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Suppression of nonlinear Zeeman effect and heading error in earth-field-range alkali-vapor magnetometersAug 17 2017The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear ... More

Tailorable Dispersion in a Four-Wave Mixing LaserMay 08 2017We present experimental results demonstrating controllable dispersion in a ring laser by monitoring the lasing-frequency response to cavity-length variations. Pumping on an N-type level configuration in ${}^{87}$Rb, we tailor the intra-cavity dispersion ... More

Remote sensing of geomagnetic fields and atomic collisions in the mesosphereFeb 09 2018Magnetic-field sensing has contributed to the formulation of the plate-tectonics theory, the discovery and mapping of underground structures on Earth, and the study of magnetism in other planets. Filling the gap between space-based and near-Earth observation, ... More

Variable Free Spectral Range Spherical Mirror Fabry-Perot InterferometerJun 18 2003A spherical Fabry-Perot interferometer with adjustable mirror spacing is used to produce interference fringes with frequency separation (c/2L)/N, N=2-15. The conditions for observation of these fringes are derived from the consideration of the eigenmodes ... More

Towards optimization of pulsed sodium laser guide starsOct 16 2015Pulsed sodium laser guide stars (LGS) are useful because they allow for Rayleigh blanking and fratricide avoidance in multiple-LGS systems. Bloch-equation simulations of sodium-light interactions show that these may be able to achieve photon returns nearly ... More

Controllable steep dispersion with gain in a four-level N-scheme with four-wave mixingMay 11 2012We present a theoretical analysis of the propagation of light pulses through a medium of four-level atoms, with two strong pump fields and a weak signal field in an N-scheme arrangement. We show that the generation of four-wave mixing has a profound effect ... More

Four-wave mixing in a ring cavityApr 17 2014We investigate a four-wave mixing process in an N interaction scheme in Rb vapor placed inside a low-finesse ring cavity. We observe strong amplification and generation of a probe signal, circulating in the cavity, in the presence of two strong optical ... More

Efficient polarization of high-angular-momentum systemsAug 31 2016We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw ... More

Magneto-Optical Cooling of AtomsSep 23 2013We propose an alternative method to laser cooling. Our approach utilizes the extreme brightness of a supersonic atomic beam, and the adiabatic atomic coilgun to slow atoms in the beam or to bring them to rest. We show how internal-state optical pumping ... More

Efficient polarization of high-angular-momentum systemsAug 31 2016Oct 21 2016We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw ... 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

A relation between electromagnetically induced absorption resonances and nonlinear magneto-optics in Lambda-systemsOct 15 2003Jun 03 2004Recent work on Lambda-resonances in alkali metal vapors (E. Mikhailov, I. Novikova, Yu. V. Rostovtsev, and G. R. Welch, quant-ph/0309171, and references therein) investigated a type of electromagnetically induced absorption resonance that occurs in three-level ... More

Nonlinear magneto-optical rotation in optically thick mediaFeb 28 2002Nonlinear magneto-optical rotation is a sensitive technique for measuring magnetic fields. Here, the shot-noise-limited magnetometric sensitivity is analyzed for the case of optically-thick media and high light power, which has been the subject of recent ... More

Book to the Future - a manifesto for book liberationJul 04 2015The Book Liberation Manifesto is an exploration of publishing outside of current corporate constraints and beyond the confines of book piracy. We believe that knowledge should be in free circulation to benefit humankind, which means an equitable and vibrant ... More

Particle Dark EnergyNov 11 2004Feb 23 2006We explore the physics of a gas of particles interacting with a condensate that spontaneously breaks Lorentz invariance. The equation of state of this gas varies from 1/3 to less than -1 and can lead to the observed cosmic acceleration. The particles ... More

Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More

Approximations of generating functions and a few conjecturesNov 25 2009This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of Integer Sequences ... More

Prediction of the Virgo axis anisotropy: CMB radiation illuminates the nature of thingsSep 25 2005Recent findings of the anisotropy in the Cosmic Microwave Background (CMB) radiation are confusing for standard cosmology. Remarkably, this fact has been predicted several years ago in the framework of our model of the physical world. Moreover, in exact ... More

Holomorphic horospherical duality "sphere-cone"Jan 02 2005We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.

Quantum entanglement analysis based on abstract interpretationJan 28 2008Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum ... More

Extending and Implementing the Stable Model SemanticsMay 08 2000An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of efficient implementation ... More

A Brezis-Browder theorem for SSDB spacesApr 24 2010Sep 26 2010In this paper, we show how the Brezis-Browder theorem for maximally monotone multifunctions with a linear graph on a reflexive Banach space, and a consequence of it due to Yao, can be generalized to SSDB spaces.

Banach SSD spaces and classes of monotone setsAug 04 2009Jul 05 2010In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D), type ... More

The Evolution of Ellipticals, Spirals and Irregulars: Overcoming Selection BiasDec 07 2000The Hubble Deep Fields represent our best opportunity for probing galaxy evolution over a substantive look-back time. However as with any dataset the HDFs are prone to selection biases. These biases are extremely severe beyond z \~1.25 such that a meaningful ... More

Spin Structures on Riemann Surfaces and the Perfect NumbersDec 28 1998Dec 23 1999The equality between the number of odd spin structures on a Riemann surface of genus g, with $2^g - 1$ being a Mersenne prime, and the even perfect numbers, is an indication that the action of the modular group on the set of spin structures has special ... More

Modular Invariance and the Finiteness of Superstring TheoryApr 01 1995Apr 03 1996The genus-dependence of multi-loop superstring amplitudes is bounded at large orders in perturbation theory using the super-Schottky group parametrization of supermoduli space. Partial estimates of supermoduli space integrals suggest an exponential dependence ... More

Configurations of Handles and the Classification of Divergences in the String Partition FunctionApr 13 1994Apr 22 1994The divergences that arise in the regularized partition function for closed bosonic string theory in flat space lead to three types of perturbation series expansions, distinguished by their genus dependence. This classification of infinities can be traced ... More

A metric theorem for restricted Diophantine approximation in positive characteristicJan 28 2004Oct 10 2005We calculate the measure and Hausdorff dimension of sets of matrices over fields of formal power series with good approximation properties for a restricted set of denominators.

Subspaces of almost Daugavet spacesJul 17 2010We study the almost Daugavet property, a generalization of the Daugavet property. It is analysed what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is: if $Z$ is ... More

A Rationality Condition for the Existence of Odd Perfect NumbersNov 24 2000A rationality condition is derived for the existence of odd perfect numbers involving the square root of a product, which consists of a sequence of repunits, multiplied by twice the base of one of the repunits. This constraint also provides an upper bound ... More

On the Closing Lemma problem for vector fields of bounded type on the torusNov 07 2008We investigate the open Closing Lemma problem for vector fields on the 2-dimensional torus. Under the assumption of bounded type rotation number, the $C^r$ Closing Lemma is verified for smooth vector fields that are area-preserving at all saddle points. ... More

Polar subspaces and automatic maximalityDec 11 2012Mar 28 2013This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and ... More

Space-Time and ProbabilityDec 14 2001Special relativity is most naturally formulated as a theory of space-time geometry, but within the space-time framework probability apears to be at best an epistemic notion - a matter of what can be known, not of the status of events in themselves. However, ... More

What is Probability?Dec 24 2004Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, ... More

Derivation of the Born Rule from Operational AssumptionsNov 21 2002Nov 21 2002The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to all the ... More

Prospects for Precision Higgs Physics at Linear CollidersNov 30 2012A linear e+e- collider provides excellent possibilities for precision measurements of the properties of the Higgs boson. At energies close to the Z-Higgs threshold, the Higgs boson can be studied in recoil against a Z boson, to obtain not only a precision ... More

Splitting the K-Terminal ReliabilityApr 18 2011Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is the probability that all vertices in K are mutually connected. In this article ... More

The sharp form of the strong Szego theoremFeb 06 2004Let $f$ be a function on the unit circle and $D_n(f)$ be the determinant of the $(n+1)\times (n+1)$ matrix with elements $\{c_{j-i}\}_{0\leq i,j\leq n}$ where $c_m =\hat f_m\equiv \int e^{-im\theta} f(\theta) \f{d\theta}{2\pi}$. The sharp form of the ... More

Sturm Oscillation and Comparison TheoremsNov 04 2003This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.

Simulating Dense MatterMar 19 2007I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I ... More

Lattice MatterSep 28 2001I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color ... More

The Phase Diagram of QCDMay 08 2001I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma ... More

Approximation properties of $β$-expansions IIJun 25 2015Given $\beta\in(1,2)$ and $x\in[0,\frac{1}{\beta-1}]$, a sequence $(\epsilon_{i})_{i=1}^{\infty}\in\{0,1\}^{\mathbb{N}}$ is called a $\beta$-expansion for $x$ if $$x=\sum_{i=1}^{\infty}\frac{\epsilon_{i}}{\beta^{i}}.$$ In a recent article the author studied ... More

Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon TheoremMar 21 2016Jun 13 2016We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic ... More

A First Look at the Impact of NNNLO Theory Uncertainties on Top Mass Measurements at the ILCMar 15 2016Aug 22 2016A scan of the top production threshold at a future electron-positron collider provides the possibility for a precise measurement of the top quark mass in theoretically well-defined mass schemes. With statistical uncertainties of 20 MeV or below, systematics ... More

Measure Equipartitions via Finite Fourier AnalysisMar 27 2014Jun 20 2015Applications of harmonic analysis on finite groups are introduced to measure partition problems, with equipartitions obtained as the vanishing of prescribed Fourier transforms. For elementary abelian groups $Z_p^k$, $p$ an odd prime, equipartitions are ... More

Equivariant Equipartitions: Ham Sandwich Theorems for Finite Subgroups of SpheresSep 04 2011Jun 19 2012Equivariant "Ham Sandwich" Theorems are obtained for the finite subgroups G of the unit spheres S(F) in the classical algebras F = R, C, and H. Given any n F-valued mass distributions on F^n, it is shown that there exists a G-equivariant decomposition ... More

Kergin Approximation in Banach SpacesOct 01 2008We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.

Static perfect fluids with Pant-Sah equations of stateJan 17 2008Mar 31 2008We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the ... More

Criteria for (in)finite extent of static perfect fluidsApr 09 2002In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely ... More

Conformal positive mass theoremsMar 29 2000We show the following two extensions of the standard positive mass theorem (one for either sign): Let (N,g) and (N,g') be asymptotically flat Riemannian 3-manifolds with compact interior and finite mass, such that g and g' are twice Hoelder differentiable ... More

Minimum settling time control design through direct search optimizationSep 27 2011Dec 06 2011The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature ... More

ExSample -- A Library for Sampling Sudakov-Type DistributionsAug 31 2011Mar 19 2012Sudakov-type distributions are at the heart of generating radiation in parton showers as well as contemporary NLO matching algorithms along the lines of the POWHEG algorithm. In this paper, the C++ library ExSample is introduced, which implements adaptive ... More

Stability, birational transformations and the Kahler-Einstein problemJul 23 2010We define a new notion of "b-stability" for a polarised algebraic variety, adapted to the existence problem for Kahler-Einstein metrics on Fano manifolds.

Calabi-Yau metrics on Kummer surfaces as a model glueing problemJul 23 2010This is an expository paper which aims to give a simple proof of the existence of Ricci-flat metrics on certain K3 surfaces, as an illustration of general "glueing" techniques.

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

Zero repulsion in families of elliptic curve L-functions and an observation of S. J. MillerSep 01 2011Oct 20 2011We provide a theoretical explanation for an observation of S. J. Miller that if L(s,E) is an elliptic curve L-function for which L(1/2, E) is nonzero, then the lowest lying zero of L(s,E) exhibits a repulsion from the critical point which is not explained ... More

Endoscopy and cohomology growth on U(3)Jan 30 2013We apply the endoscopic classification of automorphic forms on U(3) to prove a case of a conjecture of Sarnak and Xue on cohomology growth.

Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22Jul 08 2015In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way. Automorphisms of Salem degree 22 do not lift to any characteristic ... More

Simulating the formation of massive seed black holes in the early Universe. I: An improved chemical modelJan 23 2015Jun 06 2015The direct collapse model for the formation of massive seed black holes in the early Universe attempts to explain the observed number density of supermassive black holes (SMBHs) at $z \sim 6$ by assuming that they grow from seeds with masses M > 10000 ... More

Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)Aug 29 2012May 29 2013We produce a decidable classical normal modal logic of internalised negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP). LDiiP internalises ... More

A Logic of Interactive Proofs (Formal Theory of Knowledge Transfer)Jan 17 2012Apr 05 2016We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as embedded into ... More

Positive stable densities and the bell-shapeFeb 05 2013We show that positive stable densities are bell-shaped, that is their n-th derivatives vanish exactly n times on (0,+oo) and have an alternating sign sequence. This confirms the graphic predictions of Holt and Crow (1973) in the positive case.

Produit Beta-Gamma et régularité du signeJul 27 2012We study the total positivity of the multiplicative convolution kernel T associated with the independent product of two random variables $B(a,b)$ and $\Gamma(c).$ This kernel is totally positive of infinite order if $b$ or $d = a+b -c$ are integers. Otherwise ... More

Hitting densities for spectrally positive stable processesFeb 08 2010A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable L\'evy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute fractional ... More

Coupled Critical Models: Applications to Ising-Potts ModelsMay 28 1997We discuss the critical behaviour of 2D Ising and q-states Potts models coupled by their energy density. We found new tricritical points. The procedure employed is the renormalisation approach of the perturbations series around conformal field theories ... More

Rosenthal compacta and NIP formulasJul 22 2014Aug 07 2015We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about phi-types for phi NIP. In particular, we show that if M is a countable model, then an M-invariant phi-type is Borel definable. Also ... More

Distal and non-distal NIP theoriesMar 11 2011Oct 27 2012We study one way in which stable phenomena can exist in an NIP theory. We start by defining a notion of 'pure instability' that we call 'distality' in which no such phenomenon occurs. O-minimal theories and the p-adics for example are distal. Next, we ... More

Coupled Minimal Models with and without DisorderOct 02 1997We analyse in this article the critical behavior of $M$ $q_1$-state Potts models coupled to $N$ $q_2$-state Potts models ($q_1,q_2\in [2..4]$) with and without disorder. The technics we use are based on perturbed conformal theories. Calculations have ... More

On a theorem of Kac and GilbertMay 06 2004We prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum.

Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circleJun 01 2006We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC.

The 3/5-conjecture for weakly $S(K_{1,3})$-free forestsJul 10 2015The $3/5$-conjecture for the domination game states that the game domination numbers of an isolate-free graph $G$ on $n$ vertices are bounded as follows: $\gamma_g(G)\leq \frac{3n}5 $ and $\gamma_g'(G)\leq \frac{3n+2}5 $. Recent progress have been done ... More

Marginable functions on Fréchet spacesApr 20 2015Dec 11 2015This paper is about the technique of {\em shadow variables} that was used in the theory of monotone operators. In this paper, we use it to show that certain results that were originally proved for lower semicontinuous convex functions are in fact true ... More

Comment on "Separability of quantum states and the violation of Bell-type inequalities"Oct 05 2004The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. ... More

The Foundations of Quantum Information and Feasible ExperimentsMar 12 2001This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric down-conversion are analyzed ... More

Aizenman's Theorem for Orthogonal Polynomials on the Unit CircleNov 17 2004For suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if \[ \mathbb{E} \biggl(\int\frac{d\theta}{2\pi} \biggl|\biggl(\frac{\mathcal{C} + e^{i\theta}}{\mathcal{C} ... More

Generalized regularity and solution concepts for differential equationsJun 09 2008As the title ``Generalized regularity and solution concepts for differential equations'' suggests, the main topic of my thesis is the investigation of generalized solution concepts for differential equations, in particular first order hyperbolic partial ... More

Localic Metric spaces and the localic Gelfand dualityNov 04 2014In this paper we prove, as conjectured by B.Banachewski and C.J.Mulvey, that the constructive Gelfand duality can be extended into a duality between compact regular locales and unital abelian localic C*-algebras. In order to do so we develop a constructive ... More

Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg groupMar 04 2016We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by ... More

On the remainder term of the Berezin inequality on a convex domainSep 22 2015Nov 08 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

Regularized Newton methods for simultaneous Radon inversion and phase retrieval in phase contrast tomographyFeb 17 2015Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different incident angles of ... More

On the construction of solutions to the Yang-Mills equations in higher dimensionsFeb 10 2003Aug 13 2003We describe a glueing construction for the Yang-Mills equations in dimension $n > 4$. Our method is based on a construction of approximate solutions, and a detailed analysis of the linearized operator near an approximate solution.

On solutions to the Ginzburg-Landau equations in higher dimensionsFeb 06 2003Aug 13 2003We establish a glueing theorem for the Ginzburg-Landau equations in dimension $n > 2$. To this end, we consider a nondegenerate minimal submanifold of codimension 2, and construct a one-parameter family of solutions to the Ginzburg-Landau equations such ... More

Performance of a measurement-driven 'adiabatic-like' quantum 3-SAT solverSep 02 2015I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a non-orthogonal basis. If ... More

On the absolute continuity of multidimensional Ornstein-Uhlenbeck processesAug 26 2009Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular, the law of $X_1$ ... More

Completeness criteria for modular cohomology rings of non prime power groupsApr 05 2010Aug 31 2012We introduce a criterion for the completeness of ring approximations of modular cohomology rings of finite non prime power groups, and discuss how this criterion performs in practical computations, compared with other criteria.

Some remarks about equations defining coincident root lociAug 23 2011Consider the projective variety $X_\lambda$ of binary forms of degree $d$ whose linear factors are distributed according to the partition $\lambda$ of $d$. We determine minimal sets of local generators of the fiber product of $X_\lambda$ with its normalization, ... More

Equations describing the ramification of outer simple linear projectionsSep 03 2011We explain how to determine equations describing the ramification of an outer simple linear projection of a projective scheme in a way suited for explicit computations.

A Note on "Regularity lemma for distal structures"Aug 17 2015In a recent paper, Chernikov and Starchenko prove that graphs defined in distal theories have strong regularity properties, generalizing previous results about graphs defined by semi-algebraic relations. We give a shorter, purely model-theoretic proof ... More

The almost Daugavet property and translation-invariant subspacesJul 13 2013Let $G$ be a metrizable, compact abelian group and let $\Lambda$ be a subset of its dual group $\hat G$. We show that $C_\Lambda(G)$ has the almost Daugavet property if and only if $\Lambda$ is an infinite set, and that $L^1_\Lambda(G)$ has the almost ... More

Kahler metrics with cone singularities along a divisorFeb 06 2011Feb 14 2011We develop some foundations for the study of Kahler-Einstein metrics with cone singularities transverse to a divisor. The main goal is a treatment of the deformation of the cone angle.

Geodesic restrictions of arithmetic eigenfunctionsApr 03 2012Aug 17 2013Let X be an arithmetic hyperbolic surface, \psi a Hecke-Maass form, and l a geodesic segment on X. We obtain a power saving over the local bound of Burq-G\'erard-Tzvetkov for the L^2 norm of \psi restricted to l, by extending the technique of arithmetic ... More

Asymptotically tight bounds on subset sumsMay 31 2008For a subset A of a finite abelian group G we define Sigma(A)={sum_{a\in B}a:B\subset A}. In the case that Sigma(A) has trivial stabiliser, one may deduce that the size of Sigma(A) is at least quadratic in |A|; the bound |Sigma(A)|>= |A|^{2}/64 has recently ... More

Combinatorics of tropical Hurwitz cyclesJul 15 2014Jun 25 2015We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points ... More

Introduction to Gromov-Witten TheoryJul 04 2014The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference aimed at introducing ... More

Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular formsFeb 09 2012Apr 17 2012In this paper we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surfaces using the crepant resolution conjecture and the Yau-Zaslow formula. We present a formula to compute these in terms ... More

Refining Reasoning in Qualitative Probabilistic NetworksFeb 20 2013In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a probability will ... More

Linearised Higher Variational EquationsMar 30 2013Feb 10 2015This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and computationally ... More

Rigidity of compact Riemannian spin Manifolds with BoundaryMar 21 2008Oct 29 2008In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} ... More