Seminars and Colloquia by Series

Thursday, May 3, 2012 - 16:00 , Location: Skiles 006 , Alan Diaz , Georgia Tech. , Organizer: Rafael de la Llave
In this introductory talk, we review the dynamical motivation for definingsymplectic manifolds, then describe a class of invariants called symplecticcapacities, which are closely related to both volume and the existence ofperiodic orbits. We explore the connections and differences between thesethree notions in the context of some basic phenomena/problems in symplecticgeometry: Gromov's nonsqueezing theorem, the difference between symplecticand volume-preserving diffeomorphisms, and the question of existence ofclosed characteristics on energy surfaces.
Wednesday, April 11, 2012 - 16:00 , Location: Skiles 005 , Mikel J. De Viana , Georgia Tech. , Organizer: Rafael de la Llave
In the 1990's Marina Ratner published a famous series of papers showing that ergodic measures invariant under unipotent flows over quotients $\Gamma/G$ are homogeneous. From this, she deduced many other remarkable properties for these flows (e.g that the closure of orbits are homogeneous and that orbits are uniformly distributed in their closures). To prove this result will require several lectures, but already the case of horocycle flow in $\Gamma/SL(2, \mathbb{R})$ presents several or her ideas. In this talk we will present the ideas of the proof in this case and present an application due to Margulis.