[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-957878","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 Connexions de Cartan et g\u00e9om\u00e9trie complexe homog\u00e8ne 2025-2026\n\u003C\/h2\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n 6\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 2\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\u003E20\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\u003EUne formation M1-M2 de base en g\u00e9om\u00e9trie diff\u00e9rentielle, en groupes de Lie ou en g\u00e9om\u00e9trie complexe.\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 de ce cours est d\u0027introduire \u00e0 la th\u00e9orie d\u0027Elie Cartan concernant l\u0027existence de structures g\u00e9om\u00e9triques non rigides et leur \u00e9quivalence \u00e0 diff\u00e9omorphisme pr\u00e8s, par l\u0027exploration alg\u00e9brique de certains syst\u00e8mes de formes diff\u00e9rentielles. On commencera par pr\u00e9senter la th\u00e9orie des connexions lin\u00e9aires, affines, projectives, conformes, etc., qui s\u0027unifie dans le concept de connexion de Cartan, \u00e0 valeurs dans l\u0027alg\u00e8bre de Lie d\u0027un mod\u00e8le maximal. On pr\u00e9sentera ensuite deux m\u00e9thodes d\u0027\u00e9quivalence : celle due \u00e0 Cartan, puis la m\u00e9thode des s\u00e9ries formelles. Ce cours comportera une composante de g\u00e9om\u00e9trie alg\u00e9brique complexe effective, car les structures g\u00e9om\u00e9triques homog\u00e8nes recherch\u00e9es s\u0027organisent le plus souvent en espaces de modules, qui sont certaines vari\u00e9t\u00e9s alg\u00e9briques complexes explicites.\u003C\/p\u003E\n\u003Cp\u003EThe objective of this course is to introduce Elie Cartan\u0027s theory concerning the existence of non-rigid geometric structures and their equivalences up to diffeomorphism, through the algebraic exploration of certain systems of differential forms. We will begin by presenting the theory of linear, affine, projective, conformal, etc., connections, which is unified in the concept of Cartan connection, with values \u200b\u200bin the Lie algebra of a maximally symmetric model. We will then present two equivalence methods: the Cartan method and the formal power series method. This course will include a component in effective complex algebraic geometry, since the sought homogeneous geometric structures are most of the times organized into moduli spaces, which are certain explicit complex algebraic varieties.\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\u003EBibliographie\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003E\u003Cp\u003E[*] Chern, S. S.; Chen, W. H.; Lam, K. S.: Lectures on differential geometry. World Scientific, 1999, x+356 pp. [*] Merker, J.; Nurowski, P.: Homogeneous CR and para-CR structures in dimensions 5 and 3: a survey, J. Geom. Anal. 34 (2024), Paper No. 27, 50 pp. [*] Kobayashi, S.; Nomizu, K.: Foundations of differential geometry. Vol I. Interscience Publishers, 1963. xi+329 pp. [*] Olver, P.J.: Equivalence, Invariants and Symmetry. Cambridge University Press, 1995, xvi+525 pp. [*] Sharpe, R. W.: Differential geometry. Cartan\u0027s generalization of Klein\u0027s Erlangen program. Graduate Texts in Mathematics, 166. Springer-Verlag, 1997, xx+421 pp.\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\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003EEvaluation Terminale\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}]