Professor Leonid Polterovich
(Tel Aviv University)
"Symplectic maps: algebra, geometry, dynamics"
Abstract: Symplectic maps appear as a natural generalization of area-preserving diffeomorphisms of surfaces. They play a central role in the mathematical model of classical mechanics.
We will focus on the following topics:
(a) growth rate of symplectic maps and the trichotomy hyperbolic/parabolic/elliptic in the context of diffeomorphisms;
(b) obstructions to symplectic actions of finitely generated groups, including a symplectic version of the Zimmer program on actions of lattices.
We describe recent progress in these directions based on modern methods of symplectic topology.