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Preconditioned Conjugate Gradients, Radial Basis Functions and Toeplitz MatricesJun 12 2010Radial basis functions provide highly useful and flexible interpolants to multivariate functions. Further, they are beginning to be used in the numerical solution of partial differential equations. Unfortunately, their construction requires the solution ... More

The Interpolation Theory of Radial Basis FunctionsJun 12 2010In this dissertation, it is first shown that, when the radial basis function is a $p$-norm and $1 < p < 2$, interpolation is always possible when the points are all different and there are at least two of them. We then show that interpolation is not always ... More

Stable furry black holes in $\mathfrak{su}(\infty)$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinitude of global chargesFeb 10 2019We present solutions to classical field equations for purely magnetic $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory in asymptotically Anti-de Sitter space. These solutions are found to be stable under linear, time-dependent perturbations. Recent ... More

The Riemann surface of the chiral Potts model free energy functionDec 03 2002In a recent paper we derived the free energy or partition function of the $N$-state chiral Potts model by using the infinite lattice ``inversion relation'' method, together with a non-obvious extra symmetry. This gave us three recursion relations for ... More

Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising modelMar 17 2011Apr 18 2011Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C. N. Yang published a derivation ... More

Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQDec 23 2009Jan 11 2010For the Ising model, the calculation of the spontaneous magnetization leads to the problem of evaluating a determinant. Yang did this by calculating the eigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed it as a Toeplitz determinant ... More

A conjecture for the superintegrable chiral Potts modelMar 28 2008Jul 12 2008We adapt our previous results for the ``partition function'' of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{-\alpha H}, where H is the associated hamiltonian. The spontaneous magnetization ... More

The "inversion relation" method for obtaining the free energy of the chiral Potts modelDec 03 2002We derive the free energy of the chiral Potts model by the infinite lattice ``inversion relation'' method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice ... More

Surface and corner free energies of the self-dual Potts modelJun 06 2016Jun 08 2016We calculate the surface free energies $f_s, f_s'$ of the anisotropic self-dual $Q$-state Potts model for $Q > 4$ and find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic case. Each of $f_s, f_s'$ satisifies (as $f_b$ ... More

Algebraic reduction of the Ising modelMar 28 2008Jul 12 2008We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the ... More

Hard Squares for z = -1Sep 27 2007Nov 21 2007The hard square model in statistical mechanics has been investigated for the case when the activity z is -1. For cyclic boundary conditions, the characteristic polynomial of the transfer matrix has an intriguingly simple structure, all the eigenvalues ... More

Corner transfer matrices in statistical mechanicsNov 07 2006Corner transfer matrices are a useful tool in the statistical mechanics of simple two-dimensinal models. They can be very effective way of obtaining series expansions of unsolved models, and of calculating the order parameters of solved ones. Here we ... More

Equivalence of the two results for the free energy of the chiral Potts modelMay 13 1999May 14 1999The free energy of the chiral Potts model has been obtained in two ways. The first used only the star-triangle relation, symmetries and invariances, and led to a system of equations that implicitly define the free energy, and from which the critical behaviour ... More

Derivation of the order parameter of the chiral Potts modelJan 11 2005Feb 21 2005We derive the order parameter of the chiral Potts model, using the method of Jimbo et al. The result agrees with previous conjectures.

Completeness of the Bethe ansatz for the six and eight-vertex modelsNov 10 2001Feb 07 2002We discuss some of the difficulties that have been mentioned in the literature in connection with the Bethe ansatz for the six-vertex model and XXZ chain, and for the eight-vertex model. In particular we discuss the ``beyond the equator'', infinite momenta ... More

Dichromatic polynomials and Potts models summed over rooted mapsNov 23 2000Jan 12 2001We consider the sum of dichromatic polynomials over non-separable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the $q$-state ... More

A direct proof of Kim's identitiesJan 15 1998As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. ... More

A Maximum Likelihood Approach to Estimating Correlation FunctionsMay 20 2013Nov 26 2013We define a Maximum Likelihood (ML for short) estimator for the correlation function, {\xi}, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (1993, LS for short) estimator. The ML estimator outperforms ... More

Star-Triangle Relation for a Three Dimensional ModelDec 10 1992The solvable $sl(n)$-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice with two- and ... More

Putting in All the Stops: Execution Control for JavaScriptFeb 08 2018Scores of compilers produce JavaScript, enabling programmers to use many languages on the Web, reuse existing code, and even use Web IDEs. Unfortunately, most compilers expose the browser's compromised execution model, so long-running programs freeze ... More

Stopping time convergence for processes associated with Dirichlet formsMay 27 2017Jun 29 2017Convergence is proved for solutions of Dirichlet problems in regions with many small excluded sets (holes), as the holes become smaller and more numerous. The problem is formulated in the context of Markov processes associated with general Dirichlet forms, ... More

Putting in All the Stops: Execution Control for JavaScriptFeb 08 2018Apr 16 2018Scores of compilers produce JavaScript, enabling programmers to use many languages on the Web, reuse existing code, and even use Web IDEs. Unfortunately, most compilers inherit the browser's compromised execution model, so long-running programs freeze ... More

Formal Foundations of Serverless ComputingFeb 15 2019Feb 18 2019A robust, large-scale web service can be difficult to engineer. When demand spikes, it must configure new machines and manage load-balancing; when demand falls, it must shut down idle machines to reduce costs; and when a machine crashes, it must quickly ... More

Regulation and the Integrity of Spreadsheets in the Information Supply ChainJan 23 2008Spreadsheets provide many of the key links between information systems, closing the gap between business needs and the capability of central systems. Recent regulations have brought these vulnerable parts of information supply chains into focus. The risk ... More

Enterprise Spreadsheet Management: A Necessary GoodJan 21 2008This paper presents the arguments and supporting business metrics for Enterprise Spreadsheet Management to be seen as a necessary good. These arguments are divided into a summary of external business drivers that make it necessary and the good that may ... More

A special case of the $Γ_{00}$ conjectureApr 03 2008Sep 02 2010In this paper we prove the $\Gamma_{00}$ conjecture of van Geemen and van der Geer, under the additional assumption that the matrix of coefficients of the tangent has rank at most 2. This assumption is satisfied by Jacobians, and thus our result gives ... More

Simple fixed-brane gauges in $S_1/Z_2$ braneworldsApr 07 2006For five-dimensional braneworlds with an $S_1/\mathbb{Z}_2$ orbifold topology for the extra dimension $x^5$, we discuss the validity of recent claims that a gauge exists where the two boundary branes lie at fixed positions and the metric satisfies $g_{\mu ... More

A Sequent Calculus for Dynamic Topological LogicJul 25 2014Aug 03 2014We introduce a sequent calculus for the temporal-over-topological fragment $\textbf{DTL}_{0}^{\circ * \slash \Box}$ of dynamic topological logic $\textbf{DTL}$, prove soundness semantically, and prove completeness syntactically using the axiomatization ... More

On Improved Bounds on Bounded Degree Spanning Trees for Points in Arbitrary DimensionMay 13 2013Jan 05 2014Given points in Euclidean space of arbitrary dimension, we prove that there exists a spanning tree having no vertices of degree greater than 3 with weight at most 1.559 times the weight of the minimum spanning tree. We also prove that there is a set of ... More

Exploratory topic modeling with distributional semanticsJul 16 2015As we continue to collect and store textual data in a multitude of domains, we are regularly confronted with material whose largely unknown thematic structure we want to uncover. With unsupervised, exploratory analysis, no prior knowledge about the content ... More

On Quantum NoncompressionNov 16 2015This article presents a quantum transmission problem, in which Alice is trying to send a number of qbits to Bob. Alice has access to two channels, one that sends classical bits and another that sends quantum bits. We show that under certain error terms, ... More

Canonical Cartan connection for $4$-dimensional CR-manifolds belonging to general class ${\sf II}$May 05 2014We study the equivalence problem for $4$-dimensional CR-manifolds of CR-dimension $1$ and codimension $2$ which are referred to as Engel CR-manifolds. We construct a canonical Cartan connection on such CR-manifolds through Cartan equivalence's method. ... More

Towards 3-Dimensional Rewriting TheoryMar 17 2014Apr 02 2014String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is confluent and terminating, ... More

A Dichotomy in Machine KnowledgeAug 04 2011We show that a machine, which knows basic logic and arithmetic and basic axioms of knowledge, and which is factive (knows nothing false), can either know that it is factive, or know its own Goedel number, but not both.

Highly lopsided information and the Borel hierarchyJun 01 2011In a game where both contestants have perfect information, there is a strict limit on how perfect that information can be. By contrast, when one player is deprived of all information, the limit on the other player's information disappears, admitting a ... More

Extraction of Cosmological Information from WiggleZApr 06 2016In this thesis, I analyse the 2D anisotropic Baryon Acoustic Oscillation (BAO) signal present in the final WiggleZ dataset. I utilise newly released covariance matrices from the WizCOLA simulations and follow well tested methodologies used in prior analyses ... More

Escaping the Tragedy of the Commons through Targeted PunishmentJun 04 2015Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread ... More

Interplay between Network Topology and Dynamics in Neural SystemsFeb 16 2013This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes, can shape the ... More

Chern classes of the tangent bundle on the Hilbert scheme of points on the affine planeOct 21 2004Mar 31 2005The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for the Chern classes ... More

Infinite graphs in systematic biology, with an application to the species problemJan 13 2012Dec 13 2012We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs ... More

The global gravitational anomaly of the self-dual field theoryOct 20 2011May 10 2013We derive a formula for the global gravitational anomaly of the self-dual field theory on an arbitrary compact oriented Riemannian manifold. Along the way, we uncover interesting links between the theory of determinant line bundles of Dirac operators, ... More

On weighted optimality of experimental designsOct 20 2016When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality criteria for ... More

Polar actions on Hermitian and quaternion-Kähler symmetric spacesDec 18 2006Jan 17 2007We analyze polar actions on Hermitian and quaternion-K\"ahler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry ... More

A quantum point contact as a (near) perfect spin polariserNov 28 2018In this paper, I present a simple method of obtaining spin-polarised current from a QPC with a large Rashba interaction. The origin of this spin polarisation is the adiabatic evolution of spin "up" of the first QPC sub-band, into spin "down" of the second ... More

Propagation in media as a probe for topological propertiesSep 23 2017The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete classification of ... More

Real-Time Multiple Object Tracking - A Study on the Importance of SpeedSep 11 2017Oct 02 2017In this project, we implement a multiple object tracker, following the tracking-by-detection paradigm, as an extension of an existing method. It works by modelling the movement of objects by solving the filtering problem, and associating detections with ... More

On Certain Tilting Modules for SL2May 19 2017Sep 19 2017We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by nature, we give ... More

A theoretical framework for retinal computations: insights from textbook knowledgeJun 07 2018Neural circuits in the retina divide the incoming visual scene into more than a dozen distinct representations that are sent on to central brain areas, such as the lateral geniculate nucleus and the superior colliculus. The retina can be viewed as a parallel ... More

Almost prime values of the order of abelian varieties over finite fieldsMar 09 2018Let $E/\mathbb Q$ be an elliptic curve, and denote by $N(p)$ the number of $\mathbb{F}_p$-points of the reduction modulo $p$ of $E$. A conjecture of Koblitz, refined by Zywina, states that the number of primes $p \leq X$ at which $N(p)$ is also prime ... More

Context-Independent Polyphonic Piano Onset Transcription with an Infinite Training DatasetJul 26 2017Many of the recent approaches to polyphonic piano note onset transcription require training a machine learning model on a large piano database. However, such approaches are limited by dataset availability; additional training data is difficult to produce, ... More

Superstring scattering amplitudes in higher genusMar 24 2008May 20 2008In this paper we continue the program pioneered by D'Hoker and Phong, and recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the chiral superstring measure by constructing modular forms satisfying certain factorization constraints. ... More

The global anomaly of the self-dual field in general backgroundsSep 25 2013Aug 04 2015We prove a formula for the global gravitational anomaly of the self-dual field theory in the presence of background gauge fields, assuming the results of arXiv:1110.4639. Along the way, we also clarify various points about the self-dual field theory. ... More

Randomness Conservation over AlgorithmsJul 11 2013Oct 14 2013Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation inequalities. ... More

Presenting Finite PosetsMay 27 2015We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of generators and relations, ... More

On Contact Numbers of Finite Lattice Sphere Packings and the Maximal Coordination of Monatomic CrystalsFeb 06 2016We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in $\mathbb{R}^d$ and show that in $\mathbb{R}^3$ this problem is equivalent to determining the maximal coordination of a monatomic crystal. ... More

Some Notes on Temporal Justification LogicOct 25 2015Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal ... More

Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular casesAug 20 2014Jan 16 2015The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The eigenvalues and ... More

Higher abelian Dijkgraaf-Witten theoryFeb 16 2015Jul 06 2016Dijkgraaf-Witten theories are quantum field theories based on (form degree 1) gauge fields valued in finite groups. We describe their generalization based on $p$-form gauge fields valued in finite abelian groups, as field theories extended to codimension ... More

General Linear and Symplectic Nilpotent Orbit VarietiesMar 12 2014The condition of nilpotency is studied in the general linear Lie algebra $\mathfrak{gl}_{n}(\mathbb{K})$ and the symplectic Lie algebra $\mathfrak{sp}_{2m}(\mathbb{K})$ over an algebraically closed field of characteristic 0. In particular, the conjugacy ... More

A gluing theorem for negatively curved complexesOct 09 2015Jul 09 2016A simplicial complex is called negatively curved if all its simplices are isometric to simplices in hyperbolic space, and it satisfies Gromov's Link Condition. We prove that, subject to certain conditions, a compact graph of spaces whose vertex spaces ... More

A Small Model for the Cohomology of Some Principal BundlesSep 25 2013Let G be a compact, connected and simply connected Lie group, and {\Omega}G the space of the loops in G based at the identity. This note shows a way to compute the cohomology of the total space of a principal {\Omega}G-bundle over a manifold M, from the ... More

Some criteria for the symmetry of stratified water wavesMar 05 2009This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This is done by first ... More

Convergence of the Yang-Mills-Higgs flow on gauged holomorphic maps and applicationsOct 07 2016Jan 10 2018The symplectic vortex equations admit a variational description as global minimum of the Yang-Mills-Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$ over a closed ... More

Graphes, moyennabilité et bas du spectre de variétés topologiquement infiniesJan 14 2010From a graph $G$ with constant valency $v$ and a (non-compact) manifold $C$ with $v$ boundary components, we build a $G$-periodic manifold $M$. This process gives a class of topologically infinite manifolds which generalizes periodic manifolds and includes ... More

Generic metrics, eigenfunctions and riemannian coverings of non compact manifoldsJan 14 2010Let $(M,g)$ be a non-compact riemannian $n$-manifold with bounded geometry at order $k\geq\frac{n}{2}$. We show that if the spectrum of the Laplacian starts with $q+1$ discrete eigenvalues isolated from the essential spectrum, and if the metric is generic ... More

On Arrangements of Six, Seven, and Eight Spheres: Maximal Bonding of Monatomic Ionic CompoundsMar 27 2016Let $C(n)$ be the solution to the contact number problem, i.e., the maximum number of touching pairs among any packing of $n$ congruent spheres in $\mathbb{R}^3$. We prove the long conjectured values of $C(6)=12, C(7)=15$, and $C(8)=18$. The proof strategy ... More

Memory-Centred Cognitive Architectures for Robots Interacting Socially with HumansFeb 18 2016The Memory-Centred Cognition perspective places an active association substrate at the heart of cognition, rather than as a passive adjunct. Consequently, it places prediction and priming on the basis of prior experience to be inherent and fundamental ... More

Conditionally Positive Functions and p-norm Distance MatricesJun 12 2010In Micchelli's paper "Interpolation of scattered data: distance matrices and conditionally positive functions", deep results were obtained concerning the invertibility of matrices arising from radial basis function interpolation. In particular, the Euclidean ... More

A Model of Inductive Bias LearningJun 01 2011A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonably-sized ... More

Lazy Transformation-Based LearningJun 03 1998We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all possible rules, ... More

Noncommutativity inspired Black Holes as Dark Matter CandidateApr 17 2015May 30 2016We study a black hole with a blurred mass density instead of a singular one, which could be caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses new properties, which become ... More

The degree of the Jacobian locus and the Schottky problemFeb 29 2004We show that the degree of the images of the moduli space of (principally polarized) abelian varieties A_g and of the moduli space of curves M_g in the projective space under the theta constant embedding are equal to the top self-intersection numbers ... More

Geometry of A_g and Its CompactificationsNov 01 2007Sep 02 2010In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed include: compactifications; ... More

Explicit upper bound for the Weil-Petersson volumesMar 30 2000Jun 20 2001An explicit upper bound for the Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces is obtained, using Penner's combinatorial integration scheme with embedded trivalent graphs. It is shown that for a fixed number of punctures n and ... More

Measuring the primordial power spectrum: Principal component analysis of the cosmic microwave backgroundJun 16 2005Sep 19 2006We implement and investigate a method for measuring departures from scale-invariance, both scale-dependent as well as scale-free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C_l data and a principal ... More

A Cantor-Bendixson-like process which detects Delta_2^0Jun 13 2011Jan 23 2012For each subset of Baire space, we define, in away similar to a common proof of the Cantor-Bendixson Theorem, a sequence of decreasing subsets S_alpha of N^N, indexed by ordinals. We use this to obtain two new characterizations of the boldface Delta_2^0 ... More

The First-Order Syntax of Variadic FunctionsMay 20 2011Jan 23 2012We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

Automatic Determination of Chord RootsJan 11 2016Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and detect nonharmonic ... More

Noncommutativity inspired Black Holes as Dark Matter CandidateApr 17 2015Oct 25 2016We study a black hole with a blurred mass density instead of a singular one, which could be caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses new properties, which become ... More

Analysing Survey Propagation Guided Decimation on Random FormulasFeb 22 2016Let $\varPhi$ be a uniformly distributed random $k$-SAT formula with $n$ variables and $m$ clauses. For clauses/variables ratio $m/n \leq r_{k\text{-SAT}} \sim 2^k\ln2$ the formula $\varPhi$ is satisfiable with high probability. However, no efficient ... More

Guessing, Mind-changing, and the Second Ambiguous ClassJan 09 2014In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable iff it is in the second ambiguous class (boldface Delta^0_2), iff it is eventually annihilated ... More

Multi-agent flocking under topological interactionsNov 23 2013In this paper, we consider a multi-agent system consisting of mobile agents with second-order dynamics. The communication network is determined by the so-called topological interaction rule: agents interact with a fixed number of their closest neighbors. ... More

Sub-Compton quantum non-equilibrium and Majorana systemsJun 05 2013We study the Majorana equation from the point of view of the de Broglie-Bohm pilot-wave theory (according to which a quantum ensemble of fermions is not only described by a spinor but also by a distribution of position configurations). Although the Majorana ... More

Accelerating Implicit Finite Difference Schemes Using a Hardware Optimized Tridiagonal Solver for FPGAsFeb 20 2014Oct 14 2015We present a design and implementation of the Thomas algorithm optimized for hardware acceleration on an FPGA, the Thomas Core. The hardware-based algorithm combined with the custom data flow and low level parallelism available in an FPGA reduces the ... More

Explicit absolute parallelism for $2$-nondegenerate real hypersurfaces $M^5 \subset \mathbb{C}^3$ of constant Levi rank $1$Dec 22 2013May 05 2014We study the local equivalence problem for five dimensional real hypersurfaces $M^5$ of $\mathbb{C}^3$ which are $2$-nondegenerate and of constant Levi rank $1$ under biholomorphisms. We find two invariants, $J$ and $W$, which are expressed explicitly ... More

On Non-Standard Models of Peano Arithmetic and Tennenbaum's TheoremNov 25 2013Throughout the course of mathematical history, generalizations of previously understood concepts and structures have led to the fruitful development of the hierarchy of number systems, non-euclidean geometry, and many other epochal phases in mathematical ... More

CP Violation and Mixing in Multi-body $D$ decaysNov 19 2013We present recent LHCb results and future prospects for CP violation and mixing measurements in multi-body charm decays. The complex amplitude structure of multi-body decays provides unique sensitivity to CP violation localised in certain phase space ... More

Quantifying the Ease of Scientific DiscoveryDec 08 2009May 14 2010It has long been known that scientific output proceeds on an exponential increase, or more properly, a logistic growth curve. The interplay between effort and discovery is clear, and the nature of the functional form has been thought to be due to many ... More

Stratified Steady Periodic Water WavesJul 03 2008Feb 11 2009This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic and traveling. ... More

Curvature Free Rigidity for Higher Rank Three-ManifoldsAug 16 2016We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank ... More

f-Vectors of Triangulated BallsDec 10 2009We describe two methods for showing that a vector can not be the f-vector of a homology d-ball. As a consequence, we disprove a conjectured characterization of the f-vectors of balls of dimension five and higher due to Billera and Lee. We also provide ... More

Unimodality of Partitions in Near-Rectangular Ferrers DiagramsAug 18 2014May 20 2015We look at the rank generating function $G_\lambda$ of partitions inside the Ferrers diagram of some partition $\lambda$, investigated by Stanton in 1990, as well as a closely related problem investigated by Stanley and Zanello in 2013. We show that $G_\lambda$ ... More

Automorphismes naturels de l'espace de Douady de points sur une surfaceMay 27 2009We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their action on the ... More

A survey of the GIT picture for the Yang-Mills equation over Riemann surfacesNov 25 2015Dec 11 2015The purpose of this paper is to give a self-contained exposition of the Atiyah-Bott picture for the Yang-Mills equation over Riemann surfaces with an emphasis on the analogy to finite dimensional geometric invariant theory. The main motivation is to provide ... More

The global anomalies of (2,0) superconformal field theories in six dimensionsJun 17 2014Sep 02 2014We compute the global gauge and gravitational anomalies of the A-type (2,0) superconformal quantum field theories in six dimensions, and conjecture a formula valid for the D- and E-type theories. We show that the anomaly contains terms that do not contribute ... More

Ramsey expansions of $Λ$-ultrametric spacesOct 03 2017For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces are a convenient language for describing structures equipped with a family of equivalence relations. When $\Lambda$ is finite and distributive, there exists a generic $\Lambda$-ultrametric space, ... More

Infinite Limits of Finite-Dimensional Permutation Structures, and their Automorphism Groups: Between Model Theory and CombinatoricsMay 11 2018In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is concerned with ... More

The anomaly field theories of six-dimensional (2,0) superconformal theoriesJun 06 2017Jun 16 2017We construct 7-dimensional quantum field theories encoding the anomalies of conformal field theories with (2,0) supersymmetry in six dimensions. We explain how the conformal blocks of the (2,0) theories arise in this context. A result of independent interest ... More

Multidimensional Inverse Scattering of Integrable Lattice EquationsJan 23 2012Mar 21 2012We present a discrete inverse scattering transform for all ABS equations excluding Q4. The nonlinear partial difference equations presented in the ABS hierarchy represent a comprehensive class of scalar affine-linear lattice equations which possess the ... More

Veech surfaces associated with rational billiardsMay 23 2002A nice trick for studying the billiard flow in a rational polygon is to unfold the polygon along the trajectories. This gives rise to a translation or half-translation surface tiled by the original polygon, or equivalently an Abelian or quadratic differential. ... More