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Symplectic dominationMay 14 2019Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is a theorem ... More

Toric anti-self-dual 4-manifolds via complex geometryFeb 20 2006Sep 13 2006Using the twistor correspondence, this article gives a one-to-one correspondence between germs of toric anti-self-dual conformal classes and certain holomorphic data determined by the induced action on twistor space. Recovering the metric from the holomorphic ... More

Toric anti-self-dual Einstein metrics via complex geometrySep 18 2006Feb 25 2008Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general ... More

Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spacesFeb 11 2016The twistor space of a Riemannian 4-manifold carries two almost complex structures, $J_+$ and $J_-$, and a natural closed 2-form $\omega$. This article studies limits of manifolds for which $\omega$ tames either $J_+$ or $J_-$. This amounts to a curvature ... More

Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spacesFeb 11 2016Nov 15 2016The twistor space of a Riemannian 4-manifold carries two almost complex structures, $J_+$ and $J_-$, and a natural closed 2-form $\omega$. This article studies limits of manifolds for which $\omega$ tames either $J_+$ or $J_-$. This amounts to a curvature ... More

A gauge theoretic approach to the anti-self-dual Einstein equationsNov 21 2011Nov 29 2011In [29], Plebanski reformulated the anti-self-dual Einstein equations with non-zero scalar curvature as a first order PDE for a connection in an SO(3)-bundle over the four-manifold. The aim of this article is to place this differential equation in a new ... More

Calabi flow and projective embeddingsNov 03 2008Jan 09 2009Let X be a smooth subvariety of CP^N. We study a flow, called balancing flow, on the space of projectively equivalent embeddings of X, which attempts to deform the given embedding into a balanced one. If L->X is an ample line bundle, considering embeddings ... More

Fibrations with constant scalar curvature Kahler metrics and the CM-line bundleOct 04 2005Mar 04 2006Let X --> B be a holomorphic submersion between compact Kahler manifolds of any dimension, whose fibres and base have no non-zero holomorphic vector fields and whose fibres all admit constant scalar curvature Kahler metrics. This article gives a sufficient ... More

Quantisation and the Hessian of Mabuchi energySep 23 2010May 03 2012Let L be an ample bundle over a compact complex manifold X. Fix a Hermitian metric in L whose curvature defines a K\"ahler metric on X. The Hessian of Mabuchi energy is a fourth-order elliptic operator D on functions which arises in the study of scalar ... More

Constant scalar curvature Kahler metrics on fibred complex surfacesJan 21 2004Mar 05 2004This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic limit. An ... More

The Hamiltonian geometry of the space of unitary connections with symplectic curvatureJan 12 2011Let L->M be a Hermitian line bundle over a compact manifold. Write S for the space of all unitary connections in L whose curvatures define symplectic forms on M and G for the group of unitary bundle isometries of L, which acts on S by pull-back. The main ... More

An ambient approach to conformal geodesicsJul 05 2019Jul 11 2019Conformal geodesics are distinguished curves on a conformal manifold, loosely analogous to geodesics of Riemannian geometry. One definition of them is as solutions to a third order differential equation determined by the conformal structure. There is ... More

Symplectic Calabi-Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifoldFeb 25 2008Mar 05 2008Given an SO(3)-bundle with connection, the associated two-sphere bundle carries a natural closed 2-form. Asking that this be symplectic gives a curvature inequality first considered by Reznikov. We study this inequality in the case when the base has dimension ... More

Circle-invariant fat bundles and symplectic Fano 6-manifoldsJul 03 2014We prove that a compact 4-manifold which supports a circle-invariant fat SO(3)-bundle is diffeomorphic to either S^4 or CP^2-bar. The proof involves studying the resulting Hamiltonian circle action on an associated symplectic 6-manifold. Applying our ... More

Hyperbolic geometry and non-Kahler manifolds with trivial canonical bundleMay 20 2009Dec 22 2009We use hyperbolic geometry to construct simply-connected symplectic or complex manifolds with trivial canonical bundle and with no compatible Kahler structure. We start with the desingularisations of the quadric cone in C^4: the smoothing is a natural ... More

An ambient approach to conformal geodesicsJul 05 2019Conformal geodesics are distinguished curves on a conformal manifold, loosely analogous to geodesics of Riemannian geometry. One definition of them is as solutions to a third order differential equation determined by the conformal structure. There is ... More

Hypersymplectic 4-manifolds, the $G_2$-Laplacian flow and extension assuming bounded scalar curvatureApr 25 2017May 08 2017A hypersymplectic structure on a 4-manifold $X$ is a triple $\underline{\omega}$ of symplectic forms which at every point span a maximal positive-definite subspace of $\Lambda^2$ for the wedge product. This article is motivated by a conjecture of Donaldson: ... More

The diversity of symplectic Calabi-Yau six-manifoldsAug 30 2011Oct 14 2011Given an integer b and a finitely presented group G we produce a compact symplectic six-manifold with c_1 = 0, b_2 > b, b_3 > b and fundamental group G. In the simply-connected case we can also arrange for b_3 = 0; in particular these examples are not ... More

Examples of compact Einstein four-manifolds with negative curvatureFeb 02 2018We give new examples of compact, negatively curved Einstein manifolds of dimension $4$. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of 4-manifolds $(X_k)$ previously considered by ... More

Linear homology in a nutshellJul 31 2019In 1985 Bayer and Billera defined a flag vector $f(X)$ for every convex polytope $X$, and proved some fundamental properties. The flag vectors $f(X)$ span a graded ring $\mathcal{R}=\bigoplus_{d\geq0}\mathcal{R}_d$. Here $\mathcal{R}_d$ is the span of ... More

The space of hyperkähler metrics on a 4-manifold with boundaryMar 27 2016Nov 02 2016Let X be a compact 4-manifold with boundary. We study the space of hyperk\"ahler triples on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent ... More

A gauge theoretic approach to Einstein 4-manifoldsDec 10 2013Aug 07 2016This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent ... More

The space of hyperkähler metrics on a 4-manifold with boundaryMar 27 2016Let X be a compact 4-manifold with boundary. We study the space of hyperk\"ahler triples on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent ... More

The space of hyperkähler metrics on a 4-manifold with boundaryMar 27 2016Feb 06 2017Let X be a compact 4-manifold with boundary. We study the space of hyperk\"ahler triples on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent ... More

On Zurek's derivation of the Born ruleDec 06 2003Sep 22 2004Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or "envariance" [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions ... More

Comment on "Broken translational and rotational symmetry via charge stripe order in underdoped YBa2Cu3O6+y"Feb 02 2016Comin et al. [Science 347, 1335 (2015)] have interpreted their resonant X-ray scattering experiment as indicating that charge inhomogeneities in the family of high-temperature superconductors YBa2Cu3O6+y (YBCO) have the character of one-dimensional stripes ... More

Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted DiracMay 23 2016Jan 05 2017Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator ... More

Asymptotically hyperbolic connectionsDec 22 2015General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion ... More

Stability of Quantum Statistical Ensembles with Respect to Local MeasurementsJan 24 2016Oct 23 2016We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the total energy ... More

Spin excitation spectrum of high-temperature cuprate superconductors from finite cluster simulationsDec 28 2017A cluster of spins $1/2$ of a finite size can be regarded as a basic building block of a spin texture in high-temperature cuprate superconductors. If this texture has the character of a network of weakly coupled spin clusters, then spin excitation spectra ... More

Sensitivity to small perturbations in systems of large quantum spinsSep 16 2014We investigate the sensitivity of nonintegrable large-spin quantum lattices to small perturbations with a particular focus on the time reversal experiments known in statistical physics as "Loschmidt echoes" and in nuclear magnetic resonance (NMR) as "magic ... More

Sophus Lie, Friedrich Engel and the Riemann-Helmholtz problemOct 05 2009Feb 08 2010A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.

Four explicit formulas for the prolongations of an infinitesimal Lie symmetry and multivariate Faa di Bruno formulasNov 30 2004In 1979, building on S. Lie's theory of symmetries of (partial) differrential equations, P.J. Olver formulated inductive formulas which are appropriate for the computation of the prolongations of an infinitesimal Lie symmetry to jet spaces, for an arbitrary ... More

New examples of p-adically rigid automorphic formsMay 14 2008We give examples of cohomological automorphic forms for unitary groups which are $p$-adically rigid.

Introduction to the $p$-adic SpaceOct 22 2017In this paper, we offer a brief introduction to the $p$-adic numbers and operations in the metric space defined under the $p$-adic norm. Specifically, we provide a clear description of the derivation of the $p$-adic number via the completion of the rationals. ... More

Affine Rigidity Without IntegrationMar 03 2019Real analytic ($\mathcal{C}^\omega$) surfaces $S^2$ in $\mathbb{R}^3 \ni (x,y,u)$ graphed as $\big\{ u = F(x,y) \big\}$ with $F_{xx} \neq 0$ whose Gaussian curvature vanishes identically: \[ 0 \,\equiv\, F_{xx}\,F_{yy} - F_{xy}^2, \] possess, under the ... More

What is an Almost Normal SurfaceAug 02 2012Oct 16 2012A major breakthrough in the theory of topological algorithms occurred in 1992 when Hyam Rubinstein introduced the idea of an almost normal surface. We explain how almost normal surfaces emerged naturally from the study of geodesics and minimal surfaces. ... More

Sheaves on Graphs and Their Homological InvariantsApr 14 2011Jun 17 2011We introduce a notion of a sheaf of vector spaces on a graph, and develop the foundations of homology theories for such sheaves. One sheaf invariant, its "maximum excess," has a number of remarkable properties. It has a simple definition, with no reference ... More

Rationality in Differential Algebraic GeometryMay 29 2014Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.

Equivalences of 5-dimensional CR-manifolds IV: Six ambiguity matrix groups (Initial G-structures)Dec 04 2013Class I CR manifolds have initial G-structure a certain 4-dimensional subgroup of GL_3(C). Class II CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_4(C). Class III-1 CR manifolds have initial G-structure a certain 10-dimensional ... More

Vector field construction of Segre setsJan 05 1999Oct 24 2000A CR generic real analytic CR manifold M carries two families of Segre varieties and conjugate Segre varieties. We observe in this article that their complexifications give rise to two families of foliations of the complexification of M which coincide ... More

The Minimum Perfect Matching in Pseudo-dimension 0<q<1Mar 14 2014Feb 17 2016It is known that for $K_{n,n}$ equipped with i.i.d. $exp(1)$ edge costs, the minimum total cost of a perfect matching converges to $\pi^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q ... More

Cosmic Neutrinos and Other Light RelicsMay 18 2016Cosmological measurements of the radiation density in the early universe can be used as a sensitive probe of physics beyond the standard model. Observations of primordial light element abundances have long been used to place non-trivial constraints on ... More

Cohomology in Grothendieck Topologies and Lower Bounds in Boolean ComplexityDec 01 2005Dec 02 2005This paper is motivated by questions such as P vs. NP and other questions in Boolean complexity theory. We describe an approach to attacking such questions with cohomology, and we show that using Grothendieck topologies and other ideas from the Grothendieck ... More

Completion of standard-like embeddingsSep 14 2000Jan 03 2001Inequivalent standard-like observable sector embeddings in $Z_3$ orbifolds with two discrete Wilson lines, as determined by Casas, Mondragon and Mu\~noz, are completed by examining all possible ways of embedding the hidden sector. The hidden sector embeddings ... More

Critically Slow Learning in Flashcard Learning ModelsApr 30 2018Algorithmic education theory examines, among other things, the trade-off between reviewing old material and studying new material: time spent learning the new comes at the expense of reviewing and solidifying one's understanding of the old. This trade-off ... More

Inner Rank and Lower Bounds for Matrix MultiplicationJun 13 2017May 13 2019We develop a notion of {\em inner rank} as a tool for obtaining lower bounds on the rank of matrix multiplication tensors. We use it to give a short proof that the border rank (and therefore rank) of the tensor associated with $n\times n$ matrix multiplication ... More

2 Higgs Doublet Model Evolver - ManualNov 20 20182 Higgs Doublet Model Evolver (2HDME) is a C++ program that provides the functionality to perform renormalization group equation running of the general 2 Higgs Doublet Model at 2-loop order. We briefly describe the 2HDME's structure, provide a demonstration ... More

The frictional force on sliding dropsSep 14 2018The dynamic frictional force between solid surfaces in relative motion differs from the static force needed to initiate motion, but this distinction is not usually thought to occur for liquid drops moving on a solid. Recent experiments [Gao, et al., Nature ... More

I: Lie symmetries of partial differential equations and CR geometryMar 05 2007A general theory of rigid completely integrable analytic partial differential equations is endeavoured. The tube over the light cone in C^3 is shown to be the unique model (up to biholomorphisms) having CR automorphism group of maximal dimension equal ... More

Convergence of formal equivalences of hypersurfacesDec 21 2000A formal invertible equivalence between two minimal real analytic hypersurfaces converges if and only if the hypersurfaces are holomorphically nondegenerate

Algorithms for recognizing knots and 3-manifoldsDec 30 1997This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.

Quasinormal modes of Unruh's Acoustic Black HoleAug 10 2005Oct 05 2005We have studied the sound perturbation of Unruh's acoustic geometry and we present an exact expression for the quasinormal modes of this geometry. We are obtain that the quasinormal frequencies are pure-imaginary, that give a purely damped modes.

Regularity Criteria of BKM type in Distributional Spaces for the 3-D Navier-Stokes Equations on Bounded DomainsMay 14 2014In the classic work of Beale-Kato-Majda ({[}2{]}) for the Euler equations in $\mathbb{R^{\mathrm{3}}}$, regularity of a solution throughout a given interval $[0,T_{*}]$ is obtained provided that the curl $\omega$ satisfies $\omega\in L^{1}((0,T);L^{\infty}(\mathbb{R^{\textrm{\ensuremath{3}}}})$ ... More

The crystalline period of a height one $p$-adic dynamical system over $\mathbf{Z}_p$Jan 19 2015Let $f$ be a continuous ring endomorphism of $\mathbf{Z}_p[[x]]/\mathbf{Z}_p$ of degree $p.$ We prove that if $f$ acts on the tangent space at $0$ by a uniformizer and commutes with an automorphism of infinite order, then it is necessarily an endomorphism ... More

Poisson manifolds and their associated stacksMar 10 2017Sep 28 2017We associate to any integrable Poisson manifold a stack, i.e. a category fibered in groupoids over a site. The site in question has objects Dirac manifolds and morphisms pairs consisting of a smooth map and a closed 2-form. We show that two Poisson manifolds ... More

On removable singularities for CR functions in higher codimensionNov 27 2004We establish the holomorphic wedge extendability of CR functions, defined on an everywhere locally minimal generic submanifold M of C^n and having singularities contained in a submanifold N of codimension 1, 2 or 3, assuming some transversality conditions ... More

On the convergence of S-nondegenerate formal CR mapsJan 07 1999Jul 26 2000We introduce S-nondegenerate formal CR maps and establish their convergence (revision of a preliminary version).

The Best Theory of Cosmic Structure Formation is Cold + Hot Dark Matter (CHDM)Oct 10 1996Oct 24 1996I have been asked to make the case here that CHDM is the best theory of cosmic structure formation, and indeed I believe that it is the best of all those I have considered if the cosmological matter density is near critical and if the expansion rate is ... More

Inner Rank and Lower Bounds for Matrix MultiplicationJun 13 2017We develop a notion of {\em inner rank} as a tool for obtaining lower bounds on the rank of matrix multiplication tensors. We use it to give a short proof that the border rank (and therefore rank) of the tensor associated with $n\times n$ matrix multiplication ... More

Anomalous dimensions on the latticeDec 31 2015We review methods and results for extracting the anomalous dimensions of operators from lattice field theory calculations. The most important application is the anomalous mass dimension in conformal or nearly conformal gauge field theories which might ... More

On Wittgenstein's philosophy of mathematicsJan 07 2008Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays, philosophy ... More

Pitfalls of Goodness-of-Fit from LikelihoodOct 31 2003The value of the likelihood is occasionally used by high energy physicists as a statistic to measure goodness-of-fit in unbinned maximum likelihood fits. Simple examples are presented that illustrate why this (seemingly intuitive) method fails in practice ... More

Evolutionary Computation and AI Safety: Research Problems Impeding Routine and Safe Real-world Application of EvolutionJun 24 2019Recent developments in artificial intelligence and machine learning have spurred interest in the growing field of AI safety, which studies how to prevent human-harming accidents when deploying AI systems. This paper thus explores the intersection of AI ... More

The Inverse Square Law And Newtonian Dynamics space explorer (ISLAND)Sep 03 2018The ISLAND (Inverse Square Law And Newtonian Dynamics) Space Explorer is a new concept to test the gravitational Inverse Square Law at: (1) submillimeter scale and (2) at the largest Solar System scales (dozens of Astronomical Units --AU). The main idea ... More

When a `rat race' implies an intergenerational wealth trapApr 30 2018Two critical questions about intergenerational outcomes are: one, whether significant barriers or traps exist between different social or economic strata; and two, the extent to which intergenerational outcomes do (or can be used to) affect individual ... More

Polynomials with Surjective Arboreal Galois Representations Exist in Every DegreeMar 01 2018Mar 12 2018Let~$E$ be a Hilbertian field of characteristic~$0$. R.W.K. Odoni conjectured that for every positive integer~$n$ there exists a polynomial~$f\in E[X]$ of degree~$n$ such that each iterate~$f^{\circ{k}}$ of~$f$ is irreducible and the Galois group of the ... More

The Sarason Sub-Symbol and the Recovery of the Symbol of Densely Defined Toeplitz Operators over the Hardy SpaceDec 18 2014While the symbol map for the collection of bounded Toeplitz operators is well studied, there has been little work on a symbol map for densely defined Toeplitz operators. In this work a family of candidate symbols, the Sarason Sub-Symbols, is introduced ... More

On the partial algebraicity of holomorphic mappings between real algebraic setsJun 09 1999Apr 06 2004In this paper, we consider local holomorphic mappings f: M\to M' between real algebraic CR generic manifolds (or more generally, real algebraic sets with singularities) in the complex euclidean spaces of different dimensions and we search necessary and ... More

Vanishing Hachtroudi curvature and local equivalence to the Heisenberg sphereOct 15 2009Nov 26 2009To any completely integrable second-order system of real or complex partial differential equations in n > 1 independent variables and in one dependent variable, Mohsen Hachtroudi associated in 1937 a normal projective (Cartan) connection, and he computed ... More

Swap connectivity for two graph spaces between simple and pseudo graphs and disconnectivity for triangle constraintsApr 06 2017With sufficient time, double edge-swap Markov chain Monte Carlo (MCMC) methods are able to sample uniformly at random from many different and important graph spaces. For instance, for a fixed degree sequence, MCMC methods can sample any graph from: simple ... More

Geometric Realizations of the Basic Representation of $\widehat\mathfrak{gl}_r$Oct 11 2014The realizations of the basic representation of $\widehat\mathfrak{gl}_r$ are known to be parametrized by partitions of r and have an explicit description in terms of vertex operators on the bosonic/fermionic Fock space. In this paper, we give a geometric ... More

On Transformations in the Painlevé FamilyFeb 04 2015In this paper we show that generic Painlev\'e equations from different families are orthogonal. In particular, this means that there are no general Backlund transformations between Painlev\'e equations from the different families $P_I-P_{VI}$ .

Stacks in Poisson GeometryJun 05 2018This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory ... More

Complex projective hypersurfaces of general type: toward a conjecture of Green and GriffithsMay 03 2010Jun 18 2014Let X be a geometrically smooth n-dimensional projective algebraic complex hypersurface in P^{n+1}(C). Using Green-Griffiths jets, we establish the existence of nonzero global algebraic differential equations that must be satisfied by every nonconstant ... More

Low pole order frames on vertical jets of the universal hypersurfaceMay 26 2008Dec 16 2008Of the two techniques introduced by Bloch, Green-Griffiths and developed by Siu, Demailly to establish Kobayashi hyperbolicity of generic high degree complex algebraic hypersurfaces X in P^(n+1), the second one, initiated by Clemens, Ein, Voisin and developed ... More

Theory of Transformation Groups, by S. Lie and F. Engel (Vol. I, 1888). Modern Presentation and English TranslationMar 16 2010The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also, to be read.

Nonrigid spherical real analytic hypersurfaces in C^2Oct 09 2009Feb 03 2010A Levi nondegenerate real analytic hypersurface M of C^2 represented in local coordinates (z, w) in C^2 by a complex defining equation of the form w = Theta (z, \bar z, \bar w) which satisfies an appropriate reality condition, is spherical if and only ... More

Siu-Yeung jet differentials on complete intersection surfaces X^2 in P^4(C)Dec 19 2013On a generic complete intersection surface X^2 in P^4(C) having polynomial equations z^d = R(x,y) and t^e = S(x,y) with 752 <= d <= e <= d^2/648, there exist extrinsic meromorphic jet differentials of the form J(x,y,x',y') / [y^d z^{m(d-1)} t^{m(e-1)}] ... More

Self-Consistent, Self-Coupled Scalar GravityAug 15 2014Aug 18 2014A scalar theory of gravity extending Newtonian gravity to include field energy as its source is developed. The physical implications of the theory are probed through its spherically symmetric (source) solutions. The aim is to demonstrate rational physical ... More

Ranks of Selmer groups in an analytic familyJun 08 2009We study the variation of the dimension of the Bloch-Kato Selmer group of a p-adic Galois representation of a number field that varies in a refined family. We show that, if one restricts ourselves to representations that are, at every place dividing $p$, ... More

Sur la compatibilite entre les correspondances de Langlands locale et globale pour U(3). (On the compatibility between local and global Langlands correspondances for U(3))Dec 31 2003Using a level-raising argument (and a result of Larsen on the image of Galois representations in compatible systems), we prove that for any automorphic representation $\pi$ for $\U(3)$, the $l$-adic Galois representation $\rho_l$ which is attached to ... More

The Strengthened Hanna Neumann Conjecture I: A Combinatorial ProofMar 30 2010Apr 14 2011We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in a succession ... More

Propagation of analyticity for essentially finite C^infty-smooth CR mappingsApr 06 2004Nov 16 2004An analytico-geometric reflection principle is established by means of normal deformations of analytic discs.

Minimal Fibrations of Hyperbolic 3-manifoldsDec 14 2015There are hyperbolic 3-manifolds that fiber over the circle but that do not admit fibrations by minimal surfaces. These manifolds do not admit fibrations by surfaces that are even approximately minimal.

Hydrodynamic Limit of a Boundary-Driven Elastic Exclusion Process and a Stefan ProblemOct 05 2011Feb 03 2012Burdzy, Pal, and Swanson considered solid spheres of small radius moving in the unit interval, reflecting instantaneously from each other and at x=0, and killed at x=1, with mass being added to the system from the left at constant rate. By transforming ... More

Lambda: A Mathematica-package for operator product expansions in vertex algebrasApr 29 2010Nov 09 2010We give an introduction to the Mathematica package Lambda, designed for calculating $\lambda$-brackets in both vertex algebras, and in SUSY vertex algebras. This is equivalent to calculating operator product expansions in two-dimensional conformal field ... More

Applications of computational invariant theory to Kobayashi hyperbolicity and to Green-Griffiths algebraic degeneracyAug 26 2008Jul 02 2010A major unsolved problem (according to Demailly 1997) towards the Kobayashi hyperbolicity conjecture in optimal degree is to understand jet differentials of germs of holomorphic discs that are invariant under any reparametrization of the source. The underlying ... More

Cosmological Structure Formation With and Without Hot Dark MatterOct 10 1996Cold + Hot Dark Matter (CHDM) is perhaps the best theory of cosmic structure formation {\it if} the cosmological matter density is near critical (i.e., $\Omega_0 \approx 1$) and {\it if} the expansion rate is not too large (i.e. $h \equiv H_0/(100 \kmsMpc) ... More

Extrinsic projective curves X^1 in P^2(C): harmony with intrinsic cohomologyFeb 05 2014On a geometrically smooth complex algebraic curve X^1 in P^2(C), represented in complex affine coordinates (x,y) as the zero-locus R(x,y) = 0 of some polynomial R of degree d >= k+3, an explicit family of generating independent holomorphic jet differentials ... More

Curvature of surfaces in euclidean 3-space: philosophical analysis of Gauss' Theorema EgregiumFeb 05 2014This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically invariant character ... More

On transfer of biholomorphisms across nonminimal lociNov 20 2013A connected real analytic hypersurface M in C^(n+1) whose Levi form is nondegenerate in at least one point - hence at every point of some Zariski-open subset - is locally biholomorphic to the model Heisenberg quadric pseudosphere of signature (k, n-k) ... More

Global minimality of generic manifolds and holomorphic extendibility of CR functionsNov 26 2004Let M be a smooth generic submanifold of C^n. Tumanov showed that the direction of CR extendability parallel propagates with respect to a certain differential geometric partial connection in a quotient bundle of the normal bundle to M. M is said to be ... More

Equivalences of 5-dimensional CR-manifolds V: Six initial frames and coframes; Explicitness obstaclesDec 12 2013Local CR-generic submanifolds of C^N are in one-to-one correspondence with their respective graphing functions, but it is well known that (despite their importance) the Cartan-Hachtroudi-Chern-Moser invariants and coframes for Levi nondegenerate hypersurfaces ... More

Equivalences of 5-dimensional CR manifolds III: Six models and elementary normalizationsNov 29 2013The six nondegeneracy conditions of geometric nature that are satisfied by the only six possibly existing nondegenerate general classes I, II, III-1, III-2, IV-1, IV-2 of 5-dimensional CR manifolds are shown to be readable instantaneously from their elementarily ... More

Study of the formal CR reflection mappingMay 31 2000Jul 25 2000Corollary: Two germs of minimal real analytic CR-generic manifolds are formally equivalent if and only if they are biholomorphic.

Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity II: A Simple ExampleApr 06 2006In a previous paper we have suggested a number of ideas to attack circuit size complexity with cohomology. As a simple example, we take circuits that can only compute the AND of two inputs, which essentially reduces to SET COVER. We show a very special ... More

A proof of Alon's second eigenvalue conjecture and related problemsMay 05 2004In this paper we show the following conjecture of Noga Alon. Fix a positive integer d>2 and real epsilon > 0; consider the probability that a random d-regular graph on n vertices has the second eigenvalue of its adjacency matrix greater than 2 sqrt(d-1) ... More

The $L^p$ Dirichlet Problem for the Stokes System on Lipschitz DomainsApr 24 2009Apr 30 2009We study the $L^p$ Dirichlet problem for the Stokes system on Lipschitz domains. For any fixed $p>2$, we show that a reverse H\"{o}lder condition with exponent $p$ is sufficient for the solvability of the Dirichlet problem with boundary data in $L^p_N(\partial\Omega,\rn{d})$. ... More

A Demazure Character Formula for the Product Monomial CrystalJul 23 2019The product monomial crystal was defined by Kamnitzer, Tingley, Webster, Weekes, and Yacobi for any semisimple simply-laced Lie algebra $\mathfrak{g}$, and depends on a collection of parameters $\mathbf{R}$. We show that a family of truncations of this ... More