Symetry methods in geometrics mechanics  Tudor Ratiu

Author: Tudor Ratiu
Institution: Section de Mathematiques, Faculté des Sciences de Base EPFL, Lausanne, Switzerland
Website: http://cag.epfl.ch/page39504en.html
Video: http://www.youtube.com/watch?v=Dwk4U9jrGPM
Slides: Ratiu_symmetry methods.pdf
Presentation: https://www.see.asso.fr/node/14276
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
The goal of these lectures is to show the influence of symmetry in various aspects of theoretical mechanics. Canonical actions of Lie groups on Poisson manifolds often give rise to conservation laws, encoded in modern language by the concept of momentum maps. Reduction methods lead to a deeper understanding of the dynamics of mechanical systems. Basic results in singular Hamiltonian reduction will be presented. The Lagrangian version of reduction and its associated variational principles will also be discussed. The understanding of symmetric bifurcation phenomena in for Hamiltonian systems are based on these reduction techniques. Time permitting, discrete versions of these geometric methods will also be discussed in the context of examples from elasticity.References
 Demoures, F., GayBalmaz, F., Ratiu, T.S.: Multisymplectic variational integrators and space/time symplecticity, Communications in Analysis and Applications (2015), to appear
 GayBalmaz, F., Ratiu, T.S.: The geometric structure of complex fluids, Advances in Applied Mathematics, 42 (2009), 176275
 GayBalmaz, F., Marsden, J.E., Ratiu, T.S.: Reduced variational formulations in free boundary continuum mechanics, Journ. Nonlinear Sci., 22 (2012), 463497
 Libermann, P., Marle, C.M.: Symplectic Geometry and Analytical Mechanics. Symplectic Geometry and Analytical Mechanics. D. Reidel Publishing Company, Dordrecht (1987)
 Marsden, J.E, Ratiu, T.S.: Introduction to Mechanics and Symmetry, Texts in Applied Mathematics 17, second edition, Springer Verlag, (1998)
 Marsden, J.E, Misiolek, G., Ortega, J.P., Perlmutter, M., Ratiu, T.S.: Hamiltonian Reduction by Stages, Springer Lecture Notes in Mathematics, 1913, SpringerVerlag, New York (2007)
 Marsden J.E, West M.: Discrete mechanics and variational integrators, Acta Numer., 10 (2001), 357–514.
 Ortega, J.P., Ratiu, T.S.: Momentum Maps and Hamiltonian Reduction, Progress in Mathematics 222, Birkh"auser, Boston (2004)
Bio:
 BA in Mathematics, University of Timisoara, Romania, 1973
 MA in Applied Mathematics, University of Timisoara, Romania, 1974
 Ph.D. in Mathematics, University of California, Berkeley, 1980
 T.H. Hildebrandt Research Assistant Professor, University of Michigan, Ann Arbor, USA 19801983
 Associate Professor of Mathematics, University of Arizona, Tuscon, USA 19831988
 Professor of Mathematics, University of California, Santa Cruz, USA, 19882001
 Chaired Professor of Mathematics, Ecole Polytechnique Federale de Lausanne, Switzerland, 1998  present
 Professor of Mathematics, Skolkovo Institute of Science and Technonology, Moscow, Russia, 2014  present