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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

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

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

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

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

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

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

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

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

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 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

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

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

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

Noncommuting Observables and Local RealismMay 03 2005A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems, and these comprise ... More

A local hidden variable theory for the GHZ experimentJul 27 2000Aug 19 2002A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude ... More

Superconductivity model for a spin-vortex checkerboardMar 29 2017Jul 23 2017We introduce a microscopic model aimed at describing superconductivity that can possibly exist in the background of a magnetic texture called "spin-vortex checkerboard". This texture was proposed previously as a possible alternative to stripes to interpret ... More

Hybrid quantum-classical method for simulating high-temperature dynamics of nuclear spins in solidsJun 25 2018Jul 03 2018First-principles calculations of high-temperature spin dynamics in solids in the context of nuclear magnetic resonance (NMR) is a long-standing problem, whose conclusive solution can significantly advance the applications of NMR as a diagnostic tool for ... More

Growth rate of an endomorphism of a groupMar 29 2011In [B] Bowen defined the growth rate of an endomorphism of a finitely generated group and related it to the entropy of a map $f:M \mapsto M$ on a compact manifold. In this note we study the purely group theoretic aspects of the growth rate of an endomorphism ... 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

Pseudogap and Fermi surface in the presence of spin-vortex checkerboard for 1/8-doped lanthanum cupratesMay 23 2017Jul 26 2017Lanthanum family of high-temperature cuprate superconductors is known to exhibit both spin and charge electronic modulations around doping level 1/8. We assume that these modulations have the character of two-dimensional spin-vortex checkerboard and investigate ... 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.

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

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

Note on constancy of some formal meromorphic mapsMar 19 2008Mar 25 2008Segre sets are superfluous to verify that quotients of formal holomorphic maps that are real on a minimal generic submanifold of positive CR dimension must necessarily be constant.

On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principleMar 31 2004In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying ... More

Monochromatic sums and products in $\mathbb{N}$May 05 2016An old question in Ramsey theory asks whether any finite coloring of the natural numbers admits a monochromatic pair $\{x+y,xy\}$. We answer this question affirmatively in a strong sense by exhibiting a large new class of non-linear patterns which can ... 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

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

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

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

Isoperimetric Regions in Nonpositively Curved ManifoldsApr 11 2016Isoperimetric regions minimize the size of their boundaries among all regions with the same volume. In Euclidean and Hyperbolic space, isoperimetric regions are round balls. We show that isoperimetric regions in two and three-dimensional nonpositively ... More

Reflection principle and envelopes of holomorphyDec 21 2000The reflection function of a smooth CR diffeomorphism between two minimal real analytic hypersurfaces is everywhere real analytic.

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

Non-Gaussian Correlations Outside the Horizon in Local Thermal EquilibriumDec 18 2012Making a connection between observations of cosmological correlation functions and those calculated from theories of the early universe requires that these quantities are conserved through the periods of the universe which we do not understand. In this ... More

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

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 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

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

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 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 $P_I-P_{VI}$ .

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

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

A Proof of the Strengthened Hanna Neumann ConjectureMay 23 2009May 15 2010We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of "typical" covering maps, and use graph Galois theory to "symmetrize" the conjecture. The conjecture is then related to ... 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

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

Critical p-adic L-functionDec 15 2009We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.

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

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

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

Microfluidic tools for assaying immune cell functionJan 10 2018Joel Voldman is a professor in the Electrical Engineering and Computer Science Department at MIT. Here he describes his labs efforts to develop microfluidic devices for cell manipulation and analysis.

Correction to ``Knotted Hamiltonian cycles in spatial embeddings of complete graphs"Jul 09 2008We state and prove a correct version of a theorem presented in an earlier paper.

Jet-hadron correlations relative to the event plane at the LHC with ALICEMar 27 2017The hot, dense and strongly interacting medium known as the Quark Gluon Plasma (QGP) is produced in relativistic heavy-ion collisions at the Large Hadron Collider (LHC). Early in the collisions, quarks and gluons from the incoming nuclei collide to produce ... 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

Algebraic Independence of generic Painlevé Transcendents: P_III and P_VIAug 09 2017Apr 25 2018We prove that if y"=f(y,y',t) is a generic Painlev\'e equation from the class III and VI, and if y_1,...,y_n are distinct solutions, then y_1,y_1',...,y_n,y_n' are algebraically independent over C(t). This improves the weaker results obtained by the author ... More

Geometric Triviality of the Strongly Minimal Second Painlevé equationsFeb 18 2013We show that the strongly minimal second Painlev\'e equation (y" = 2y^3+ty+\alpha) is geometrically trivial, that is we show that if y_1,...,y_n are distinct solutions such that y_1,y_1',y_2,y_2',...,y_n,y_n' are algebraically dependent over C(t), then ... More

Explicit differential characterization of PDE systems pointwise equivalent to Y_{X^{j_1}X^{j_2}}=0, 1\leq j_1,j_2\leq n\geq 2Nov 29 2004Jan 19 2005In this paper, a direct continuation of math.DG/0411165, we generalize S. Lie's linearization criterion of an ordinary second order differential equation to the case of several independent variables (x^1, x^2 ..., x^n), n >1, and a single dependent variable ... More

Explicit differential characterization of the Newtonian free particle system in m > 1 dependent variablesNov 08 2004Nov 23 2006In 1883, as an early result, Sophus Lie established an explicit necessary and sufficient condition for an analytic second order ordinary differential equation y_xx = F(x,y,y_x) to be equivalent, through a point transformation (x,y) --> (X(x,y), Y(x,y)), ... More

Picard groups of b-symplectic manifoldsSep 17 2016We compute the Picard group of a stable b-symplectic manifold $M$ by introducing a collection of discrete invariants $\mathfrak{Gr}$ which classify $M$ up to Morita equivalence.

Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann ConjectureMay 01 2011Jun 17 2011In this paper we establish some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. We then use these ideas to prove the Hanna Neumann Conjecture of the 1950's; in fact, we prove a strengthened ... 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

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

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

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

Model Independent Searches for New Physics at the Fermilab Tevatron ColliderJun 19 2009The standard model is a successful but limited theory. There is significant theoretical motivation to believe that new physics may appear at the energy scale of a few TeV, the lower end of which is currently probed by the Fermilab Tevatron Collider. The ... 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

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.

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