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vh@nnlo-v2: New physics in Higgs StrahlungFeb 13 2018Introducing version 2 of the code vh@nnlo, we study the effects of a number of new-physics scenarios on the Higgs-Strahlung process. In particular, the cross section is evaluated within a general 2HDM and the MSSM. While the Drell-Yan-like contributions ... More

On the integral kernels of derivatives of the Ornstein-Uhlenbeck semigroupSep 18 2015This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein-Uhlenbeck semigroup $e^{tL}$. Our approach is to expand the Mehler kernel into Hermite polynomials and applying the powers $L^N$ of the ... More

Resolving multi-proxy transitive vote delegationDec 11 2014Solving a delegation graph for transitive votes is already a non-trivial task for many programmers. When extending the current main paradigm, where each voter can only appoint a single transitive delegation, to a system where each vote can be separated ... More

Harmonic morphisms and eigenfamilies on the exceptional Lie group G2Aug 31 2013We construct harmonic morphisms on the compact simple Lie group G2. The construction uses eigenfamilies in a representation theoretic scheme.

Jahn-Teller systems from a cavity QED perspectiveApr 28 2008Sep 23 2008Jahn-Teller systems and the Jahn-Teller effect are discussed in terms of cavity QED models. By expressing the field modes in a quadrature representation, it is shown that certain setups of a two-level system interacting with a bimodal cavity is described ... More

The Ground AxiomSep 02 2006A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set-forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class-forcing extension which satisfies it. The ... More

Diode for Bose-Einstein condensatesMay 13 2011Nov 18 2011Given a quantum state at some instant of time t, the underlying system Hamiltonian can not only predict how the state will evolve, but also the history of the state prior to t. Thereby, in order to have a directed motion, like in a diode, some sort of ... More

Non-leptonic D0, D+, and Ds Branching FractionsFeb 15 2010Non-leptonic charm decays provide insights into both electro-weak and strong dynamics. This includes the study of long-distance hadronic effects, the approximate symmetries of strong interactions, and precision tests of the Standard Model. In these proceedings ... More

Electromagnetics from a quasistatic perspectiveJun 13 2006Quasistatics is introduced so that it fits smoothly into the standard textbook presentation of electrodynamics. The usual path from statics to general electrodynamics is rather short and surprisingly simple. A closer look reveals however that it is not ... More

From geometry to geology: An invitation to mathematical pluralism through the phenomenon of independenceSep 01 2016This paper explores how a pluralist view can arise in a natural way out of the day-to-day practice of modern set theory. By contrast, the widely accepted orthodox view is that there is an ultimate universe of sets $V$, and it is in this universe that ... More

Expected length of a product of random reflectionsNov 24 2010We present a simple formula for the expected number of inversions in a permutation of size $n$ obtained by applying $t$ random (not necessarily adjacent) transpositions to the identity permutation. More general, for any finite irreducible Coxeter group ... More

On the use of shot noise for photon countingJan 14 2015Feb 24 2015Lieu et al. (2015) have recently claimed that it is possible to substantially improve the sensitivity of radio astronomical observations. In essence, their proposal is to make use of the intensity of the photon shot noise as a measure of the photon arrival ... More

Efficient ray tracing on 3D regular grids for fast generation of digitally reconstructed radiographs in iterative tomographic reconstruction techniquesSep 04 2016Cone beam projection is an essential and particularly time consuming part of any iterative tomographic reconstruction algorithm. On current graphics hardware especially the amount and pattern of memory accesses is a limiting factor when read-only textures ... More

Cylindrical lattice paths and the Loehr-Warrington 10^n conjectureSep 22 2005Sep 30 2005The following special case of a conjecture by Loehr and Warrington was proved recently by Ekhad, Vatter, and Zeilberger: There are 10^n zero-sum words of length 5n in the alphabet {+3,-2} such that no zero-sum consecutive subword that starts with +3 may ... More

On the sign-imbalance of skew partition shapesJul 16 2005Sep 18 2006Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan ... More

Partial Hölder continuity for Q-valued energy minimizing mapsFeb 11 2014We consider multivalued maps between $\Omega \subset \mathbb{R}^N$ open ($N \ge 2$) and a smooth, compact Riemannian manifold $\mathcal{N}$ locally minimizing the Dirichlet energy. An interior partial H\"older regularity result in the spirit of R. Schoen ... More

Computing partial transposes and related entanglement functionsSep 01 2016Nov 07 2016The partial transpose (PT) is an important function for entanglement testing and quantification and also for the study of geometrical aspects of the quantum state space. In this article, considering general bipartite and multipartite discrete systems, ... More

Fortran code for generating random probability vectors, unitaries, and quantum statesDec 16 2015Mar 14 2016The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards ... More

Classification of certain cellular classes of chain complexesJan 25 2008Let (R, m) be a local commutative ring. Suppose that m is principal and that m^2 = 0. We give a complete description of the cellular lattice of perfect chain complexes of modules over this ring.

Bi-Lipschitz parts of quasisymmetric mappingsAug 02 2013Feb 27 2015A natural quantity that measures how well a map $f:\mathbb{R}^{d}\rightarrow \mathbb{R}^{D}$ is approximated by an affine transformation is \[\omega_{f}(x,r)=\inf_{A}\left(\frac{1}{|B(x,r)|}\int_{B(x,r)}\left(\frac{|f-A|}{|A'|r}\right)^{2}\right)^{\frac{1}{2}},\] ... More

Cohomology of moduli spaces of curves of genus three via point countsNov 27 2006Jun 05 2007In this article we consider the moduli space of smooth $n$-pointed non-hyperelliptic curves of genus 3. In the pursuit of cohomological information about this space, we make $\mathbb{S}_n$-equivariant counts of its numbers of points defined over finite ... More

Anomalous decoherence and absence of thermalization in a photonic many-body systemMar 04 2011The intention of this work is twofold, first to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons, and second to study various outcomes deriving from inherent or external decoherence. A qubit induces ... More

Convergence of nodal sets in the adiabatic limitMay 08 2014Nov 09 2014We study the nodal sets of non-degenerate eigenfunctions of the Laplacian on fibre bundles $\pi{:}\, M\to B$ in the adiabatic limit. This limit consists in considering a family $G_\varepsilon$ of Riemannian metrics, that are close to Riemannian submersions, ... More

Travelling to exotic places with cavity QED systemsAug 12 2009Recent theoretical schemes for utilizing cavity QED models as quantum simulators are reviewed. By considering a quadrature representation for the fields, it is shown how Jahn-Teller models, effective Abelian or non-Abelian gauge potentials, transverse ... More

Analog of the spin-orbit induced anomalous Hall effect with quantized radiationMay 18 2009May 27 2010We demonstrate how the term describing interaction between a single two-level atom and two cavity field modes may attain a Rashba form. As an outcome, cavity QED provides a testbed for studies of phenomena reminiscent of the spin-orbit induced anomalous ... More

On the rotating wave approximation in the adiabatic limitAug 09 2012I revisit a longstanding question in quantum optics; When is the rotating wave approximation justified? In terms of the Jaynes-Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system ... More

An Exact Formula to Describe the Amplification Process in a Photomultiplier TubeJun 08 2004An analytical function is derived that exactly describes the amplification process due to a series of discrete, Poisson-like amplifications like those in a photo multiplier tube (PMT). A numerical recipe is provided that implements this function as a ... More

B Physics at CDFJun 07 2004Due to the large b-bbar cross section at 1.96 TeV p-pbar collisions, the Tevatron is currently the most copious source of B hadrons. Recent detector upgrades for Run II have made these more accessible, allowing for a wide range of B and CP violation physics ... More

The Complexity of Simple Stochastic GamesApr 20 2007In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.

Graded Betti numbers and $h$-vectors of level modulesDec 04 2006Dec 04 2006We study $h$-vectors and graded Betti numbers of level modules up to multiplication by a rational number. Assuming a conjecture on the possible graded Betti numbers of Cohen-Macaulay modules we get a description of the possible $h$-vectors of level modules ... More

The Ground Axiom (GA)Sep 10 2006Feb 21 2007A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class forcing extension which satisfies it. The ... More

Gaussian fluctuations of eigenvalues in the GUEJan 08 2004Apr 04 2007Under certain conditions on k we calculate the limit distribution of the k:th largest eigenvalue, x_k, of the Gaussian Unitary Ensemble (GUE). More specifically, if n is the dimension of a random matrix from the GUE and k is such that both k and n-k tends ... More

Improper poisson line process as sirsn in any dimensionMar 13 2015Sep 29 2016Aldous has introduced a notion of scale-invariant random spatial network (SIRSN) as a mathematical formalization of road networks. Intuitively, those are random processes that assign a route between each pair of points in Euclidean space, while being ... More

Model selection for quantum homodyne tomographyDec 18 2007This paper deals with a non-parametric problem coming from physics, namely quantum tomography. That consists in determining the quantum state of a mode of light through a homodyne measurement. We apply several model selection procedures: penalized projection ... More

Random Sampling of Quantum States: A Survey of MethodsFeb 12 2015Oct 30 2015The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating ... More

Properties of cellular classes of chain complexesFeb 01 2008Mar 19 2008In this paper we prove certain properties of cellular and acyclic classes of chain complexes of modules over a commutative Noetherian ring. In particular we show that if X is finite and belongs to some cellular class C then \Sigma^n H_X also belongs to ... More

Pluricomplex charge at weak singularitiesOct 31 2005Let $u$ be a plurisubharmonic function, defined on a neighbourhood of a point $x,$ such that the complex Monge-Amp\`ere operator is well-defined on $u.$ Suppose also that $u$ has a weak singularity, in the sense that the Lelong number of $u$ at $x$ vanish. ... More

Equivariant counts of points of the moduli spaces of pointed hyperelliptic curvesNov 27 2006Nov 30 2011We consider the moduli space $\Hh_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$. In order to get cohomological information we wish to make $\s_n$-equivariant counts of the numbers of points defined over finite fields of this moduli space. ... More

How many T-tessellations on $k$ lines? Existence of associated Gibbs measures on bounded convex domainsDec 10 2010Apr 23 2014The paper bounds the number of tessellations with T-shaped vertices on a fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms retrieve them, proving injectivity. This yields existence of a completely random T-tessellation, as ... More

A new method for constructing Anosov Lie algebrasDec 10 2013Jan 12 2015It is conjectured that every manifold admitting an Anosov diffeomorphism is, up to homeomorphism, finitely covered by a nilmanifold. Motivated by this conjecture, an important problem is to determine which nilmanifolds admit an Anosov diffeomorphism. ... More

A note on the Gaussian maximal functionsNov 20 2013Jul 08 2014This note presents a proof that the non-tangential maximal function of the Ornstein-Uhlenbeck semigroup is bounded almost surely by the Gaussian Hardy-Littlewood maximal function. In particular this entails improvement on a result by Pineda and Urbina ... More

Multiple-time-scale Landau-Zener transitions in many-body systemsOct 29 2013Jan 27 2015Motivated by recent cold atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunnelling between neighboring lattice sites this onsite ... More

Interaction induced Landau-Zener transitionsMay 27 2014By considering a quantum critical Lipkin-Meshkov-Glick model we analyze a new type of Landau-Zener transitions where the population transfer is mediated by interaction rather than from a direct diabatic coupling. For this scenario, at a mean-field level ... More

Hausdorff dimension of wiggly metric spacesMar 29 2013Jan 27 2014For a compact connected set $X\subseteq \ell^{\infty}$, we define a quantity $\beta'(x,r)$ that measures how close $X$ may be approximated in a ball $B(x,r)$ by a geodesic curve. We then show there is $c>0$ so that if $\beta'(x,r)>\beta>0$ for all $x\in ... More

Realizability Toposes from SpecificationsApr 24 2015We investigate a framework of Krivine realizability with I/O effects, and present a method of associating realizability models to specifications on the I/O behavior of processes, by using adequate interpretations of the central concepts of `pole' and ... More

A fibrational study of realizability toposesMar 14 2014This is the author's PhD thesis. It is a contribution to categorical logic, in particular to the theory of realizability toposes. While the tools of categorical logic have proven very successful in analyzing and organizing proof theoretic realizability ... More

Complete classification of 2-ramified power seriesJan 14 2016Mar 21 2016In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding lower ramification ... More

Clean positive operator valued measures for qubits and similar casesMar 14 2006Mar 22 2007In a recent paper, Buscemi and al. defined a notion of clean positive operator valued measures (POVMs). We here characterize which POVMs are clean in some class that we call quasi-qubit POVMs, namely POVMs whose elements are all rank-one or full-rank. ... More

Reduction of Statistical Power Per Event Due to Upper Lifetime Cuts in Lifetime MeasurementsFeb 25 2005Feb 09 2007A cut on the maximum lifetime in a lifetime fit not only reduces the number of events, but also, in some circumstances dramatically, decreases the statistical significance of each event. The upper impact parameter cut in the hadronic B trigger at CDF, ... More

Local Gaussian fluctuations in the Airy and discrete PNG processesJan 30 2007Apr 04 2007We prove that the Airy process, A(t), locally fluctuates like a Brownian motion. In the same spirit we also show that in a certain scaling limit, the so called discrete polynuclear growth (PNG) process behaves like a Brownian motion.

The cover pebbling theoremOct 06 2004For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a cover pebbling ... More

Boundary regularity of Dirichlet minimizing Q-valued functionsFeb 11 2014We consider the H\"older continuity for the Dirichlet problem at the boundary. Almgren introduced the multivalued; Q-valued functions for studying regularity of minimal surfaces in higher codimension. The H\"older continuity in the interior for Dirichlet ... More

Computing coherence vectors and correlation matrices, with application to quantum discord quantificationMar 16 2016Jun 30 2016Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a ... More

Non-monotonicity of trace distance under tensor productsMar 10 2015Aug 21 2015The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible ... More

The Kraus representation for the dynamics of open quantum systemsOct 30 2015May 11 2016The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a general and ... More

Gradings on Lie algebras with applications to infra-nilmanifoldsOct 14 2014Mar 03 2016In this paper, we study positive as well as non-negative and non-trivial gradings on finite dimensional Lie algebras. We give a different proof that the existence of such a grading on a Lie algebra is invariant under taking field extensions, a result ... More

Sets of absolute continuity for harmonic measure in NTA domainsOct 10 2014Mar 08 2016We show that if $\Omega$ is an NTA domain with harmonic measure $w$ and $E\subseteq \partial\Omega$ is contained in an Ahlfors regular set, then $w|_{E}\ll \mathscr{H}^{d}|_{E}$. Moreover, this holds quantitatively in the sense that for all $\tau>0$ $w$ ... More

On the Intersection Property of Conditional Independence and its Application to Causal DiscoveryMar 03 2014Mar 04 2014This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent of $(A,B)$ ... More

A chord-arc covering theorem in Hilbert spaceMay 27 2009Jun 21 2011We prove that there exists $M>0$ such that for any closed rectifiable curve $\Gamma$ in Hilbert space, almost every point in $\Gamma$ is contained in a countable union of $M$ chord-arc curves whose total length is no more than $M$ times the length of ... More

Quantum fluctuations in the mazerAug 01 2008Feb 05 2009Quantum fluctuations in the mazer are considered, arising either from the atomic motion or from the quantized intracavity field. Analytical results, for both the meza and the hyperbolic secant mode profile, predict for example an attenuation of tunneling ... More

Dynamics of the Jayne-Cummings and Rabi models: old wine in new bottlesDec 12 2006Jun 23 2007By using a wave packet approach, this paper reviews the Jaynes-Cummings model with and without the rotating wave approximation in a non-standard way. This gives new insight, not only of the two models themselves, but of the rotating wave approximation ... More

Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QEDJul 18 2011Jan 23 2012We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a non-trivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results ... More

Monte Carlo Simulations of Higgs-Fermion SystemsApr 08 1992To gain understanding of the Higgs-fermion sector of the standard model, we study the one-component $Z_2$ symmetric and the four-component O(4) symmetric scalar models coupled to staggered fermions using the hybrid Monte Carlo algorithm. We map out the ... More

Integrability vs Quantum ThermalizationApr 12 2013Nov 12 2013Non-integrability is often taken as a prerequisite for quantum thermalization. Still, a generally accepted definition of quantum integrability is lacking. With the basis in the driven Rabi model we discuss this careless usage of the term "integrability" ... More

Periodic and eventually periodic points of affine infra-nilmanifold endomorphismsJun 08 2015In this paper, we study the periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. On the one hand, we give a sufficient condition for a point of the infra-nilmanifold to be (eventually) periodic. In this way we show that if ... More

Analytic Performance Model of a Main-Memory Index StructureSep 05 2016Efficient evaluation of multi-dimensional range queries in a main-memory database is an important, but difficult task. State-of-the-art techniques rely on optimised sequential scans or tree-based structures. For range queries with small result sets, sequential ... More

Monge-Ampère measure at the boundary of some domains with cornersApr 03 2006Let $\mu^z$ be the measure obtained by sweeping out the Monge-Amp\`ere measure of the pluricomplex Green function with pole at $z. $ We prove that $\mu^z$ vanish on Levi flat parts of the boundary for 1) every relatively compact analytic polyhedron in ... More

Mean-field quantum dynamics with magnetic fieldsFeb 06 2012Jul 15 2012We consider a system of $N$ bosons in three dimensions interacting through a mean-field Coulomb potential in an external magnetic field. For initially factorized states we show that the one-particle density matrix associated with the solution of the $N$-body ... More

On snarks that are far from being 3-edge colorableMar 09 2012In this note we construct two infinite snark families which have high oddness and low circumference compared to the number of vertices. Using this construction, we also give a counterexample to a suggested strengthening of Fulkerson's conjecture by showing ... More

On the relationship between the Collatz conjecture and Mersenne prime numbersAug 01 2016Aug 08 2016The purpose of this study is to show how to get a necessary criterion for prime numbers with the help of special matrices. My special interest lies in the empirical research of these matrices and their patterns, structures and symmetries. The matrices ... More

Signs of dependence and heavy tails in non-life insurance dataJan 05 2015In this paper we study data from the yearly reports the four major Swedish non-life insurers have sent to the Swedish Financial Supervisory Authority (FSA). We aim at finding marginal distributions of, and dependence between, losses on the five largest ... More

Characterization of 2-ramified power seriesJan 14 2016Nov 27 2016In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding lower ramification ... More

A 2-Categorical Analysis of the Tripos-to-Topos ConstructionApr 14 2011We characterize the tripos-to-topos construction of Hyland, Johnstone and Pitts as a biadjunction in a bicategory enriched category of equipment-like structures. These abstract concepts are necessary to handle the presence of oplax constructs --- the ... More

Examples of holomorphic functions vanishing to infinite order at the boundarySep 12 2015Oct 02 2015We present examples of holomorphic functions that vanish to in- finite order at points at the boundary of their domain of definition. They give rise to examples of Dirichlet minimizing Q-valued functions indicating that "higher"-regularity boundary results ... More

Local Grand Unification in the Heterotic LandscapeJun 30 2009Sep 03 2009We consider the possibility that the unification of the electroweak interactions and the strong force arises from string theory, at energies significantly lower than the string scale. As a tool, an effective grand unified field theory in six dimensions ... More

Gauge-Higgs Unification from the Heterotic StringAug 31 2007We present a 6D orbifold model on $T^2/\Z2$ which emerges as intermediate step in the compactification of the heterotic string to the supersymmetric standard model in four dimensions. It has $\SU6$ gauge symmetry in the bulk and two pairs of inequivalent ... More

Understanding von Neumann's entropyFeb 16 2015Jun 03 2015We review the postulates of quantum mechanics that are needed to discuss the von Neumann's entropy. We introduce it as a generalization of Shannon's entropy and propose a simple game that makes easier understanding its physical meaning.

Distribution of Mutual Information in Multipartite StatesAug 21 2013Feb 13 2014Using the relative entropy of total correlation, we derive an expression relating the mutual information of $n$-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by ... More

Computing partial transposes and related entanglement functionsSep 01 2016The partial transpose (PT) is an important function for entanglement testing and quantification and also for the study of geometrical aspects of the quantum state space. In this article, considering general bipartite and multipartite discrete systems, ... More

Measuring CP violation in 3- and 4-body decaysDec 17 2013Multibody charm decays have a rich phenomenology and potentially unique sensitivity to CP violation. In these proceedings we discuss recent results, challenges and prospects in searches for CP violation in three and four body charm decays.

Wave packet methods in cavity QEDNov 15 2007The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled harmonic oscillators, ... More

Fast rate estimation of an unitary operation in SU(d)Mar 13 2006Feb 05 2007We give an explicit procedure based on entangled input states for estimating a $SU(d)$ operation $U$ with rate of convergence $1/N^2$ when sending $N$ particles through the device. We prove that this rate is optimal. We also evaluate the constant $C$ ... More

Circuit QED scheme for realization of the Lipkin-Meshkov-Glick modelApr 28 2010Jun 17 2010We propose a scheme in which the Lipkin-Meshkov-Glick model is realized within a circuit QED system. An array of N superconducting qubits interacts with a driven cavity mode. In the dispersive regime, the cavity mode is adiabatically eliminated generating ... More

Scheme for generating entangled states of two field modes in a cavityAug 11 2005Apr 15 2006This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes-Cummings model. For some particular field states, coherent and squeezed ... More

Heavy Flavour Lifetimes and Lifetime DifferencesJun 26 2003Oct 28 2003We give an overview of heavy flavour lifetime measurements, focusing on recent results from the Tevatron and the B factories.

A note on reduced and von Neumann algebraic free wreath productsNov 18 2014In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix quantum group. Based on recent result on their corepresentation ... More

Curvature conditions for complex-valued harmonic morphismsFeb 20 2014Oct 31 2014We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental ... More

Tangents, rectifiability, and corkscrew domainsMay 15 2015Dec 27 2015In a recent paper, Cs\"ornyei and Wilson prove that curves in Euclidean space of $\sigma$-finite length have tangents on a set of positive $\mathscr{H}^{1}$-measure. They also show that a higher dimensional analogue of this result is not possible without ... More

A Characterization of Realizability ToposesApr 28 2014Realizability toposes over partial combinatory algebras (PCAs) were introduced in 1980 by Hyland, Johnstone, and Pitts, and they are important in categorical logic as models of non-classical logics and type systems. Except for the trivial case of $\mathbf{Set}$, ... More

Strings as sigma models and in the tensionless limitMay 16 2007This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models. The tensionless limit is used to find a IIB supergravity background generated by a tensionless string. Quantization of the ... More

T-duality and Generalized Complex GeometryDec 05 2006Mar 26 2007We find the explicit T-duality transformation in the phase space formulation of the N=(1,1) sigma model. We also show that the T-duality transformation is a symplectomorphism and it is an element of O(d,d). Further, we find the explicit T-duality transformation ... More

On the sign-imbalance of partition shapesSep 15 2003Sep 30 2005Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2^[n/2]. We present ... More

A complete description of the antipodal set of most symmetric spaces of compact typeMar 29 2016It is known that the antipodal set of a Riemannian symmetric space of compact type $G/ K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we ... More

Generating pseudo-random discrete probability distributionsFeb 07 2015Jul 01 2015The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in quantum information ... More

Computing partial traces and reduced density matricesJan 27 2016Aug 23 2016Taking partial traces for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this article, we present a thorough description of this function and analyze the number of ... More

On the integral kernels of derivatives of the Ornstein-Uhlenbeck semigroupSep 18 2015Nov 18 2016This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein-Uhlenbeck semigroup $e^{tL}$. Our approach is to expand the Mehler kernel into Hermite polynomials and applying the powers $L^N$ of the ... More

Multi-loop amplitudes in maximally supersymmetric pure spinor field theorySep 29 2010This paper provides a more detailed background to the results of arXiv:1004.2692 concerning properties of multi-loop amplitudes in a pure spinor formulation of field theories with maximal supersymmetry. This involves the development of a first quantised ... More

On the holonomy groups of Weyl manifoldsOct 15 2014Jun 12 2015We classify the possible local holonomy groups of Weyl connections. The Berger-Simons theorem and the Merkulov-Schwachh\"ofer classification of holonomy groups of irreducible torsion-free connections leaves us with the remaining case, where the Weyl connection ... More

Bruhat intervals as rooks on skew Ferrers boardsJan 25 2006We characterise the permutations pi such that the elements in the closed lower Bruhat interval [id,pi] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations pi ... More

On Newman and Littlewood multiples of Borwein polynomialsSep 23 2016A Newman polynomial has all the coefficients in $\{ 0,1\}$ and constant term 1, whereas a Littlewood polynomial has all coefficients in $\{-1,1\}$. We call $P(X)\in\mathbb{Z}[X]$ a Borwein polynomial if all its coefficients belong to $\{ -1,0,1\}$ and ... More