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Graph-theoretic Simplification of Quantum Circuits with the ZX-calculusFeb 08 2019We present a new circuit-to-circuit optimisation routine based on an equational theory called the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, a flexible, lower-level language for describing quantum computations graphically. Then, ... More

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Four-Point Function on a Surface of Infinite GenusOct 26 1994Jul 30 1996The four-point function arising in the scattering of closed bosonic strings in their tachyonic ground state is evaluated on a surface of infinite genus. The amplitude has poles corresponding to physical intermediate states and divergences at the boundary ... More

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stochastic mean-field approach to fluid dynamicsNov 03 2017It is shown that the incompressible Navier-Stokes equation can be derived from an infinite dimensional mean-field stochastic differential equation.

Non-unital polygraphs form a presheaf categoriesNov 02 2017We prove, as claimed by A.Carboni and P.T.Johnstone, that the category of non-unital polygraphs, i.e. polygraphs where the source and target of each generator are not identity arrows, is a presheaf category. More generally we develop a new criterion for ... More

Sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones, and convex domainsOct 23 2017We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, aswell as a weighted sharp trace Sobolev inequality on epigraphs of convex functions. This is done by using a generalized Borell-Brascamp-Lieb inequality, coming from the ... More

The Role of Spreadsheets in Clinical Decision Support: A Survey of the Medical Algorithms Company User CommunityJan 23 2018This paper presents and discusses the results of a small scoping survey of Clinical Decision Support System (CDSS) users from the Medical Algorithms Company website which hosts 24,000 different CDSS. These results are analysed, discussed, and compared ... More

The magnitude of odd balls via Hankel determinants of reverse Bessel polynomialsAug 10 2017Magnitude is an invariant of metric spaces with origins in enriched category theory. Using potential theoretic methods, Barcel\'o and Carbery gave an algorithm for calculating the magnitude of any odd dimensional ball in Euclidean space, and they proved ... More

Origin Gaps and the Eternal Sunshine of the Second-Order PendulumDec 08 2017The rich experiences of an intentional, goal-oriented life emerge, in an unpredictable fashion, from the basic laws of physics. Here I argue that this unpredictability is no mirage: there are true gaps between life and non-life, mind and mindlessness, ... More

Orthogonal polynomials with exponentially decaying recursion coefficientsMar 03 2006We review recent results on necessary and sufficient conditions for measures on $\mathbb{R}$ and $\partial\mathbb{D}$ to yield exponential decay of the recursion coefficients of the corresponding orthogonal polynomials. We include results on the relation ... More

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

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

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

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

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

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

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

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

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

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

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

$L^p$ norms of higher rank eigenfunctions and bounds for spherical functionsJun 02 2011Jun 21 2016We prove almost sharp upper bounds for the $L^p$ norms of eigenfunctions of the full ring of invariant differential operators on a compact locally symmetric space, as well as their restrictions to maximal flat subspaces. Our proof combines techniques ... More

Superintegrability, isochronicity, and quantum harmonic behaviorOct 03 2003We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of the separated ... More

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

The Hijazi inequality on manifolds with boundaryMar 21 2006In this paper, we prove the Hijazi inequality on compact Riemannian spin manifolds under two boundary conditions: the condition associated with a chirality operator and the Riemannian version of the $\MIT$ bag condition. We then show that the limiting-case ... More

Overlapping iterated function systems from the perspective of Metric Number TheoryJan 23 2019In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets, their Lebesgue ... More

Persistence Characterisation of teledyne H2RG detectorsJul 13 2018Image persistence is a major problem in infrared detectors, potentially seriously limiting data quality in many observational regimes. The problem manifests itself as remnant images that can persist for several days after a deep exposure. In this study, ... More

Technologies for Future Vertex and Tracking Detectors at CLICDec 06 2018CLIC is a proposed linear $e^{+}e^{-}$ collider with center-of-mass energies of up to $3\,\textrm{TeV}$. Its main objectives are precise top quark and Higgs boson measurements, as well as searches for Beyond Standard Model physics. To meet the physics ... More

Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genusOct 25 2018We present a probabilistic Las Vegas algorithm for computing the local zeta function of a genus-$g$ hyperelliptic curve defined over $\mathbb F_q$ with explicit real multiplication (RM) by an order $\Z[\eta]$ in a degree-$g$ totally real number field. ... More

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

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

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

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

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

On a spin conformal invariant on manifolds with boundarySep 25 2006On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator ... More

Endoscopy and cohomology of a quasi-split U(4)Aug 31 2014Sep 18 2016We prove asymptotic upper bounds for the $L^2$ Betti numbers of the locally symmetric spaces associated to a quasi-split $U(4)$. These manifolds are 8-dimensional, and we prove bounds in degrees 2 and 3, with the behaviour in the other degrees being well ... More

The Ding functional, Berndtsson convexity and moment mapsMar 17 2015We explain how the formal aspects of the theory of Kahler-Einstein metrics can be developed in the framework of moment maps. The central result we use is the Berndtsson convexity theorem, which is interpreted as defining a metric on the space of complex ... More

Stability of algebraic varieties and Kahler geometryFeb 19 2017This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.

Kahler-Einstein metrics and algebraic geometryFeb 19 2017Mar 08 2017This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.

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

On toposes generated by cardinal finite objectsMay 19 2015Apr 05 2016We give a characterizations of toposes which admit a generating family of objects which are internally cardinal finite (i.e. Kuratowski finite and decidable) in terms of "topological" conditions. The central result is that, constructively, a hyperconnected ... More

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

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

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

Ricci Flow of regions with curvature bounded below in dimension threeJul 04 2014May 29 2017We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has curvature bounded from below by -1, then we prove estimates which show that ... More

Conditions and evidence for non-integrability in the Friedmann-Robertson-Walker HamiltonianSep 11 2013Feb 10 2015This is an example of application of Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more specifically the result by Morales, Ramis and Sim\'o on higher-order variational equations, to the well-known Friedmann-Robertson-Walker cosmological ... More

Linear $L$-positive sets and their polar subspacesDec 01 2011Mar 18 2012In this paper, we define a Banach SNL space to be a Banach space with a certain kind of linear map from it into its dual, and we develop the theory of linear $L$-positive subsets of Banach SNL spaces with Banach SNL dual spaces. We use this theory to ... More

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

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

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

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

Incidence Results and Bounds of Trilinear and Quadrilinear Exponential SumsJul 26 2017Aug 31 2017We give a new bound on the number of collinear triples for two arbitrary subsets of a finite field. This improves on existing results which rely on the Cauchy inequality. We then us this to provide a new bound on trilinear and quadrilinear exponential ... More

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

Can quantum physics help solve the hard problem of consciousness? A hypothesis based on entangled spins and photonsSep 08 2018The hard problem of consciousness is the question how subjective experience arises from brain matter. I suggest exploring the possibility that quantum physics could be part of the answer. The simultaneous unity and complexity of subjective experience ... More

Towards a global quantum networkOct 31 2017The creation of a global quantum network is within reach combining satellite links and quantum memory based approaches. Applications will range from secure communication and fundamental physics experiments to a future quantum internet.

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

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

Triple Product L Functions and Quantum Chaos on SL(2,C)Jun 16 2010Aug 13 2010We extend the results of Watson, which link quantum unique ergodicity on arithmetic hyperbolic surfaces with subconvexity for the triple product L function, to the case of arithmetic hyperbolic three manifolds. We work with the full unitary dual of SL(2,C), ... More

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

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

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

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