[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-957860","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Groupes et G\u00e9om\u00e9tries 2025-2026\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          15\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semester 1\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E50\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ETravaux dirig\u00e9s :\u003C\/span\u003E\n                                      \u003Cspan\u003E25\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                            \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ELes \u00e9tudiants devront ma\u00eetriser le contenu du cours acc\u00e9l\u00e9r\u00e9 \u0022Vari\u00e9t\u00e9s diff\u00e9rentielles et formes diff\u00e9rentielles\u0022.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EL\u0027objectif du cours est de donner une formation g\u00e9n\u00e9rale en groupes de Lie et g\u00e9om\u00e9trie riemannienne. Les \u00e9tudiants seront suppos\u00e9s ma\u00eetriser le contenu du cours acc\u00e9l\u00e9r\u00e9 de g\u00e9om\u00e9trie diff\u00e9rentielle.\u003Cbr\u003E\nOn abordera les sujets suivants :\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EGroupes et alg\u00e8bres de Lie, espaces homog\u00e8nes.\u003C\/li\u003E\n\u003Cli\u003EFibr\u00e9s vectoriels et principaux, connexions, torsion et courbure.\u003C\/li\u003E\n\u003Cli\u003EG\u00e9om\u00e9trie riemannienne : Connexion de Levi-Civita, g\u00e9od\u00e9siques, th\u00e9or\u00e8me de Hopf-Rinow, courbures, formules de variation, champs de Jacobi, th\u00e9or\u00e8me de Cartan-Hadamard, th\u00e9or\u00e8mes de comparaison, g\u00e9om\u00e9trie riemanniennes de courbure n\u00e9gative ou nulle\u003C\/li\u003E\n\u003Cli\u003EEspaces sym\u00e9triques et classification des espaces sym\u00e9triques de type non compact.\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003EThe aim of the course is to provide general training in Lie groups and Riemannian geometry. Students will be assumed to have mastered the content of the accelerated course in differential geometry.\u003Cbr\u003E\nThe following topics will be covered:\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ELie groups and algebras, homogeneous spaces.\u003C\/li\u003E\n\u003Cli\u003EVector bundles and principal bundles, connections, torsion and curvature.\u003C\/li\u003E\n\u003Cli\u003ERiemannian geometry: Levi-Civita connection, geodesics, Hopf-Rinow theorem, curvatures, variation formulas, Jacobi fields, Cartan-Hadamard theorem, comparison theorems, Riemannian geometry in non-positive curvature.\u003C\/li\u003E\n\u003Cli\u003ESymmetric spaces and classification of non-compact symmetric spaces.\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003ES. Gallot, D. Hulin, J. Lafontaine : Riemannian geometry. Universitext. Springer-Verlag, 1990\u003C\/li\u003E\n\u003Cli\u003EW.P.A. Klingenberg : Riemannian geometry. 2nd edition. De Gruyter Studies in Mathematics 1. 1995\u003C\/li\u003E\n\u003Cli\u003EJ. Cheeger, D.G. Ebin : Comparison theorems in Riemannian geometry. Revised reprint of the 1975 original. AMS Chelsea Publishing, Providence, RI. 2008\u003C\/li\u003E\n\u003Cli\u003ES. Helgason : Differential geometry, Lie groups and symmetric spaces. Academic press, 1978\u003C\/li\u003E\n\u003Cli\u003EJ.P. Serre : Alg\u00e8bres de Lie semi-simples complexes (French). W. A. Benjamin Inc. New-York 1966\u003C\/li\u003E\n\u003Cli\u003EJ.P. Serre : Lie algebras and lie groups. Lectures given at Harvard University, 1964. W. A. Benjamin Inc. New-York 1965\u003C\/li\u003E\n\u003Cli\u003EA.W. Knapp : Lie groups beyond an introduction. 2nd edition. Progress in mathematics, 140. Birkhauser 2002\u003C\/li\u003E\n\u003Cli\u003EM.R. Bridson, A. Haefliger : Metric spaces of non-positive curvature. Grundlheren der Mathematischen Wissenschaften, 319. Springer\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]