Differential Equations and Numerical Analysis Seminar - 29/02/2012

Wednesday, 29 February 2012, 12:00 p.m.

Lecturer: Philippe Didier - CMA, FCT/UNL

Title: "Séminaire Bourbaki": Henri Cartan's "Les Travaux de Koszul, part one".

Local: Room 1.5, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: This seminar is a presentation of a workgroup I would like to organize. The principal objective of this group would be to harvest the Séminaire Bourbaki for ideas for research projects in algebraic geometry and topology, differential topology, group theory, dynamical systems, differential equations or probability theory: targeting the early years of the Séminaire Bourbaki (1948 into the seventies) serves the dual purpose of accompanying some of those theories at the birth of their major developments and at the same time giving the elementary building blocks needed to understand the more recent works presented in the séminaire. There is a real  continuity between the modern séminaire and the one started by H. Cartan, A.Weil and É.Etc. The secondary objective is to further and solidify our mathematical culture in areas outside our research domains.

In this first session of the seminário semi-"Séminaire Bourbaki" we will follow the first part of Henri Cartan's presentation (see SB1) of J-L.
Koszul thesis (see Koszul): «Homology and cohomology of a compact Lie group can be studied directly on its Lie algebra (see Chevalley-Eilenberg). Following this method one can study Lie algebras on an arbitrary field; compacity hypothesis on the group are replaced by semi-simplicity ones on the algebra. This first session will introduce the elementary tools for this study and prove some of the first results obtained, in particular the theorem on the third Betti number.»