Actions of Lie groups and Lie algebras on symplectic and Poisson manifolds. Application to Lagrangian and Hamiltonian systems  CharlesMichel Marle

Author: CharlesMichel Marle
Institution: Professeur honoraire à l'Université Pierre et Marie Curie, Institut Mathématique de Jussieu, Correspondant de l’Académie des Sciences, Paris, France.
Website: http://charlesmichel.marle.pagespersoorange.fr/
Video: http://www.youtube.com/watch?v=qdySpxlolrM
Slides: Marle_Actions of Lie Groups algebras.pdf
Presentation: https://www.see.asso.fr/node/13649
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
I will present some tools in Symplectic and Poisson Geometry in view of their applications in Geometric Mechanics and Mathematical Physics. Lie group and Lie algebra actions on symplectic and Poisson manifolds, momentum maps and their equivariance properties, first integrals associated to symmetries of Hamiltonian systems will be discussed. Reduction methods taking advantage of symmetries will be discussed.References :
 Abraham, R., Marsden, J.E.: Foundations of Mechanics, 2nd edn. AddisonWesley, Reading (1978).
 Arnold, V.I.: Mathematical methods of Classical Mechanics, 2nd edn. Springer, New York (1978).
 Ganghoffer, J.F., Maldenov, E. (editors): Similarity and Symmetry Methods; Applications in Elasticity and mechanics of Materials. Lecture Notes in Applied and Computational Mechanics 73, Springer, Heidelberg (2014).
 Guillemin, V., Sternberg, S.: Symplectic Techniques in Physics. Cambridge University Press, Cambridge (1984).
 LaurentGengoux, C., Pichereau, A., Vanhaecke, P.: Poisson structures. Springer, Berlin (2013).
 Libermann, P., Marle, C.M.: Symplectic Geometry and Analytical Mechanics. Symplectic Geometry and Analytical Mechanics. D. Reidel Publishing Company, Dordrecht (1987)
Bio:
CharlesMichel Marle was born in 1934; He studied at Ecole Polytechnique (19531955), Ecole Nationale Supérieure des Mines de Paris (19571958) and Ecole Nationale Supérieure du Pétrole et des Moteurs (19571958). He obtained a doctor's degree in Mathematics at the University of Paris in 1968. From 1959 to 1969 he worked as a research engineer at the Institut Français du Pétrole. He joined the Université de Besançon as Associate Professor in 1969, and the Université Pierre et Marie Curie, first as Associate Professor (1975) and then as full Professor (1981). His resarch works were first about fluid flows through porous media, then about Differential Geometry, Hamiltonian systems and applications in Mechanics and Mathematical Physics.