Thursday, 22 April 1999, 4:00 pm
Mathematics Bldg., lecture hall 2
Professor Leonid Polterovich
"Symplectic rigidity in Ergodic Theory"
It was proved by Liouville that dynamical systems of Classical Mechanics preserve the volume in the phase space. Later on it was noticed that in fact there exists a more delicate invariant -- a differential 2-form called the symplectic structure. The preservation of volume by mechanical motions has been attracting a lot of attention for more than a century. It served as the main stimulating force for the creation of Ergodic Theory - a mathematical discipline which studies various recurrence properties of measure preserving transformations. However the significance of the role played by the invariant 2-form has only been noticed relatively recently. An attempt to understand the difference between mechanical motions and general volume preserving diffeomorphisms gave rise to the fast developing field of Symplectic Topology which investigates surprising rigidity phenomena appearing in the theory of symplectic manifolds and their morphisms.
What are the ergodic consequences of symplectic rigidity? Do new powerful symplectic methods help us in the understanding of the ergodic world? In the talk we discuss some of the first steps in this direction.
Coffee, Cookies, Company at the faculty lounge at 3:30.