Search results for "Géométrie"
showing 10 items of 24 documents
Etude asymptotique et transcendance de la fonctionvaleur en contrôle optimal. Catégorie log-exp en géométrie sous-Riemannienne dans le cas Martinet.
2000
The main subject of this work is the study and the role ofabnormal trajectories in optimal control theory.We first recall some fundamental results in optimal control. Thenwe investigate the optimality of abnormal trajectories forsingle-input affine systems with constraint on the control, firstfor the time-optimal problem, and then for any cost, the finaltime being fixed or not.Using such an affine system,we extend this theory to sub-Riemannian systems of rank 2.These results show that, under general conditions, an abnormaltrajectory is \it{isolated} among all solutions of the systemhaving the same limit conditions, and thus is \it{locallyoptimal}, until a first \it{conjugate point} which ca…
Perdre le fil: labyrinthes de la littérature française moderne
2009
From the day when Theseus killed the Minotaur, the Maze turned into a form in search of meaning, and became useless. As a result, one was enjoined to ascribe nw meanings to the empty strcuture. Modern writers, when confronted with such a void, will have explored all its possibilities: while some of them, like Michel Butor, dismiss the sacred dimensions, others, like Serge Doubrovsky, see in it the image of the self (the body, the psyche...), and others still, like Raymond Roussel, Alain Robbe-Grillet or Georges Pererc, make of the pure geometrical structure of the labyrinth an aesthetic model, and thus a mirror of the work of art. However, one still have to ask whether the labrinth is a val…
Geometry of the projectivization of ideals and applications to problems of birationality
2018
In this thesis, we interpret geometrically the torsion of the symmetric algebra of the ideal sheaf I_Z of a scheme Z defined by n+1 equations in an n-dimensional variety. This is equivalent to study the geometry of the projectivization of I_Z. The applications of this point of view concern, in particular, the topic of birational maps of the projective space of dimension 3 for which we construct explicit birational maps that have the same algebraic degree as their inverse, free and nearly-free curves for which we generalise a characterization of free curves by extending the notion of Milnor and Tjurina numbers. We tackle also the topic of homaloidal hypersurfaces, our original motivation, fo…
From resurgent functions to real resummation through combinatorial Hopf algebras
2014
Pas de résumé en anglais.
Actions de tores algébriques sur des corps de caractéristique zéro
2023
Over an algebraically closed field of characteristic zero, normal affine varieties endowed with an effective torus action were described by Altmann and Hausen in 2006 by a geometrico-combinatorial presentation.Using Galois descent tools, we extend this presentation to the case where the ground field is an arbitrary field of characteristic zero. In this context, the acting torus may be non split and may have non-trivial torsors, thus we need additional data to encode such varieties. We provide some situations where the generalized Altmann-Hausen presentation simplifies. For instance, if the acting torus is split, we recover mutatis mutandis the original Altmann-Hausen presentation. Finally, …
La morphologie des tissus urbains et périurbains à travers une lecture fractale
2005
Urban expansion produces an irregular urban fabric. This phenomenon influences areas which are distant from urban centres, a problem for sustainable development. Solutions proposed to reduce urban expansion are modelled on the pattern of the compact town. Generally, it is believed that these solutions are unacceptable to the people concerned. In this article we present an alternative approach to the study of urban fabric, which shows that, despite their irregular form, it is possible to describe their development using fractal analysis. This permits understanding of the socio-economic causes of this process and the development an alternative conceptual approach to the management of urban ex…
Instanton Counting, Quantum Geometry and Algebra
2020
The aim of this memoir for "Habilitation \`a Diriger des Recherches" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by instantons. We start with a brief summary of the equivariant localization of the instanton moduli space, and show how to obtain the instanton partition function and its generalization to quiver gauge theory and supergroup gauge theory in three ways: the equivariant index formula, the contour integral formula, and the combinatorial formula. We then explore the geometric description of $\mathcal{N} = 2$ gauge theory based on Seiberg-Witten geometry together with it…
Real Algebraic Geometry
2011
144 Pages; Cet ouvrage constitue les actes de la conférence de Géométrie Algébrique Réelle qui a eu lieu à Rennes du 20 au 24 Juin 2011
Transport optimal sur les structures sous-Riemanniennes admettant des géodésiques minimisantes singulières
2017
This thesis is devoted to the study of the Monge transport problem for the quadratic cost in sub-Riemannian geometry and the essential conditions to obtain existence and uniqueness of solutions. These works consist in extending these results to the case of sub-Riemannian structures admitting singular minimizing geodesics. In a first part, we develop techniques inspired by works by Cavalletti and Huesmann in order to obtain significant results for structures of rank 2 in dimension 4. In a second part, we study analytical tools of the h-semiconcavity of the sub-Riemannian distance and we show how this type of regularity can lead to the well-posedness of the Monge problem in general cases.
Análisis de la adecuación de libros de texto de E. Primaria a la enseñanza a estudiantes de altas capacidades matemáticas
2013
Un problema al que se enfrentan los profesores de matemáticas de Enseñanza Primaria es la necesidad de hacer adaptaciones en sus programaciones para ofrecer una educación adecuada a sus alumnos de altas capacidades matemáticas. Las editoriales de libros de texto de matemáticas de estos niveles educativos ofrecen diversas soluciones que, usualmente, consisten en incluir, en el libro del alumno, algunos problemas más difíciles y, en la documentación del profesor, una propuesta de problemas de ampliación. Una cuestión que se plantea al analizar un libro de texto de matemáticas es valorar cómo de útil puede ser el material proporcionado por la editorial (libro de texto y materiales complementar…