitehead Cantor Sets

Bing-Whitehead Cantor sets were introduced by DeGryse and Osborne in dimension three and greater to produce examples of Cantor sets that were non standard (wild), but still had simply connected complement. In contrast to an earlier example of Kirkor, the construction techniques could be generalized to dimensions bigger than three. These Cantor sets in $S^{3}$ are constructed by using Bing or Whitehead links as stages in defining sequences. Ancel and Starbird, and separately Wright characterized the number of Bing links needed in such constructions so as to produce Cantor sets. However it was unknown whether varying the number of Bing and Whitehead links in the construction would produce non equivalent Cantor sets. Using a generalization of geometric index, and a careful analysis of three dimensional intersection patterns, we prove that Bing-Whitehead Cantor sets are equivalently embedded in $S^3$ if and only if their defining sequences differ by some finite number of Whitehead constructions. As a consequence, there are uncountably many non equivalent such Cantor sets in $S^{3}$ constructed with genus one tori and with simply connected complement.

math.GT↗

arXiv2006

The Jacobian Conjecture as a problem in combinatorics

The Jacobian Conjecture has been reduced to the symmetric homogeneous case. In this paper we give an inversion formula for the symmetric case and relate it to a combinatoric structure called the Grossman-Larson Algebra. We use these tools to prove the symmetric Jacobian Conjecture for the case $F=X-H$ with $H$ homogeneous and $JH^{3}=0$. Other special results are also derived. We pose a combinatorial statement which would give a complete proof the Jacobian Conjecture.

math.CO↗

arXiv2003

A New Approach to Order Polynomials of Labeled Posets and Their Generalizations

In this paper, we first give formulas for the order polynomial $Ω(\Pw; t)$ and the Eulerian polynomial $e(\Pw; λ)$ of a finite labeled poset $(P, ω)$ using the adjacency matrix of what we call the $ω$-graph of $(P, ω)$. We then derive various recursion formulas for $Ω(\Pw; t)$ and $e(\Pw; λ)$ and discuss some applications of these formulas to Bernoulli numbers and Bernoulli polynomials. Finally, we give a recursive algorithm using a single linear operator on a vector space. This algorithm provides a uniform method to construct a family of new invariants for labeled posets $(\Pw)$, which includes the order polynomial $Ω(\Pw; t)$ and the invariant $\tilde e(\Pw; λ) =\frac {e(\Pw; λ)}{(1-λ)^{|P|+1}}$. The well-known quasi-symmetric function invariant of labeled posets and a further generalization of our construction are also discussed.

math.CO↗

arXiv2002

D-log and formal flow for analytic isomorphisms of n-space

Given a formal map $F=(F_1...,F_n)$ of the form $z+\text{higher}$ order terms, we give tree expansion formulas and associated algorithms for the D-Log of F and the formal flow F_t. The coefficients which appear in these formulas can be viewed as certain generalizations of the Bernoulli numbers and the Bernoulli polynomials. Moreover the coefficient polynomials in the formal flow formula coincide with the strict order polynomials in combinatorics for the partially ordered sets induced by trees. Applications of these formulas to the Jacobian Conjecture are discussed.

math.CV↗

arXiv2000

New Constraints on "Cool" Dark Matter

It has been suggested that a sterile neutrino ν_s which mixes with standard neutrinos can form nonthermal ``cool'' Dark Matter if its mass and mixing angle fall in the ranges 0.1 keV \lsim m_s \lsim 10 keV and 10^{-10} \lsim \sin^2 θ\lsim 10^{-4}, respectively. We point out that the required mixing makes these heavy neutrinos unstable. The dominant decay mode is into three light neutrinos, but the most stringent constraint comes from the non-observation of radiative decays into a single light neutrino and a photon. Moreover, we point out that the density of thermal relics of such ν_{s}'s would be too high, unless the reheating temperature after inflation was below \sim 10 GeV.

hep-ph↗

arXiv2000

Leptogenesis with Dirac Neutrinos

We describe a "neutrinogenesis" mechanism whereby, in the presence of right-handed neutrinos with sufficiently small pure Dirac masses, (B+L)-violating sphaleron processes create the baryon asymmetry of the Universe, even when B=L=0 initially. It is shown that the resulting neutrino mass constraints are easily fulfilled by the neutrino masses suggested by current experiments. We present a simple toy model which uses this mechanism to produce the observed baryon asymmetry of the Universe. (PostScript Errors corrected in latest Version).

hep-ph↗

arXiv1998

Naturally Nonminimal Supersymmetry

We consider the bounds imposed by naturalness on the masses of superpartners for arbitrary points in nonminimal supersymmetric extensions of the standard model and for arbitrary messenger scales. This constitutes a significant generalization of previous work along these lines. We discuss appropriate measures of naturalness and the status of nonminimal supersymmetry in the light of recent experimental results.

hep-ph↗

arXiv1997

Horizontal, Anomalous U(1) Symmetry for the More Minimal Supersymmetric Standard Model

We construct explicit examples with a horizontal, ``anomalous'' $U(1)$ gauge group, which, in a supersymmetric extension of the standard model, reproduce qualitative features of the fermion spectrum and CKM matrix, and suppress FCNC and proton decay rates without the imposition of global symmetries. We review the motivation for such ``more'' minimal supersymmetric standard models and their predictions for the sparticle spectrum. There is a mass hierarchy in the scalar sector which is the inverse of the fermion mass hierarchy. We show in detail why DeltaS = 2 FCNC are suppressed when compared with naive estimates for nondegenerate squarks.

hep-ph↗

arXiv1996

The tricritical point of finite-temperature phase transitions in large N(Higgs) gauge theories

Gauge theories broken by a single Higgs field are known to have first-order phase transitions in temperature if $λ/g^2 \ll 1$, where $g$ is the gauge coupling and $λ$ the Higgs self-coupling. If the theory is extended from one to $N$ Higgs doublets, with U($N$) flavor symmetry, the transition is known to be second order for $λ/g^2 \gtrsim 1$ in the $N\to\infty$ limit. We show that one can in principal compute the tricritical value of $λ/g^2$, separating first from second-order transitions, to any order in $1/N$. In particular, scalar fluctuations at the transition damp away the usual problems with the infrared behavior of high-temperature non-Abelian gauge theories. We explicitly compute the tricritical value of $λ/g^2$ for U(1) and SU(2) gauge theory to next-to-leading order in $1/N$.

hep-ph↗

arXiv1995

Open problems on open algebraic varieties

This report records a large number of open problems in Affine Algebraic Geometry that were proposed by participants in a Conference on Open Algebraic Varieties at the Centre de Recherches en Mathematiques in Montreal at December 1994.

alg-geom↗