Institut de Recherche Mathématique Avancée

On montre que, dans certaines conditions, l'image de l'application moment de l'action d'un tore dans une varit symplectique (qui est un polydre convexe d'aprs un thorme de Atiyah, Guillemin et Sternberg) dtermine compltement cette varit.

We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of a duality statement between the cone of pseudo-effective divisors and the cone of “movable curves”, which is obtained from a general theory of movable intersections and approximate Zariski decomposition for closed positive <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 1 comma 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(1,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -currents. As a corollary, a projective manifold has a pseudo-effective canonical bundle if and only if it is not uniruled. We also prove that a 4-fold with a canonical bundle which is pseudo-effective and of numerical class zero in restriction to curves of a good covering family, has non-negative Kodaira dimension.

This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 144 and the only perfect powers in the Lucas sequence are 1 and 4.

Endotoxin-stimulated monocytes can elicit a dual procoagulant response. They express tissue factor and expose phosphatidylserine in the outer leaflet of the plasma membrane. Tissue factor, a membrane glycoprotein, is the cellular trigger of blood coagulation reactions. Phosphatidylserine is an essential anionic phospholipid for surface amplification of thrombin generation. In this study the distribution of these two procoagulant entities between activated monocytes and derived microparticles was assessed after stimulation by LPS. The presence of CD14, CD11a, and CD18, and possible associated adhesion potential were examined, particularly on microparticles. Tissue factor was evidenced by using a specific functional assay and flow cytometry. Phosphatidylserine exposure was monitored through its catalytic activity in a thrombin generation assay and by flow cytometry with the use of FITC-conjugated annexin V, a protein probe of anionic phospholipids. CD14, CD11a, and CD18 were detected by flow cytometry. The interaction of microparticle CD11a/CD18 with intracellular adhesion molecule-1 was demonstrated by using immobilized recombinant intracellular adhesion molecule-1 fusion protein. The major part of tissue factor and phosphatidylserine-dependent procoagulant activity was associated with microparticles after LPS stimulation. This was confirmed by flow cytometry. The presence of functional CD11a/CD18, and CD14 on microparticles testifies to an associated adhesion potential. These results show that membrane vesiculation could be responsible for dissemination of inducible monocyte procoagulant activities and suggest that derived microparticles could also participate in endothelium stimulation. This emphasizes the role of monocyte as a central element in the coupling between inflammation/infection and thrombosis.

A quantum hydrodynamic (fluid) model, derived from the Wigner-Poisson equations, is used to investigate the ultrafast electron dynamics in thin metal films. The hydrodynamic equations, which include exchange and correlation effects, can be combined into a single nonlinear Schr\"odinger-type equation. The fluid model is first benchmarked against a density-functional calculation for the ground state, with good agreement between the two approaches. The ultrafast nonlinear electron dynamics is then investigated and compared to recent semiclassical results obtained with a Vlasov-Poisson approach.

This is an extended second edition of Topology of Torus Actions on Symplectic Manifolds published in this series in 1991. The material and references have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity theorems, it contains much more results, proofs and examples. Chapter I deals with Lie group actions on manifolds. In Chapters II and III, symplectic geometry and Hamiltonian group actions are introduced, especially torus actions and action-angle variables. The core of the book is Chapter IV which is devoted to applications of Morse theory to Hamiltonian group actions, including convexity theorems. As a family of examples of symplectic manifolds, moduli spaces of flat connections are discussed in Chapter V. Then, Chapter VI centers on the Duistermaat-Heckman theorem. In Chapter VII, a topological construction of complex toric varieties is presented, and the last chapter illustrates the introduced methods for Hamiltonian circle actions on 4-manifolds.

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that three greedy algorithms converge; the last algorithm, based on the use of an a posteriori estimator, is the approach actually employed in the calculations.

International audience

Witten invariant 8W M of M. They proved that the Alexander polynomial of M can be explicitly computed from 8W M. Their proof uses the theory of sign-refined torsions mentioned above.Using the results of Meng and Taubes and capitalizing on the theory of Euler structures, I showed that the Seiberg-Witten invariant 8WM is equivalent (at least up to sign) to the refined maximal abelian torsion of M. This yields a combinatorial computation of the

Introduction: Applications of pseudo-holomorphic curves to symplectic topology.- 1 Examples of problems and results in symplectic topology.- 2 Pseudo-holomorphic curves in almost complex manifolds.- 3 Proofs of the symplectic rigidity results.- 4 What is in the book... and what is not.- 1: Basic symplectic geometry.- I An introduction to symplectic geometry.- 1 Linear symplectic geometry.- 2 Symplectic manifolds and vector bundles.- Appendix: the Maslov class M. Audin, A. Banyaga, F. Lalonde, L. Polterovich.- II Symplectic and almost complex manifolds.- 1 Almost complex structures.- 2 Hirzebruch surfaces.- 3 Coadjoint orbits (of U(n)).- 4 Symplectic reduction.- 5 Surgery.- Appendix: The canonical almost complex structure on the manifold of 1-jets of pseudo-holomorphic mappings between two almost complexmanifolds P. Gauduchon.- 2: Riemannian geometry and linear connections.- III Some relevant Riemannian geometry.- 1 Riemannian manifolds as metric spaces.- 2 The geodesic flow and its linearisation.- 3 Minimal manifolds.- 4 Two-dimensional Riemannian manifolds.- 5 An application to pseudo-holomorphic curves.- Appendix: the isoperimetric inequality M.-P. Muller.- IV Connexions lineaires, classes de Chern, theoreme de Riemann-Roch.- 1 Connexions lineaires.- 2 Classes de Chern.- 3 Le theoreme de Riemann-Roch.- Bibliographie.- 3: Pseudo-holomorphic curves and applications.- V Some properties of holomorphic curves in almost complex manifolds.- 1 The equation $$ \bar \partial f$$ in C.- 2 Regularity of holomorphic curves.- 3 Other local properties.- 4 Properties of the area of holomorphic curves.- 5 Gromov's compactness theorem for holomorphic curves.- Appendix: Stokes' theorem for forms with differentiable coefficients.- VI Singularities and positivity of intersections of J-holomorphic curves.- 1 Elementary properties.- 2 Positivity of intersections.- 3 Local deformations.- 4 Perturbing away singularities.- Appendix: The smoothness of the dependence on ? Gang Liu.- VII Gromov's Schwarz lemma as an estimate of the gradient for holomorphic curves.- 1 Introduction.- 2 A review of some classical Schwarz lemmas.- 3 Isoperimetric inequalities for J-curves.- 4 The Schwarz and monotonicity lemmas.- 5 Continuous Lipschitz extension across a puncture.- 6 Higher derivatives.- VIII Compactness.- 1 Riemann surfaces with nodes.- 2 Cusp-curves.- 3 Proof of the compactness theorem 2.2.1.- 4 Convergence of parametrised curves.- IX Exemples de courbes pseudo-holomorphes en geometrie riemannienne.- 1 Immersions isometriques elliptiques.- 2 Courbure de Gauss prescrite.- 3 Autres exemples et constructions.- Appendice: convergence d'applications pseudo-holomorphes.- Bibliographie.- X Symplectic rigidity: Lagrangian submanifolds.- 1 Lagrangian constructions.- 2 Symplectic area and Maslov classes-rigidity in split manifolds.- 3 Soft and hard Lagrangian obstructions to Lagrangian embeddings in Cn.- 4 Rigidity in cotangent bundles and applications to mechanics.- 5 Pseudo-holomorphic curves: proof of the main rigidity theorem.- Appendix: Exotic structures on R2n.- Authors' addresses.

The purpose of the lectures is to make a brief introduction to tropical algebraic geometry and to present several important applications of tropical geometry in enumerative geometry.

Introductory preface.- How I have (re-)written this book.- Acknowledgements.- What I have written in this book.- I. Smooth Lie group actions on manifolds.- I.1. Generalities.- I.2. Equivariant tubular neighborhoods and orbit types decomposition.- I.3. Examples: S 1-actions on manifolds of dimension 2 and 3.- I.4. Appendix: Lie groups, Lie algebras, homogeneous spaces.- Exercises.- II. Symplectic manifolds.- II.1What is a symplectic manifold?.- II.2. Calibrated almost complex structures.- II.3. Hamiltonian vector fields and Poisson brackets.- Exercises.- III. Symplectic and Hamiltonian group actions.- III.1. Hamiltonian group actions.- III.2. Properties of momentum mappings.- III.3. Torus actions and integrable systems.- Exercises.- IV. Morse theory for Hamiltonians.- IV.1. Critical points of almost periodic Hamiltonians.- IV.2. Morse functions (in the sense of Bott).- IV.3. Connectedness of the fibers of the momentum mapping.- IV.4. Application to convexity theorems.- IV.5. Appendix: compact symplectic SU(2)-manifolds of dimension 4.- Exercises.- V. Moduli spaces of flat connections.- V.1. The moduli space of fiat connections.- V.2. A Poisson structure on the moduli space of flat connections.- V.3. Construction of commuting functions on M.- V.4. Appendix: connections on principal bundles.- Exercises.- VI. Equivariant cohomology and the Duistermaat-Heckman theorem.- VI.1. Milnor joins, Borel construction and equivariant cohomology.- VI.2. Hamiltonian actions and the Duistermaat-Heckman theorem.- VI.3. Localization at fixed points and the Duistermaat-Heckman formula.- VI.4. Appendix: some algebraic topology.- VI.5. Appendix: various notions of Euler classes.- Exercises.- VII. Toric manifolds.- VII.1. Fans and toric varieties.- VII.2. Symplectic reduction and convex polyhedra.- VII.3. Cohomology of X ?.- VII.4. Complex toric surfaces.- Exercises.- VIII. Hamiltonian circle actions on manifolds of dimension 4.- VIII.1. Symplectic S 1-actions, generalities.- VIII.2. Periodic Hamiltonians on 4-dimensional manifolds.- Exercises.

Risk measurements go hand in hand with setting of capital minima by companies as well as by regulators. We review the properties of coherent risk measures and examine their implications for capital requirement in insurance. We also comment on the specific risk-based capital computations.

We show that the family of standard simplices and the family of Stasheff polytopes are dual to each other in the following sense. The chain modules of the standard simplices, resp. the Stasheff polytopes, assemble to give an operad. We show that these operads are dual of each other in the operadic sense. The main result of this paper is to show that they are both Koszul operads. As a consequence the generating series of the standard simplices and the generating series of the Stasheff polytopes are inverse to each other. The two operads give rise to new types of algebras with 3 generating operations, 11 relations, respectively 7 relations, that we call {\it associative trialgebras} and {\it dendriform trialgebras} respectively. The free dendriform trialgebra, which is based on planar trees, has an interesting Hopf algebra structure, which will be dealt with in another paper. Similarly the family of cubes gives rise to an operad which happens to be self-dual for Koszul duality.

On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. Moduli spaces of these objects are obtained with fixed generic polar parts at each singularity, which amounts to fixing a coadjoint orbit of the group . We prove that they carry complete hyper-Kähler metrics.

Let b ≥ 2 be an integer. We prove that the b-adic expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.

In the local, characteristic 0, non-Archimedean case, we consider distributions on GL(n + 1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from GL(n + 1) to GL(n). Similar theorems are obtained for orthogonal or unitary groups.

Summary Statistical issues arising in modelling univariate extremes of a random sample have been successfully used in the most diverse fields, such as biometrics, finance, insurance and risk theory. Statistics of univariate extremes (SUE), the subject to be dealt with in this review paper, has recently faced a huge development, partially because rare events can have catastrophic consequences for human activities, through their impact on the natural and constructed environments. In the last decades, there has been a shift from the area of parametric SUE, based on probabilistic asymptotic results in extreme value theory, towards semi‐parametric approaches. After a brief reference to Gumbel's block methodology and more recent improvements in the parametric framework, we present an overview of the developments on the estimation of parameters of extreme events and on the testing of extreme value conditions under a semi‐parametric framework. We further discuss a few challenging topics in the area of SUE. © 2014 The Authors. International Statistical Review © 2014 International Statistical Institute

This book uses techniques of Fourier and functional analysis to deal with certain problems in differential equations. The Fourier and functional analysis are merely tools; the authors' real interest lies in the differential equations that they study. It has been known since 1967 that a wide variety of sets {ewikt} of complex exponential functions play an important role in the control theory of systems governed by partial differential equations. However, this book is the first serious attempt to gather all of the available theory of these nonharmonic Fourier series in one place, combining published results with new results by the authors, to create a unique source of such material for practicing applied mathematicians, engineers and other scientific professionals.

A new very efficient linear algorithm for the segmentation of 8-connected digital curves is given. The simplicity comes from a definition of digital lines using a linear double diophantine inequality. A complete Pascal source code is given.