ieu: IHP, salle 201.
11:00 Anna Florio (Jussieu)
On the set of zero torsion for twist maps of the annulus..
Abstract: For a C^1 diffeomorphism f:A-->A isotopic to the identity, the torsion of a point x is the limit of the average rotational velocity of tangent vectors in T_xA under the action of the linearized dynamical system. For twist maps on the annulus (not necessarily conservative) we will show that on every C^1 essential curve there is at least one point of zero torsion. As an outcome, we will deduce that the Hausdorff dimension of the set of points of zero torsion is greater or equal 1.
14:15 Emmanuel Giroux (ENS)
From Morse functions to Lefschetz fibrations on cotangent bundles.
Abstract: the main goal of the talk is to prove the following theorem: any Morse
function on a closed manifold extends to a symplectic Lefschetz fibration on the
cotangent bundle which has the same critical points and is equivariant under the
actions of the fiberwise antipodal involution and the complex conjugation. If
time permits, after explaing some geometric consequences of this result, we will
discuss a number of realted questions and potential applications.
16:00 Lev Buhovsky (Tel Aviv)
Bounding the Poisson bracket invariant on surfaces.
Abstract: I will discuss the Poisson bracket invariant of a cover, which was introduced by L. Polterovich.
Initially, this invariant was studied via Floer theory, and lower bounds for it were established in
some situations. I will try to explain how one can obtain the conjectural lower bound in dimension 2,
using only elementary arguments. This is a joint work with A. Logunov and S. Tanny, with a
contribution of F. Nazarov.
Prochaines séances: 6 mars (Bertelson, De Groote, ?), 3 avril (Fermé, ? , ?)
Autre activité symplectique à Paris:
Séminaire Nantes-Orsay
