Results for "Simon Kristensen"

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Badly approximable systems of linear forms over a field of formal seriesJun 26 2003Aug 05 2004We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field is maximal. This is a analogue of Schmidt's multi-dimensional generalisation ... More
Metric Diophantine approximation with respect to planar distance functionsJan 27 2004We outline a proof of an analogue of Khintchine's Theorem in R^2, where the ordinary height is replaced by a distance function satisfying an irrationality condition as well as certain decay and symmetry conditions.
Diophantine approximation and the solubility of the Schroedinger equationOct 22 2002Apr 29 2003We characterise the set of periods for which number theoretical obstructions prevent us from finding periodic solutions of the Schroedinger equation on a two dimensional torus as well as the asymptotic occurrence of possible resonances.
A metric theorem for restricted Diophantine approximation in positive characteristicJan 28 2004Oct 10 2005We calculate the measure and Hausdorff dimension of sets of matrices over fields of formal power series with good approximation properties for a restricted set of denominators.
Metrical results on systems of small linear formsDec 20 2011In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine-Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating ... More
Metrical irrationality results related to values of the Riemann $ζ$-functionFeb 12 2018We introduce a one-parameter family of series associated to the Riemann $\zeta$-function and prove that the values of the elements of this family at integers are linearly independent over the rationals for almost all values of the parameter, where almost ... More
Metrical theorems on systems of small inhomogeneous linear formsJun 16 2014In this paper we establish complete Khintchine--Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.
Diophantine exponents for mildly restricted approximationSep 06 2007We are studying the Diophantine exponent \mu_{n,l}$ defined for integers 1 \leq l < n and a vector \alpha \in \mathbb{R}^n by letting \mu_{n,l} = \sup{\mu \geq 0: 0 < ||x \cdot \alpha|| < H(x)^{-\mu} for infinitely many x \in C_{n,l} \cap \mathbb{Z}^n}, ... More
Badly approximable systems of linear forms in absolute valueNov 25 2011In this paper we show that the set of mixed type badly approximable simultaneously small linear forms is of maximal dimension. As a consequence of this theorem we settle a conjecture of the first author.
Irrationality and transcendence of continued fractions with algebraic integersFeb 12 2019We extend a result of Han\v{c}l, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence $\{\alpha_n\}$ of algebraic integers of bounded degree, each attaining the maximum absolute value among their ... More
Hausdorff Dimension and Diophantine ApproximationMay 28 2003Jun 12 2003We begin with a brief treatment of Hausdorff measure and Hausdorff dimension. We then explain some of the principal results in Diophantine approximation and the Hausdorff dimension of related sets, originating in the pioneering work of Vojtech Jarnik. ... More
A problem in non-linear Diophantine approximationMay 22 2015In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is also associated with a class of linear inhomogeneous partial differential equations ... More
Some remarks on Mahler's classification in higher dimensionJun 20 2016We prove a number of results on the metric and non-metric theory of Diophantine approximation for Yu's multidimensional variant of Mahler's classification of transcendental numbers. Our results arise as applications of well known results in Diophantine ... More
High-fidelity conditional two-qubit swapping gate using tunable ancillasSep 24 2018Oct 16 2018Scalable quantum computing relies crucially on high-fidelity entangling operations. Here we demonstrate that four coupled qubits can operate as a high-fidelity two-qubit entangling gate that swaps two target qubits and adds a relative sign on the $\lvert ... More
Diophantine approximation and badly approximable setsMay 24 2004Apr 13 2005Let (X,d) be a metric space and (\Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of \Omega. Loosely speaking, these consist of points in \Omega which `stay clear' ... More
Metrical musings on Littlewood and friendsApr 04 2012We prove a metrical result on a family of conjectures related to the Littlewood conjecture, namely the original Littlewood conjecture, the mixed Littlewood conjecture of de Mathan and Teuli\'e and a hybrid between a conjecture of Cassels and the Littlewood ... More
A problem in non-linear Diophantine approximationMay 22 2015Apr 19 2018In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose ... More
A converse to linear independence criteria, valid almost everywhereFeb 08 2013We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over the field ... More
On shrinking targets for Z^m actions on toriJul 24 2008Dec 08 2008Let A be an n by m matrix with real entries. Consider the set Bad_A of x \in [0,1)^n for which there exists a constant c(x)>0 such that for any q \in Z^m the distance between x and the point {Aq} is at least c(x) |q|^{-m/n}. It is shown that the intersection ... More
Evolution of CO lines in time-dependent models of protostellar disk formationApr 18 2013(Abridged) Star and planet formation theories predict an evolution in the density, temperature, and velocity structure as the envelope collapses and forms an accretion disk. The aim of this work is to model the evolution of the molecular excitation, line ... More
cphVB: A System for Automated Runtime Optimization and Parallelization of Vectorized ApplicationsOct 26 2012Mar 25 2013Modern processor architectures, in addition to having still more cores, also require still more consideration to memory-layout in order to run at full capacity. The usefulness of most languages is deprecating as their abstractions, structures or objects ... More
Fusion of Array Operations at RuntimeJan 20 2016Jan 21 2016We address the problem of fusing array operations based on criteria such as shape compatibility, data reusability, and communication. We formulate the problem as a graph partition problem that is general enough to handle loop fusion, combinator fusion, ... More
Oxygen budget in low-mass protostars: the NGC1333-IRAS4A R1 shock observed in [OI] at 63 um with SOFIA-GREATApr 25 2017In molecular outflows from forming low-mass protostars, most oxygen is expected to be locked up in water. However, Herschel observations have shown that typically an order of magnitude or more of the oxygen is still unaccounted for. To test if the oxygen ... More
Ultracold-atom collisions in atomic waveguides : A two-channel analysisDec 16 2014Apr 16 2015Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used allowing an exhaustive ... More
Sobolev regularity for Symmetric-Convex FunctionalsOct 26 2016We study Sobolev regularity results for minimisers of autonomous, convex variational of linear growth which depend on the symmetric gradient rather than the full gradient. This extends the results available in the literature for the BV-setting to the ... More
Bias dependent subband edges and the 0.7 conductance anomalyNov 07 2001The 0.7 2e^2/h conductance anomaly is studied in strongly confined, etched GaAs/GaAlAs quantum point contacts by measuring the differential conductance G as a function of source-drain bias V_sd and gate-source bias V_gs as well as a function of temperature. ... More
One-dimensional ultracold atomic gases: Impact of the effective range on integrabilityJun 12 2015Mar 24 2016Three identical bosons or fermions are considered in the limit of zero-range interactions and finite effective range. By using a two channel model, we show that these systems are not integrable and that the wave function verifies specific continuity conditions ... More
Lower semicontinuity for an integral functional in BVDec 17 2015We prove a lower semicontinuity result for a functional of linear growth initially defined by \[ \int_{\Omega}F\left(\frac{dDu}{d\mu}\right)\,d\mu \] for $u\in BV(\Omega;\mathbb{R}^N)$ with $Du\ll \mu$. The positive Radon measure $\mu$ is only assumed ... More
Piecewise affine approximations for functions of bounded variationNov 08 2012Jul 22 2015BV functions cannot be approximated well by piecewise constant functions, but this work will show that a good approximation is still possible with (countably) piecewise affine functions. In particular, this approximation is area-strictly close to the ... More
On Rank-One Convex Functions that are homogeneous of Degree OneMay 18 2015We show that positively $1$--homogeneous rank one convex functions are convex at $0$ and at matrices of rank one. The result is a special case of an abstract convexity result that we establish for positively $1$--homogeneous directionally convex functions ... More
Evidence for a single hydrogen molecule connected by an atomic chainDec 29 2006Stable, single-molecule conducting-bridge configurations are typically identified from peak structures in a conductance histogram. In previous work on Pt with H$_2$ at cryogenic temperatures it has been shown that a peak near 1 $G{_0}$ identifies a single ... More
Book to the Future - a manifesto for book liberationJul 04 2015The Book Liberation Manifesto is an exploration of publishing outside of current corporate constraints and beyond the confines of book piracy. We believe that knowledge should be in free circulation to benefit humankind, which means an equitable and vibrant ... More
Particle Dark EnergyNov 11 2004Feb 23 2006We explore the physics of a gas of particles interacting with a condensate that spontaneously breaks Lorentz invariance. The equation of state of this gas varies from 1/3 to less than -1 and can lead to the observed cosmic acceleration. The particles ... More
Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More
Approximations of generating functions and a few conjecturesNov 25 2009This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of Integer Sequences ... More
Prediction of the Virgo axis anisotropy: CMB radiation illuminates the nature of thingsSep 25 2005Recent findings of the anisotropy in the Cosmic Microwave Background (CMB) radiation are confusing for standard cosmology. Remarkably, this fact has been predicted several years ago in the framework of our model of the physical world. Moreover, in exact ... More
Holomorphic horospherical duality "sphere-cone"Jan 02 2005We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.
Quantum entanglement analysis based on abstract interpretationJan 28 2008Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum ... More
Extending and Implementing the Stable Model SemanticsMay 08 2000An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of efficient implementation ... More
A Brezis-Browder theorem for SSDB spacesApr 24 2010Sep 26 2010In this paper, we show how the Brezis-Browder theorem for maximally monotone multifunctions with a linear graph on a reflexive Banach space, and a consequence of it due to Yao, can be generalized to SSDB spaces.
Banach SSD spaces and classes of monotone setsAug 04 2009Jul 05 2010In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D), type ... More
On the Closing Lemma problem for vector fields of bounded type on the torusNov 07 2008We investigate the open Closing Lemma problem for vector fields on the 2-dimensional torus. Under the assumption of bounded type rotation number, the $C^r$ Closing Lemma is verified for smooth vector fields that are area-preserving at all saddle points. ... More
Polar subspaces and automatic maximalityDec 11 2012Mar 28 2013This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and ... More
Space-Time and ProbabilityDec 14 2001Special relativity is most naturally formulated as a theory of space-time geometry, but within the space-time framework probability apears to be at best an epistemic notion - a matter of what can be known, not of the status of events in themselves. However, ... More
What is Probability?Dec 24 2004Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, ... More
Derivation of the Born Rule from Operational AssumptionsNov 21 2002Nov 21 2002The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to all the ... More
Prospects for Precision Higgs Physics at Linear CollidersNov 30 2012A linear e+e- collider provides excellent possibilities for precision measurements of the properties of the Higgs boson. At energies close to the Z-Higgs threshold, the Higgs boson can be studied in recoil against a Z boson, to obtain not only a precision ... More
Splitting the K-Terminal ReliabilityApr 18 2011Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is the probability that all vertices in K are mutually connected. In this article ... More
The sharp form of the strong Szego theoremFeb 06 2004Let $f$ be a function on the unit circle and $D_n(f)$ be the determinant of the $(n+1)\times (n+1)$ matrix with elements $\{c_{j-i}\}_{0\leq i,j\leq n}$ where $c_m =\hat f_m\equiv \int e^{-im\theta} f(\theta) \f{d\theta}{2\pi}$. The sharp form of the ... More
Sturm Oscillation and Comparison TheoremsNov 04 2003This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.
Simulating Dense MatterMar 19 2007I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I ... More
Lattice MatterSep 28 2001I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color ... More
The Phase Diagram of QCDMay 08 2001I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma ... 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
Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon TheoremMar 21 2016Jun 13 2016We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic ... More
A First Look at the Impact of NNNLO Theory Uncertainties on Top Mass Measurements at the ILCMar 15 2016Aug 22 2016A scan of the top production threshold at a future electron-positron collider provides the possibility for a precise measurement of the top quark mass in theoretically well-defined mass schemes. With statistical uncertainties of 20 MeV or below, systematics ... More
Measure Equipartitions via Finite Fourier AnalysisMar 27 2014Jun 20 2015Applications of harmonic analysis on finite groups are introduced to measure partition problems, with equipartitions obtained as the vanishing of prescribed Fourier transforms. For elementary abelian groups $Z_p^k$, $p$ an odd prime, equipartitions are ... More
Equivariant Equipartitions: Ham Sandwich Theorems for Finite Subgroups of SpheresSep 04 2011Jun 19 2012Equivariant "Ham Sandwich" Theorems are obtained for the finite subgroups G of the unit spheres S(F) in the classical algebras F = R, C, and H. Given any n F-valued mass distributions on F^n, it is shown that there exists a G-equivariant decomposition ... More
Kergin Approximation in Banach SpacesOct 01 2008We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.
Static perfect fluids with Pant-Sah equations of stateJan 17 2008Mar 31 2008We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the ... More
Criteria for (in)finite extent of static perfect fluidsApr 09 2002In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely ... More
Conformal positive mass theoremsMar 29 2000We show the following two extensions of the standard positive mass theorem (one for either sign): Let (N,g) and (N,g') be asymptotically flat Riemannian 3-manifolds with compact interior and finite mass, such that g and g' are twice Hoelder differentiable ... More
Minimum settling time control design through direct search optimizationSep 27 2011Dec 06 2011The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature ... More
ExSample -- A Library for Sampling Sudakov-Type DistributionsAug 31 2011Mar 19 2012Sudakov-type distributions are at the heart of generating radiation in parton showers as well as contemporary NLO matching algorithms along the lines of the POWHEG algorithm. In this paper, the C++ library ExSample is introduced, which implements adaptive ... More
Stability, birational transformations and the Kahler-Einstein problemJul 23 2010We define a new notion of "b-stability" for a polarised algebraic variety, adapted to the existence problem for Kahler-Einstein metrics on Fano manifolds.
Calabi-Yau metrics on Kummer surfaces as a model glueing problemJul 23 2010This is an expository paper which aims to give a simple proof of the existence of Ricci-flat metrics on certain K3 surfaces, as an illustration of general "glueing" techniques.
Ricci Flow of regions with curvature bounded below in dimension threeJul 04 2014We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has curvature bounded from below by -1, then we prove estimates which show that ... More
Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22Jul 08 2015In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way. Automorphisms of Salem degree 22 do not lift to any characteristic ... More
Simulating the formation of massive seed black holes in the early Universe. I: An improved chemical modelJan 23 2015Jun 06 2015The direct collapse model for the formation of massive seed black holes in the early Universe attempts to explain the observed number density of supermassive black holes (SMBHs) at $z \sim 6$ by assuming that they grow from seeds with masses M > 10000 ... More
Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)Aug 29 2012May 29 2013We produce a decidable classical normal modal logic of internalised negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP). LDiiP internalises ... More
A Logic of Interactive Proofs (Formal Theory of Knowledge Transfer)Jan 17 2012Apr 05 2016We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as embedded into ... More
Coupled Critical Models: Applications to Ising-Potts ModelsMay 28 1997We discuss the critical behaviour of 2D Ising and q-states Potts models coupled by their energy density. We found new tricritical points. The procedure employed is the renormalisation approach of the perturbations series around conformal field theories ... More
Rosenthal compacta and NIP formulasJul 22 2014Aug 07 2015We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about phi-types for phi NIP. In particular, we show that if M is a countable model, then an M-invariant phi-type is Borel definable. Also ... More
Distal and non-distal NIP theoriesMar 11 2011Oct 27 2012We study one way in which stable phenomena can exist in an NIP theory. We start by defining a notion of 'pure instability' that we call 'distality' in which no such phenomenon occurs. O-minimal theories and the p-adics for example are distal. Next, we ... More
Coupled Minimal Models with and without DisorderOct 02 1997We analyse in this article the critical behavior of $M$ $q_1$-state Potts models coupled to $N$ $q_2$-state Potts models ($q_1,q_2\in [2..4]$) with and without disorder. The technics we use are based on perturbed conformal theories. Calculations have ... More
On a theorem of Kac and GilbertMay 06 2004We prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum.
Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circleJun 01 2006We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC.
Generalized regularity and solution concepts for differential equationsJun 09 2008As the title ``Generalized regularity and solution concepts for differential equations'' suggests, the main topic of my thesis is the investigation of generalized solution concepts for differential equations, in particular first order hyperbolic partial ... More
Localic Metric spaces and the localic Gelfand dualityNov 04 2014In this paper we prove, as conjectured by B.Banachewski and C.J.Mulvey, that the constructive Gelfand duality can be extended into a duality between compact regular locales and unital abelian localic C*-algebras. In order to do so we develop a constructive ... More
Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg groupMar 04 2016We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by ... More
Regularized Newton methods for simultaneous Radon inversion and phase retrieval in phase contrast tomographyFeb 17 2015Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different incident angles of ... More
Performance of a measurement-driven 'adiabatic-like' quantum 3-SAT solverSep 02 2015I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a non-orthogonal basis. If ... More
Technical Report: Modelling Multiple Cell Types with Partial Differential EquationsSep 28 2015Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly. However, in case ... More
On the absolute continuity of multidimensional Ornstein-Uhlenbeck processesAug 26 2009Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular, the law of $X_1$ ... More
Some remarks about equations defining coincident root lociAug 23 2011Consider the projective variety $X_\lambda$ of binary forms of degree $d$ whose linear factors are distributed according to the partition $\lambda$ of $d$. We determine minimal sets of local generators of the fiber product of $X_\lambda$ with its normalization, ... More
Equations describing the ramification of outer simple linear projectionsSep 03 2011We explain how to determine equations describing the ramification of an outer simple linear projection of a projective scheme in a way suited for explicit computations.
Jost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicityMar 18 2005We show that the parameters $a_n, b_n$ of a Jacobi matrix have a complete asymptotic series $ a_n^2 -1 &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n} + O(R^{-2n}) b_n &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n+1} + O(R^{-2n}) $ where $1 < |\mu_j| < R$ for $j\leq ... More
A uniqueness result for propagation-based phase contrast imaging from a single measurementSep 16 2014Apr 27 2015Phase contrast imaging seeks to reconstruct the complex refractive index of an unknown sample from scattering intensities, measured for example under illumination with coherent X-rays. By incorporating refraction, this method yields improved contrast ... More
Hyperplane Equipartitions Plus ConstraintsAug 01 2017Oct 09 2017While equivariant methods have seen many fruitful applications in geometric combinatorics, their inability to answer the now settled Topological Tverberg Conjecture has made apparent the need to move beyond the use of Borsuk-Ulam type theorems alone. ... 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
The localic Istropy group of a toposJun 15 2017It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of T. We show that this group is in fact the group of points ... More
Topological phases in the non-Hermitian Su-Schrieffer-Heeger modelSep 12 2017Jan 02 2018We address the conditions required for a $\mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally-symmetric SSH model will possess a "conjugated-pseudo-Hermiticity" which we show ... More
The Moore and the Myhill Property For Strongly Irreducible Subshifts Of Finite Type Over Group SetsJun 19 2017We prove the Moore and the Myhill property for strongly irreducible subshifts over right amenable and finitely right generated left homogeneous spaces with finite stabilisers. Both properties together mean that the global transition function of each big-cellular ... More
Hyperbolicity and Cubulability Are Preserved Under Elementary EquivalenceJan 29 2018The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated ... More
Azumaya skew group algebras and an application to quantum Kleinian singularitiesNov 23 2017Nov 27 2017We provide easily-verified necessary and sufficient conditions for a skew group ring, or more generally, a crossed product ring, to be an Azumaya algebra. We use our results to show that (suitable localisations of) skew group rings associated to the quantum ... More
La théorie de Hodge des bimodules de Soergel (d'après Soergel et Elias-Williamson)Nov 07 2017Soergel bimodules are certain bimodules over polynomial algebras, associated with Coxeter groups, and introduced by Soergel in the 1990's while studying the category O of complex semisimple Lie algebras. Even though their definition is algebraic and rather ... More
Tosio Kato's Work on Non--Relativistic Quantum MechanicsNov 01 2017We review the work of Tosio Kato on the mathematics of non--relativistic quantum mechanics and some of the research that was motivated by this. Topics include analytic and asymptotic eigenvalue perturbation theory, Temple--Kato inequality, self--adjointness ... More
Tosio Kato's Work on Non-Relativistic Quantum Mechanics: An OutlineOct 19 2017Based at a talk given at the Kato Centennial Symposium in Sept. 2017, this article discusses the scientific life and some of the scientific work of T. Kato.
Maximizing Riesz means of anisotropic harmonic oscillatorsDec 29 2017We consider problems related to the asymptotic minimization of eigenvalues of anisotropic harmonic oscillators in the plane. In particular we study Riesz means of the eigenvalues and the trace of the corresponding heat kernels. The eigenvalue minimization ... More
The almost Daugavet property and translation-invariant subspacesJul 13 2013Let $G$ be a metrizable, compact abelian group and let $\Lambda$ be a subset of its dual group $\hat G$. We show that $C_\Lambda(G)$ has the almost Daugavet property if and only if $\Lambda$ is an infinite set, and that $L^1_\Lambda(G)$ has the almost ... More