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Orientational order on surfaces - the coupling of topology, geometry, and dynamicsJul 21 2016Jun 21 2017We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, ... More

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal EquationJan 27 2015We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and thus offers the ... More

A Navier Stokes Phase Field Crystal Model for Colloidal SuspensionsOct 21 2013Jan 26 2015We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail ... More

Liquid crystalline growth within a phase-field crystal modelJan 09 2015By using a phase-field crystal (PFC) model, the liquid-crystal growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from ... More

Topological and geometrical quantities in active cellular structuresDec 17 2018Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied equilibrium ... More

Topological and geometrical quantities in active cellular structuresDec 17 2018Apr 05 2019Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied equilibrium ... More

A linear Uzawa-type solver for nonlinear transmission problemsMar 31 2017We propose an Uzawa-type iteration for the Johnson-N\'ed\'elec formulation of a Laplace-type transmission problem with possible (strongly monotone) nonlinearity in the interior domain. In each step, we sequentially solve one BEM for the weakly-singular ... More

An efficient numerical framework for the amplitude expansion of the phase-field crystal modelFeb 26 2019The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on diffusive ... More

A mechanism for cell motility by active polar gelsDec 17 2014May 05 2015We analyse a generic motility model, with the motility mechanism arising by contractile stress due to the interaction of myosin and actin. A hydrodynamic active polar gel theory is used to model the cytoplasm of a cell and is combined with a Helfrich-type ... More

A mesoscopic field theoretical approach for active systemsApr 22 2016We introduce a mesocopic modeling approach for active systems. The continuum model allows to consider microscopic details as well as emerging macroscopic behavior and can be considered as a minimal continuum model to describe generic properties of active ... More

An efficient numerical framework for the amplitude expansion of the phase-field crystal modelFeb 26 2019Apr 24 2019The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on diffusive ... More

Structure and dynamics of interfaces between two coexisting liquid crystalline phasesFeb 01 2013The phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid crystalline phases in two spatial dimensions. Depending on the model parameters there is a variety of possible coexistences between ... More

Orientational order on surfaces - the coupling of topology, geometry and dynamicsJul 21 2016We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, ... More

Active crystals on a sphereFeb 14 2018Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here, we consider "active crystals" on a sphere, which are composed of self-propelled colloidal particles. Our work is based on a new phase-field-crystal-type model that ... More

Nematic liquid crystals on curved surfaces - a thin film limitSep 27 2017We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main ... More

An abstract analysis of optimal goal-oriented adaptivityMay 18 2015We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of [Carstensen et al., Comput. Math. Appl. 67 (2014)]. We prove that this framework covers standard discretizations ... More

Efficient additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulationsSep 11 2013For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal mesh-size. Therefore, reliable and effective numerical computations, in particular on adaptively refined ... More

Adaptive vertex-centered finite volume methods with convergence ratesAug 25 2015Mar 22 2016We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive algorithm leads to ... More

Kondo screening and beyond: an x-ray absorption and dichroism study of CePt$_5$/Pt(111)Nov 08 2016We use x-ray absorption spectroscopy as well as its linear and circular magnetic dichroisms to characterize relevant interactions and energy scales in the surface intermetallic CePt$_5$/Pt(111). The experiments provide insight into crystal field splitting, ... More

Optimal Adaptivity for the SUPG Finite Element MethodJun 28 2018For convection dominated problems, the streamline upwind Petrov--Galerkin method (SUPG), also named streamline diffusion finite element method (SDFEM), ensures a stable finite element solution. Based on robust a posteriori error estimators, we propose ... More

Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivityNov 18 2012We consider a (possibly) nonlinear interface problem in 2D and 3D, which is solved by use of various adaptive FEM-BEM coupling strategies, namely the Johnson-N\'ed\'elec coupling, the Bielak-MacCamy coupling, and Costabel's symmetric coupling. We provide ... More

Local inverse estimates for non-local boundary integral operatorsApr 16 2015We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded d-dimensional Lipschitz domain Omega for d >= 2 with piecewise smooth boundary. For piecewise polynomial ansatz ... More

Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEsSep 21 2017We prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work Erath and Praetorius [SIAM J. Numer. Anal., 54 (2016), pp. 2228--2255] ... More

Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamicsDec 11 2017Jan 07 2019We consider the numerical approximation of the Landau-Lifshitz-Gilbert equation, which describes the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic contributions, the energy comprises the Dzyaloshinskii-Moriya ... More

Iterative solution and preconditioning for the tangent plane scheme in computational micromagneticsAug 30 2018The tangent plane scheme is a time-marching scheme for the numerical solution of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which describes the time evolution of ferromagnetic configurations. Exploiting the geometric structure of ... More

The intrinsic torsion of SU(3) and G_2 structuresFeb 26 2002We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with ... More

On Estimating Many Means, Selection Bias, and the BootstrapNov 15 2013With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated ... More

Wrong side of the tracks: Big Data and Protected CategoriesDec 15 2014Jun 24 2016When we use machine learning for public policy, we find that many useful variables are associated with others on which it would be ethically problematic to base decisions. This problem becomes particularly acute in the Big Data era, when predictions are ... More

Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groupsDec 11 2010Dec 14 2010Let $G$ be an almost simple group. We prove that if $x \in G$ has prime order $p \ge 5$, then there exists an involution $y$ such that $<x,y>$ is not solvable. Also, if $x$ is an involution then there exist three conjugates of $x$ that generate a nonsolvable ... More

Towards a Theory of GlueDec 17 2012We propose and study the notions of behaviour type and composition operator making a first step towards the definition of a formal framework for studying behaviour composition in a setting sufficiently general to provide insight into how the component-based ... More

Population genetics models of local ancestryFeb 22 2012Apr 25 2012Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population structure and ... More

Euler characteristics and compact p-adic Lie groupsSep 21 2009Oct 08 2009We discuss Euler characteristics for finitely generated modules over Iwasawa algebras. We show that the Euler characteristic of a module is well-defined whenever the 0th homology group is finite if and only if the relevant compact p-adic Lie group is ... More

The hadronization of partonsOct 23 2008Oct 07 2010We review the description of inclusive single unpolarized light hadron production using fragmentation functions in the framework of the factorization theorem. We summarize the factorization of quantities into perturbatively calculable quantities and these ... More

Perturbative description of inclusive single hadron production at HERAAug 07 2008Light charged hadron production data in the current fragmentation region at HERA are calculated using next-to-leading order perturbative calculations and fragmentation functions obtained from similar data from e+ e- reactions. General good agreement is ... More

On the remainder term of the Berezin inequality on a convex domainSep 22 2015Jan 02 2016We study the Dirichlet eigenvalues of the Laplacian on a convex domain in $\mathbb{R}^n$, with $n\geq 2$. In particular, we generalize and improve upper bounds for the Riesz means of order $\sigma\geq 3/2$ established in an article by Geisinger, Laptev ... More

Masers : High resolution probes of massive star formationSep 26 2003Astrophysical masers are one of the most readily detected signposts of high-mass star formation. Their presence indicates special conditions, probably indicative of a specific evolutionary phase. Masers also represent the ultimate high-resolution probe ... More

Quasi-random oriented graphsJan 28 2011Aug 10 2011We show that a number of conditions on oriented graphs, all of which are satisfied with high probability by randomly oriented graphs, are equivalent. These equivalences are similar to those given by Chung, Graham and Wilson in the case of unoriented graphs, ... More

Detector Systems at CLICSep 15 2011The Compact Linear Collider CLIC is designed to deliver e+e- collisions at a center of mass energy of up to 3 TeV. The detector systems at this collider have to provide highly efficient tracking and excellent jet energy resolution and hermeticity for ... More

Domain Wall Fermions for Planar PhysicsJul 28 2015Aug 22 2015In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores lattice formulations ... More

High Density Effective Theory Confronts the Fermi LiquidOct 07 2003Nov 20 2003The high density effective theory recently introduced by Hong and Hsu to describe ultradense relativistic fermionic matter is used to calculate the tree-level forward scattering amplitude between two particles at the Fermi surface. While the direct term ... More

Fixed Point Four-Fermi TheoriesJun 24 1997I review dynamical chiral symmetry breaking in four-fermi models, including results of Monte Carlo simulations with dynamical fermions. For 2<d<4, where the phase transition defines an ultraviolet fixed point of the renormalisation group, the continuum ... More

Bounds on area and charge for marginally trapped surfaces with cosmological constantSep 28 2011May 03 2012We sharpen the known inequalities $A \Lambda \le 4\pi (1-g)$ and $A\ge 4\pi Q^2$ between the area $A$ and the electric charge $Q$ of a stable marginally outer trapped surface (MOTS) of genus g in the presence of a cosmological constant $\Lambda$. In particular, ... More

A Mass Partition Problem Related to Equivariant Sections of Stiefel BundlesNov 08 2010Jun 19 2012We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of m mass distributions on R^n, the existence of k linearly independent regular q-fans, each of which equipartitions ... More

Star formation histories from multi-band photometry: A new approachJun 09 2008A new method of determining galaxy star-formation histories (SFHs) is presented. Using the method, the feasibility of recovering SFHs with multi-band photometry is investigated. The method divides a galaxy's history into discrete time intervals and reconstructs ... More

JSJ decompositions of doubles of free groupsNov 04 2016We classify all possible JSJ decompositions of doubles of free groups of rank two and their corresponding modular groups. We then compute the Makanin-Razborov diagram of a special double of a free group and deduce that in general limit groups are not ... More

Major Transitions in Political OrderDec 10 2015Jun 11 2016We present three major transitions that occur on the way to the elaborate and diverse societies of the modern era. Our account links the worlds of social animals such as pigtail macaques and monk parakeets to examples from human history, including 18th ... More

From Domain Wall to Overlap in 2+1dDec 18 2015The equivalence of domain wall and overlap fermion formulations is demonstrated for lattice gauge theories in 2+1 spacetime dimensions with parity-invariant mass terms. Even though the domain wall approach distinguishes propagation along a third direction ... More

Status of the CMS Phase I Pixel Detector UpgradeNov 19 2015A new pixel detector for the CMS experiment is being built, owing to the instantaneous luminosities anticipated for the Phase I Upgrade of the LHC. The new CMS pixel detector provides four-hit tracking while featuring a significantly reduced material ... More

Fermion mass without symmetry breakingOct 14 2015Jan 07 2016We examine a model of reduced staggered fermions in three dimensions interacting through an $SO(4)$ invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan \cite{Ayyar:2014eua}. We present ... More

Cooperation Networks: Endogeneity and ComplexityJul 17 2006Insights from the Complex Systems literature are employed to develop a computational model of truly endogenous strategic network formation. Artificial Adaptive Agents, implemented as Finite State Automata (FSA), play a modified two-player IPD game with ... More

IndistinguishabilitySep 18 2016This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical indistinguishability, ... More

Summing Large-N Towers in Colour Flow EvolutionDec 09 2013We consider soft gluon evolution in the colour flow basis. We give explicit expressions for the colour structure of the (one-loop) soft anomalous dimension matrix for an arbitrary number of partons, and show how the successive exponentiation of classes ... More

Almost Parallel StructuresJul 20 2001A discussion of torsion of Riemannian G-structures leads to a survey of contributions of Alfred Gray and others on almost Hermitian manifolds, G_2-manifolds, curvature identities, volume expansions, plotting geodesics, and the geometry of nilmanifolds. ... More

EuSpRIG 2006 Commercial Spreadsheet ReviewFeb 29 2008This management summary provides an outline of a commercial spreadsheet review process. The aim of this process is to ensure remedial or enhancement work can safely be undertaken on a spreadsheet with a commercially acceptable level of risk of introducing ... More

Physical Mechanism of the d->d+is TransitionJun 02 2000We discuss the basic physical mechanism of the d->d+is transition, which is the currently accepted explanation for the results of tunneling experiments into $ab$ planes. Using the first-order perturbation theory, we show that the zero-bias states drive ... More

A Galois-Connection between Myers-Briggs' Type Indicators and Szondi's Personality ProfilesMar 08 2014We propose a computable Galois-connection between Myers-Briggs' Type Indicators (MBTIs), the most widely-used personality measure for non-psychiatric populations (based on C.G. Jung's personality types), and Szondi's personality profiles (SPPs), a less ... More

Total positivity in stable semigroupsNov 29 2014We characterize the total positivity in space-time of real strictly stable semigroups. In the positive case, this solves a problem which had been raised by Karlin. In the drifted Cauchy case, this concludes a study which we had initiated in a previous ... More

How to spell out the epistemic conception of quantum statesJan 10 2011The paper investigates the epistemic conception of quantum states---the view that quantum states are not descriptions of quantum systems but rather reflect the assigning agents' epistemic relations to the systems. This idea, which can be found already ... More

Quasidense monotone multifunctionsDec 08 2016In this paper, we discuss quasidense multifunctions from a Banach space into its dual, and use the two sum theorems proved in a previous paper to give various characterizations of quasidensity. We prove that, for closed monotone multifunctions, quasidensity ... More

Improving three-dimensional mass mapping with weak gravitational lensing using galaxy clusteringMar 28 2012Nov 01 2013The weak gravitational lensing distortion of distant galaxy images (defined as sources) probes the projected large-scale matter distribution in the Universe. To improve quality in the 3D mass mapping using 3D-lensing, we combine the lensing information ... More

Extending four dimensional Ricci flows with bounded scalar curvatureApr 11 2015We consider smooth solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, connected, four dimensional manifolds without boundary. We assume that the scalar curvature is bounded uniformly, and that T is finite. In this case, we show that the metric space ... More

Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from belowMar 12 2009Dec 01 2009We consider complete (possibly non-compact) three dimensional Riemannian manifolds (M,g) such that: a) (M,g) is non-collapsed, b) the Ricci curvature of (M,g) is bounded from below, c) the geometry of (M,g) at infinity is not too extreme. Given such initial ... More

Hydrodynamic limit for the velocity flip modelJun 11 2012Feb 20 2013We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally conserved. We ... More

A Formula for the Reliability of a $d$-dimensional Consecutive-$k$-out-of-$n$:F SystemJun 11 2015Aug 14 2015We derive a formula for the reliability of a $d$-dimensional consecutive-$k$-out-of-$n$:F system. That is, a formula for the probability that an $n_1 \times \ldots \times n_d$ array whose entries are (independently of each other) $0$ with probability ... More

Measure Partitions via Fourier Analysis II: Center Transversality in the $L^2$-norm for Complex HyperplanesJun 22 2015Sep 13 2015Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms. Considering the ... More

A Ham Sandwich Analogue for Quaternionic Measures and Finite Subgroups of S^3Sep 29 2010Sep 03 2011A "ham sandwich" theorem is established for n quaternionic Borel measures on quaternionic space H^n. For each finite subgroup G of S^3, it is shown that there is a quaternionic hyperplane H and a corresponding tiling of H^n into |G| fundamental regions ... More

From the Ham Sandwich to the Pizza Pie: A Simultaneous Z_m Equipartition of Complex MeasuresJun 23 2010Sep 03 2011A "ham sandwich" theorem is derived for n complex Borel measures on C^n. For each integer m>=2, it shown that there exists a regular m-fan centered about a complex hyperplane, satisfying the condition that for each complex measure, the "Z_m rotational ... More

A method for obtaining the algebraic generating function from a seriesDec 01 2009We describe here an experimental method that permits to compute a good candidate for the closed form of a generating function if we know the first few terms of a series. The method is based on integer relations algorithms and uses either two programs ... More

The Daugavet property and translation-invariant subspacesSep 18 2013Let $G$ be an infinite, compact abelian group and let $\varLambda$ be a subset of its dual group $\varGamma$. We study the question which spaces of the form $C_\varLambda(G)$ or $L^1_\varLambda(G)$ and which quotients of the form $C(G)/C_\varLambda(G)$ ... More

An integral lift, starting in odd Khovanov homology, of Szabó's spectral sequenceMay 10 2012Ozsv\'ath, Rasmussen and Szab\'o constructed odd Khovanov homology. It is a link invariant which has the same reduction modulo 2 as (even) Khovanov homology. Szab\'o introduced a spectral sequence with mod 2 coefficients from mod 2 Khovanov homology to ... More

Science With The Australian Square Kilometre Array PathfinderNov 14 2007The future of cm and m-wave astronomy lies with the Square Kilometre Array (SKA), a telescope under development by a consortium of 17 countries that will be 50 times more sensitive than any existing radio facility. Most of the key science for the SKA ... More

Single pulses from PSR B1641-45Nov 19 2003The integrated profile of PSR B1641-45 can be decomposed into four Gaussian components. The sum of these Gaussian components can be made to replicate the total intensity, linear and circular polarization of the integrated profile, and the discontinuity ... More

Single Dish Polarization CalibrationMay 03 2002Using the formalism of Hamaker et al. (1996), I derive a method for the polarization calibration of observations made with a single radio telescope. This method is particularly appropriate for observations of pulsars, where the sign and magnitude of the ... More

Random time series in AstronomySep 25 2013Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle, and over time (usually called light ... More

A topological constraint for monotone Lagrangians in hypersurfaces of Kähler manifoldsApr 07 2014Apr 15 2014In this paper is established a topological constraint for monotone Lagrangian embeddings in certain complex hypersurfaces of integral K\"ahler manifolds. As an application, we prove that it is impossible to embed a connected sum of $S^{1}\times S^{2k}$s ... More

Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficientsDec 16 2004We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to ... More

Symmetric Powers of Symmetric Bilinear Forms, Homogeneous Orthogonal Polynomials on the Sphere and an Application to Compact Hyperkähler ManifoldsJul 01 2015Jan 18 2016The Beauville-Fujiki relation for a compact Hyperk\"ahler manifold $X$ of dimension $2k$ allows to equip the symmetric power $\text{Sym}^kH^2(X)$ with a symmetric bilinear form induced by the Beauville-Bogomolov form. We study some of its properties and ... More

Complex horospherical transform on real sphereJan 02 2005We define a new integral transform on the real sphere which is invariant relative to the orthogonal group and similar to the horospherical Radon transform for the hyperbolic space. This transform involves complex geometry associated with the sphere.

Horospherical Cauchy-Radon transform on compact symmetric spacesJan 02 2005Harmonic analysis on noncompact Riemannian symmetric spaces is in a sense equivalent to the theory of the horospherical transform. There are no horospheres on compact symmetric spaces, but we define a complex version of horospherical transform which plays ... More

Small Black holes vs horizonless solutions in AdSOct 16 2009Nov 20 2009It is argued that the appropriate macroscopic description of half-BPS mesonic chiral operators in generic $d=4$ ${\cal N}=1$ toric gauge theories is in terms of the geometric quantization of smooth horizonless configurations. The relevance of different ... More

Bounds for the number of cohomological automorphic representations of $GL_3/\mathbb{Q}$ in the weight aspectDec 07 2018We prove a power saving over the trivial bound for the number of cohomological cuspidal automorphic representations of fixed level and growing weight on $GL_3/\mathbb{Q}$, by adapting the methods of our earlier paper on $GL_2$.

Visible Points On Exponential CurvesOct 16 2017We provide two new bounds on the number of visible points on exponential curves modulo a prime for all choices of primes. We also provide one new bound on the number of visible points on exponential curves modulo a prime for almost all primes.

Low frequency dispersive estimates for the wave equation in higher dimensionsApr 26 2007Sep 17 2007We prove dispersive estimates at low frequency in dimensions n greater or equal to 4 for the wave equation for a very large class of real-valued potentials, provided the zero is neither an eigenvalue nor a resonance.

Decomposition of subsets in finite fieldsMar 29 2018We extend a bound of Roche-Newton, Shparlinski and Winterhof which says any subset of a finite field can be decomposed into two disjoint subset $\cU$ and $\cV$ of which the additive energy of $\cU$ and $f(\cV)$ are small, for suitably chosen rational ... More

Characters and invariant random subgroups of the finitary symmetric groupDec 06 2018We will describe the relationship between the indecomposable characters of the finitary symmetric group and its ergodic invariant random subgroups; and we will interpret each Thoma character as an asymptotic limit of a naturally associated sequence of ... More

The Quantum Cosmological Wavefunction at Very Early Times for a Quadratic Gravity TheoryMay 28 2003The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, ... More

Divergences in the Moduli Space Integral and Accumulating Handles in the Infinite-Genus LimitOct 24 1994The symmetries associated with the closed bosonic string partition function are examined so that the integration region in Teichmuller space can be determined. The conditions on the period matrix defining the fundamental region can be translated to relations ... More

An abstract elementary class non-axiomatizable in $L_{(\infty,κ)}$Dec 03 2018We show that for any uncountable cardinal $\lambda$, the category of sets of cardinality at least $\lambda$ and monomorphisms between them cannot appear as the category of point of a topos, in particular is not the category of models of a $L_{(\infty,\omega)}$-theory. ... More

Toward a non-commutative Gelfand duality: Boolean locally separated toposes and Monoidal monotone complete $C^{*}$-categoriesJan 28 2015** Draft Version ** To any boolean topos one can associate its category of internal Hilbert spaces, and if the topos is locally separated one can consider a full subcategory of square integrable Hilbert spaces. In both case it is a symmetric monoidal ... More

The convolution algebra of an absolutely locally compact toposDec 31 2016We introduce a class of toposes called "absolutely locally compact" toposes and of "admissible" sheaf of rings over such toposes. To any such ringed topos $(\mathcal{T},A)$ we attach an involutive convolution algebra $\mathcal{C}_c(\mathcal{T},A)$ which ... More

Regularity and the Cesaro-Nevai classNov 16 2007We consider OPRL and OPUC with measures regular in the sense of Ullman-Stahl-Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on $[-2,2]$ implies $\lim_{N\to\infty} N^{-1} [\sum_{n=1}^N (a_n-1)^2 ... More

Critical Lieb-Thirring bounds for one-dimensional Schrodinger operators and Jacobi matrices with regular ground statesMay 24 2007Jul 09 2007This paper has been withdrawn by the author in favor of a stronger result proven by the author with R. Frank and T. Weidl in arXiv:0707.0998

Zeros of OPUC and Long Time Asymptotics of Schur and Related FlowsOct 31 2006We provide a complete analysis of the asymptotics for the semi-infinite Schur flow: $\alpha_j(t)=(1- |\alpha_j(t)|^2) (\alpha_{j+1}(t)-\alpha_{j-1}(t))$ for $\alpha_{-1}(t)= 1$ boundary conditions and $n=0,1,2,...$, with initial condition $\alpha_j(0)\in ... More

Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domainsNov 17 2016Apr 09 2019For $\Omega \subset \mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\Delta_\Omega$ the Dirichlet Laplacian on $\Omega$. For $\Lambda\geq0$ and $\gamma \geq 0$ let $\Omega_{\Lambda, \gamma}(\mathcal{A})$ denote any extremal set of ... More

Spinning particles in a Yang-Mills fieldFeb 03 2006Suppose that a Lie group $G$ acts properly on a configuration manifold $Q$. We study the symplectic quotient of $T^*Q$ with respect to the cotangent lifted $G$-action at an arbitrary coadjoint orbit level $\mathcal{O}$. In particular, if $Q=Q_{(H)}$ is ... More

Ricci Flow of regions with curvature bounded below in dimension threeJul 04 2014May 29 2017We 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

A BDF2-Approach for the Non-linear Fokker-Planck EquationJan 29 2018We prove convergence of a variational formulation of the BDF2 method applied to the non-linear Fokker-Planck equation. Our approach is inspired by the JKO-method and exploits the differential structure of the underlying $L^2$-Wasserstein space. The technique ... More

A-Tint: A polymake extension for algorithmic tropical intersection theoryAug 21 2012Oct 09 2013In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study of moduli spaces, ... More

Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modulesApr 04 2018Apr 21 2018The minimal model $\mathfrak{osp}(1|2)$ vertex operator superalgebras are the simple quotients of affine vertex operator superalgebras constructed from the affine Lie super algebra $\widehat{\mathfrak{osp}}(1|2)$ at certain rational values of the level ... More

Symmetric Variations of the Metric and Extrema of the Action for Pure GravityAug 10 1996Sep 10 1996Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism ... More