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A remark on the group-completion theoremSep 07 2017Suppose that $M$ is a topological monoid satisfying $\pi_0M=\mathbb{N}$ to which the McDuff-Segal group-completion theorem applies. This implies that a certain map $f: \mathbb{M}_{\infty}\rightarrow \Omega BM$ defined on an infinite mapping telescope ... More

The ring of coefficients for commutative complex $K$-theoryNov 11 2016We determine the integral coefficient ring for "commutative complex $K$-theory". This is a cohomology theory which was first defined by Adem and G\'omez and then generalised by Adem, G\'omez, Lind and Tillmann. We use the work of Lawson on unitary deformation ... More

Commuting matrices and Atiyah's Real K-theoryJul 18 2018Mar 22 2019We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n-tuples in the ... More

Commuting matrices and Atiyah's Real K-theoryJul 18 2018We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n-tuples in the ... More

Classifying spaces for commutativity of low-dimensional Lie groupsFeb 10 2018For each of the groups $G = O(2), SU(2), U(2)$, we compute the integral and $\mathbb{F}_2$-cohomology rings of $B_\text{com} G$ (the classifying space for commutativity of $G$), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy ... More

Two loop soft function for secondary massive quarksSep 24 2013Jan 23 2014We present the calculation of the $\mathcal{O}(\alpha_s^2 C_F T_F)$ massive quark corrections to the soft function for the double hemisphere jet mass distribution in $e^+ e^-$ collisions, a necessary ingredient for the calculation of several event shape ... More

Secondary Heavy Quark Production in Jets through Mass ModesFeb 19 2013Jul 19 2013We present an effective field theory method to determine secondary massive quark effects in jet production taking the thrust distribution for e+ e- collisions in the dijet limit as a concrete example. The method is based on the field theoretic treatment ... More

Variable Flavor Number Scheme for Final State Jets in ThrustMay 19 2014Feb 24 2016We present results for mass effects coming from secondary radiation of heavy quark pairs related to gluon splitting in the thrust distribution for e+e- collisions. The results are given in the dijet limit where the hard interaction scale and the scales ... 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

Zero-Bias States and the Mechanism of the Surface d->d+is TransitionAug 28 2000We study the physical mechanism of the surface d->d+is transition proposed as the interpretation of results of tunneling experiments into ab planes. We base our argument on first-order perturbation theory and show that the zero-bias states drive the transition. ... More

Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noiseFeb 14 2014Apr 05 2015We investigate the macroscopic behavior of the disordered harmonic chain of oscillators, through energy diffusion. The Hamiltonian dynamics of the system is perturbed by a degenerate conservative noise. After rescaling space and time diffusively, we prove ... More

Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)Sep 05 2013Apr 08 2014We produce a decidable super-intuitionistic normal modal logic of internalised intuitionistic (and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical monotonic non-disjunctive interactive proofs ... More

Computer-Aided Discovery and Categorisation of Personality AxiomsMar 24 2014We propose a computer-algebraic, order-theoretic framework based on intuitionistic logic for the computer-aided discovery of personality axioms from personality-test data and their mathematical categorisation into formal personality theories in the spirit ... More

Correlated radiative electron capture in ion-atom collisionsAug 30 2010Radiative double electron capture (RDEC) is a one-step process where two free (or quasi-free) target electrons are captured into a bound state of the projectile, e.g. into an empty K-shell, and the energy excess is released as a single photon. This process ... More

Mittag-Leffler functions and complete monotonicityDec 16 2013Dec 17 2013We consider two operations on the Mittag-Leffler function which cancel the exponential term in the expansion at infinity, and generate a completely monotonic function. The first one is the action of a certain differential-difference operator, and leads ... More

Comparing Fréchet and positive stable lawsOct 07 2013Jan 27 2014Let ${\bf L}$ be the unit exponential random variable and ${\bf Z}_\alpha$ the standard positive $\alpha$-stable random variable. We prove that $\{(1-\alpha) \alpha^{\gamma_\alpha} {\bf Z}_\alpha^{-\gamma_\alpha}, 0< \alpha <1\}$ is decreasing for the ... More

Total positivity of a Cauchy kernelMay 06 2013We study the total positivity of the kernel $1/(x^2 + 2 \cos(\pi\a)xy +y^2).$ The case of infinite order is characterized by an application of Schoenberg's theorem. We then give necessary conditions for the cases of any given finite order with the help ... More

Impact of Theory Uncertainties on the Precision of the Top Quark Mass in a Threshold Scan at Future e+e- CollidersNov 10 2016Future energy-frontier electron-positron colliders will be capable of high-precision studies of top quark properties. The measurement of the top-pair production cross section around the threshold provides access to the mass of the top quark in theoretically ... More

Topological constraints in magnetic field relaxationMar 17 2013Stability and reconnection of magnetic fields play a fundamental role in natural and man-made plasma. In these applications the field's topology determines the stability of the magnetic field. Here I will describe the importance of one topology quantifier, ... More

Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous DiffusionOct 13 2016We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly in $\theta$ ... More

Canonicity for Cubical Type TheoryJul 14 2016Cubical type theory is an extension of Martin-L\"of type theory recently proposed by Cohen, Coquand, M\"ortberg and the author which allows for direct manipulation of $n$-dimensional cubes and where Voevodsky's Univalence Axiom is provable. In this paper ... More

Defending the future: An MSc module in End User Computing Risk ManagementSep 28 2010This paper describes the rationale, curriculum and subject matter of a new MSc module being taught on an MSc Finance and Information Management course at the University of Wales Institute in Cardiff. Academic research on spreadsheet risks now has some ... More

Computing Cup-Products in integral cohomology of Hilbert schemes of points on K3 surfacesOct 30 2014Jan 18 2016We study cup products in integral cohomology of the Hilbert scheme of $n$ points on a K3 surface and present a computer program for this purpose. In particular, we deal with the question, which classes can be represented by products of lower degrees.

On the remote interaction of biological objects with identical genetic structuresJul 03 2002The paper puts forward an unusual prediction that cultivating a clone can curtail the lifespan of the clone donor. Neither the arrangement of this suggested empirical study nor the analyses of the anticipated outcomes rely on the accompanying theoretical ... More

Complementarity and Scientific RationalityDec 24 2004Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his ... More

The Classical Moment Problem as a Self-Adjoint Finite Difference OperatorJun 08 1999This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence ... More

Four Fermion Models at Non-Zero DensityJun 22 1998I review the properties of the three-dimensional Gross-Neveu model formulated with non-zero chemical potential and temperature, focussing on results obtained by lattice Monte Carlo simulation.

Log Triviality in the Nambu -- Jona-Lasinio ModelSep 15 1997Results are presented from a Monte Carlo simulation of the Nambu -- Jona-Lasinio model with SU(2)xSU(2) chiral symmetry and N_f=2 flavors of fermion. We show that fits to the equation of state are sensitive to the shape and extent of the assumed scaling ... More

O(1/N_f) Corrections to the Thirring Model in 2<d<4Nov 02 1994Nov 10 1994The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to ... More

The Noncommutative Topology of Anti-Self-Dual Gauge FieldsMar 07 2013May 09 2013Through techniques afforded by $C^*$-algebras and Hilbert modules, we study the topology of spaces which parametrize families of instanton gauge fields on noncommutative Euclidean four-spheres $S^4_\sigma$. By deforming the ADHM construction of instantons ... More

The long history of the Rossiter-McLaughlin effect and its recent applicationsSep 08 2011Nov 21 2011In this paper I will review the Rossiter-McLaughlin (RM) effect; its history, how it manifests itself during stellar eclipses and planetary transits, and the increasingly important role its measurements play in guiding our understanding of the formation ... More

Rethinking Newton's $\textit{Principia}$Sep 20 2016It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean space-time. I argue to the ... More

Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large DeviationsAug 17 2016Short blurb for invited talk at AMS annual meeting in Atlanta; will appear in January AMS Notices

Right Amenable Left Group Sets and the Tarski-Følner TheoremMar 21 2016Mar 24 2016We introduce right amenability, right F{\o}lner nets, and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-F{\o}lner theorem for left homogeneous spaces with finite stabilisers. It states that right amenability, the existence ... More

The Garden of Eden Theorem for Cellular Automata on Group SetsMar 21 2016Sep 05 2016We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective ... More

Resolved observations of transition disksFeb 21 2016Resolved observations are bringing new constraints on the origin of radial gaps in protoplanetary disks. The kinematics, sampled in detail in one case-study, are indicative of non-Keplerian flows, corresponding to warped structures and accretion which ... More

FreeSASA: An open source C library for solvent accessible surface area calculationsJan 25 2016Calculating solvent accessible surface areas (SASA) is a run-of-the-mill calculation in structural biology. Although there are many programs available for this calculation, there are no free-standing, open-source tools designed for easy tool-chain integration. ... More

RAMBO on dietAug 13 2013We describe a phase space generator which is flat for massless particles, and approximately flat for massive particles of masses much smaller than the typical mometum scales involved in the process. The same goal is achieved by the RAMBO algorithm, contrary ... More

Inclusive Cross Sections in ME+PS MergingJul 02 2013We discuss an extension of matrix element plus parton shower merging at leading and next-to-leading order. The algorithm does preserve inclusive cross sections at the respective input order. This constraint avoids potentially large logarithmic contributions, ... More

Improvement and generalisation of Papasoglu's lemmaAug 31 2017We improve an isoperimetric inequality due to Panos Papasoglu. We also generalize this inequality to the Finsler case by proving an optimal Finsler version of the Besicovitch's lemma which holds for any notion of Finsler volume.

Signal Machine And Cellular Automaton Time-Optimal Quasi-Solutions Of The Firing Squad/Mob Synchronisation Problem On Connected GraphsJun 19 2017We construct a time-optimal quasi-solution of the firing mob synchronisation problem over finite, connected, and undirected multigraphs whose maximum degrees are uniformly bounded by a constant. It is only a quasi-solution because its number of states ... More

In defence of non-ontic accounts of quantum statesApr 30 2012Feb 07 2013The paper discusses objections against non-hidden variable versions of the epistemic conception of quantum states - the view that quantum states do not describe the properties of quantum systems but reflect, in some way to be specified, the epistemic ... More

Gauge symmetry breaking in gauge theories---In search of clarificationJul 23 2011Aug 05 2012The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions ... More

A new approach to inverse spectral theory, I. Fundamental formalismJun 17 1999Nov 01 1999We present a new approach (distinct from Gel'fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schr\"odinger operator determines the potential. Our approach is an analog ... More

Radio Observations of Two Isolated Neutron Stars, RXJ0720.4-3125 and RX J0806.4-4132Feb 24 2003Radio observations of two isolated neutron stars, RXJ0720.4-3125 and RX J0806.4-4132, have been made with the Australia Telescope Compact Array at a frequency of 1.4 GHz. No continuum emission is detected from either object with a 3 sigma upper limit ... More

Proceedings of the Ninth Prague Topological Symposium. Contributed papers from the symposium held in Prague, August 19-25, 2001Apr 12 2002This collection of thirty two reviewed articles covers several fields of General Topology. Several contributions represent invited presentations at the Ninth Prague Topological Symposium.

Fusion Rules of the ${\cal W}_{p,q}$ Triplet ModelsJul 26 2009Jan 11 2010In this paper we determine the fusion rules of the logarithmic ${\calW}_{p,q}$ triplet theory and construct the Grothendieck group with subgroups for which consistent product structures can be defined. The fusion rules are then used to determine projective ... More

VC-sets and generic compact dominationFeb 16 2015Jan 26 2016Let X be a closed subset of a locally compact second countable group G whose family of translates has finite VC-dimension. We show that the topological border of X has Haar measure 0. Under an extra technical hypothesis, this also holds if X is constructible. ... More

Type decomposition in NIP theoriesApr 13 2016Aug 02 2017We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.

Invariant types in NIP theoriesJan 27 2014Sep 23 2015We study invariant types in NIP theories. Amongst other things: we prove a definable version of the (p,q)-theorem in theories of small or medium directionality; we construct a canonical retraction from the space of M-invariant types to that of M-finitely ... More

Dp-minimality: invariant types and dp-rankOct 16 2012Jul 01 2014This paper has two parts. In the first one, we prove that an invariant dp-minimal type is either finitely satisfiable or definable. We also prove that a definable version of the (p,q)-theorem holds in dp-minimal theories of small or medium directionality. ... More

One-sided asymptotically mean stationary channelsMar 26 2014This paper proposes an analysis of asymptotically mean stationary (AMS) communication channels. A hierarchy based on stability properties (stationarity, quasi-stationarity, recurrence and asymptotically mean stationarity) of channels is identified. Stationary ... More

An Illustrated Introduction to the Basic Biological PrinciplesDec 13 2007Dec 14 2009Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More

Molecular Labor Division: Its Cause and ConsequenceDec 04 2007Aug 21 2011Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More

The exact number of r-regular elements in finite exceptional groupsJan 26 2013We calculate the precise number of r-regular elements in the finite exceptional groups. As a corollary we find that the proportion of r-regular elements is at least 3577/18432 and for all \epsilon>0, there are infinitely finite simple exceptional groups ... More

Remarks on $G_{2}$-manifolds with boundaryFeb 27 2018This article is based on a lecture at the Journal of Differential Geometry Conference, Harvard 2017. We discuss closed and torsion-free $G_{2}$-structures on a 7-manifold with boundary, with prescribed $3$-form on the boundary. Much of the article is ... More

Small deviations in p-variation norm for multidimensional Levy processesMay 31 2003Let Z be an Rd-valued Levy process with strong finite p-variation for some p<2. We prove that the ''decompensated'' process Y obtained from Z by annihilating its generalized drift has a small deviations property in p-variation. This property means that ... More

High frequency dispersive estimates in dimension twoJul 25 2007Sep 13 2007We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrodinger groupes for a very large class of real-valued potentials.

Singular cotangent bundle reduction and spin Calogero-Moser systemsNov 03 2004Oct 30 2008We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a formula for the reduced symplectic form in this setting. Furthermore, as an application of this bundle picture we consider Calogero-Moser ... More

Relative Zeta Determinants and the Quillen MetricOct 27 1999We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary ... More

Symmetrization of monoïds as hypergroupsSep 08 2013We adapt the construction of the Grothendieck group associated to a commutative mono\"id to handle idempotent mono\"ids. Our construction works for a restricted class of commutative mono\"ids, it agrees with the Grothendieck group construction in many ... More

Unitaries Permuting Two Orthogonal ProjectionsMar 16 2017Mar 27 2017Let $P$ and $Q$ be two orthogonal projections on a separable Hilbert space, $\calH$. Wang, Du and Dou proved that there exists a unitary, $U$, with $UPU^{-1} =Q, \quad UQU^{-1} = P$ if and only if $\dim(\ker P \cap \ker(1-Q)) = \dim(\ker Q \cap \ker(1-P))$ ... More

Small deviations in p-variation for stable processesMay 31 2003Let $\{Z_t, t\geq 0\}$ be a strictly stable process on $\R$ with index $\alpha\in (0,2]$. We prove that for every $p > \alpha$, there exists $\gamma = \gamma (\alpha, p)$ and $\k = \k (\alpha, p)\in (0, +\infty)$ such that $$\lim_{\ee\downarrow 0}\ee^{\gamma}\log\pb\lcr ... More

The asymmetric sandwich theoremAug 29 2011Sep 22 2011We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel ... More

Quasidense monotone multifunctionsDec 08 2016Jul 10 2017In 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 investigate the Fitzpatrick extension of such a multifunction. ... More

Quadrivariate existence theorems and strong representabilitySep 01 2008Feb 22 2011In this paper, we give conditions under which we can compute the conjugate of a convex function on the product of two Frechet spaces defined in terms of another convex function on the product of two (possibly different) Frechet spaces. We use this result ... More

Singularity categories of deformations of Kleinian singularitiesOct 26 2016Let $G$ be a finite subgroup of $\text{SL}(2,\Bbbk)$ and let $R = \Bbbk[x,y]^G$ be the coordinate ring of the corresponding Kleinian singularity. In 1998, Crawley-Boevey and Holland defined deformations $\mathcal{O}^\lambda$ of $R$ parametrised by weights ... More

NIP omega-categorical structures: the rank 1 caseJul 18 2018Sep 13 2018We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets. For a fixed number of 4-types, we show that there are only finitely many such structures and that all are built out of finitely many linear orders ... More

The intersection ring of matroidsFeb 23 2016Aug 30 2016We study a particular graded ring structure on the set of all loopfree matroids on a fixed labeled ground set, which occurs naturally in tropical geometry. The product is given by matroid intersection and the additive structure is defined by assigning ... More

Categorical semantics of metric spaces and continuous logicJan 25 2019Using the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this "continuous semantics" is equivalent to the a priori ... More

The Gradient Flow of O'Hara's Knot EnergiesJan 12 2016Jun O'Hara invented a family of knot energies $E^{j,p}$, $j,p \in (0, \infty)$. We study the negative gradient flow of the sum of one of the energies $E^\alpha = E^{\alpha,1}$, $\alpha \in (2,3)$, and a positive multiple of the length. Showing that the ... More

On the magnitude of odd balls via potential functionsApr 06 2018Magnitude is a measure of size defined for certain classes of metric spaces; it arose from ideas in category theory. In particular, magnitude is defined for compact subsets of Euclidean space and, in arXiv:1507.02502, Barcel\'o and Carbery gave a procedure ... More

Feedback control of charged ideal fluidsMay 12 2019The theory of controlled mechanical systems of [6, 3, 4] is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and depends on the ... More

Unconditional bounds for the multiplicity of automorphic forms of cohomological type on GL_2Mar 12 2011We prove an unconditional power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL_2 over any number field which is not totally real. Our proof involves the theory of p-adically completed cohomology ... More

Unifying notions of pasting diagramsMar 01 2019In this work, we relate the three main formalisms for the notion of pasting diagram in strict $\omega$-categories: Street's parity complexes, Johnson's pasting schemes and Steiner's augmented directed complexes. We first show that parity complexes and ... More

Weak convergence of CD kernels and applicationsJul 17 2007We prove a general result on equality of the weak limits of the zero counting measure, $d\nu_n$, of orthogonal polynomials (defined by a measure $d\mu$) and $\frac{1}{n} K_n(x,x) d\mu(x)$. By combining this with Mate--Nevai and Totik upper bounds on $n\lambda_n(x)$, ... More

A constructive account of the Kan-Quillen model structure and of Kan's Ex$^{\infty}$ functorMay 15 2019We give a fully constructive proof that there is a proper cartesian $\omega$-combinatorial model structure on the category of simplicial sets, whose generating cofibrations and trivial cofibrations are the usual boundary inclusion and horn inclusion. ... More

A bound for the perimeter of inner parallel bodiesAug 26 2015Mar 04 2016We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body $\Omega$. The bound depends only on the perimeter and inradius $r$ of the original body and states that \[|\partial\Omega_t| \geq \Bigl(1-\frac{t}{r}\Bigr)^{n-1}_+ ... More

Some recent developments in Kähler geometry and exceptional holonomyAug 12 2018Aug 23 2018This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)

Optimal eigenvalues estimate for the Dirac operator on domains with boundaryMar 21 2006We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the $\MIT$ bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.

Measure theory over boolean toposesNov 06 2014In this paper we develop a notion of measure theory over boolean toposes which is analogous to noncommutative measure theory, i.e. to the theory of von Neumann algebras. This is part of a larger project to study relations between topos theory and noncommutative ... More

Higher-Derivative Quantum CosmologyNov 06 1999Nov 10 1999The quantum cosmology of a higher-derivative derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler-DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques ... More

A Proof of the Odd Perfect Number ConjectureJan 08 2004May 31 2008It is sufficient to prove that there is an excess of prime factors in the product of repunits with odd prime bases defined by the sum of divisors of the integer $N=(4k+1)^{4m+1}\prod_{i=1}^\ell ~ q_i^{2\alpha_i}$ to establish that there do not exist any ... More

OPUC on One FootFeb 23 2005We present an expository introduction to orthogonal polynomials on the unit circle.

Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two PicturesNov 17 2004Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large $n$. Motivated by two plots, we look at the finer structure for the case of random Verblunsky coefficients and for what we call the ... More

On omega-categorical structures with few finite substructuresOct 15 2018We establish new results on the possible growth rates for the sequence (f_n) counting the number of orbits of a given oligomorphic group on unordered sets of size n. Macpherson showed that for primitive actions, the growth is at least exponential (if ... More

Minimal generating sets of non-modular invariant rings of finite groupsMar 01 2007Apr 12 2007It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case. Apart from very ... More

Multiplicative strong unimodality for positive stable lawsFeb 26 2010It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu, the only remaining relevant situation for the multiplicative ... More

Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distributionNov 16 2010Feb 01 2011The probability distribution of the current in the asymmetric simple exclusion process is expected to undergo a phase transition in the regime of weak asymmetry of the jumping rates. This transition was first predicted by Bodineau and Derrida using a ... More

Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundariesMar 28 2009Jun 23 2009The asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large deviation ... More

Equilibrium measures and capacities in spectral theoryNov 16 2007This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl-Totik theory of regular measures, especially the case of OPRL and OPUC. Links are made to ... More

Schrodinger Operators with Purely Discrete SpectrumOct 17 2008We prove $-\Delta +V$ has purely discrete spectrum if $V\geq 0$ and, for all $M$, $|\{x\mid V(x)<M\}|<\infty$ and various extensions.

Approximation properties of $β$-expansionsSep 09 2014Let $\beta\in(1,2)$ and $x\in [0,\frac{1}{\beta-1}]$. We call a sequence $(\epsilon_{i})_{i=1}^\infty\in\{0,1\}^{\mathbb{N}}$ a $\beta$-expansion for $x$ if $x=\sum_{i=1}^{\infty}\epsilon_{i}\beta^{-i}$. We call a finite sequence $(\epsilon_{i})_{i=1}^{n}\in\{0,1\}^{n}$ ... More

On small bases which admit countably many expansionsMay 16 2013Let $q\in(1,2)$ and $x\in[0,\frac1{q-1}]$. We say that a sequence $(\epsilon_i)_{i=1}^{\infty}\in\{0,1\}^{\mathbb{N}}$ is an expansion of $x$ in base $q$ (or a $q$-expansion) if x=\sum_{i=1}^{\infty}\epsilon_iq^{-i}. Let $\mathcal{B}_{\aleph_{0}}$ denote ... More

Generalised golden ratios over integer alphabetsOct 31 2012It is a well known result that for $\beta\in(1,\frac{1+\sqrt{5}}{2})$ and $x\in(0,\frac{1}{\beta-1})$ there exists uncountably many $(\epsilon_{i})_{i=1}^{\infty}\in {0,1}^{\mathbb{N}}$ such that $x=\sum_{i=1}^{\infty}\epsilon_{i}\beta^{-i}.$ When $\beta\in(\frac{1+\sqrt{5}}{2},2]$ ... More

A Feynman-Kac Formula for Unbounded SemigroupsJul 27 1999We prove a Feynman-Kac formula for Schrodinger operators with potentials V(x) that obey (for all \epsilon > 0): V(x) \geq - \epsilon |x|^2 - C_\epsilon. Even though e^{-tH} is an unbounded operator, any \phi, \psi \in L^2 with compact support lie in D(e^{-tH}) ... More

An application of continuous logic to fixed point theoryOct 18 2016Jan 25 2019In aiming to apply to a broader class of examples the Avigad-Iovino "ultraproducts and metastability" approach to obtaining uniformity for convergence of sequences, we construct a framework using continuous logic that in particular is able to handle discontinuous ... More

A Homogeneous Function Constant along the Leaves of a FoliationJul 03 2018Given a smooth foliation by complex curves (locally around a point $x\in\mathbb{C}^2\setminus\{0\}$) which is "compatible" with the foliation by spheres centered at the origin, we construct a smooth real-valued function $g$ in a neighborhood of said point, ... More

A Parameter Version of Forstnerič's Splitting LemmaFeb 05 2018We construct solution operators to the $\overline{\partial}$-equation that depend continuously on the domain. This is applied to derive a parameter version of Forstneri\v{c}'s splitting lemma: If both the maps and the domains they are defined on vary ... More