Deblogging $b^m$-Symplectic manifolds : Going to infinity and coming back

Vendredi 18 novembre 2016 14:00-15:00 - Eva Miranda - Barcelone

Résumé : Several problems in celestial mechanics (like the elliptic restricted 3-body problem) and their singularities (« collisions ») can be described using symplectic forms away from a critical set ( known in the literature of celestial mechanics as the line at infinity or the collision manifold). In these examples the symplectic form either vanishes or goes to infinity along the critical set. It is possible to give a global description of these objects using $b^m$-symplectic forms and folded symplectic forms.
In this talk we will explain a desingularization procedure called deblogging which associates a family of symplectic forms or folded symplectic forms to a given $b^m$·-symplectic form depending on the parity of $m$. Time permitting, several applications of this procedure will be discussed. This talk is based on joint work with Victor Guillemin and Jonathan Weitsman.

Lieu : Petit Amphi

Deblogging $b^m$-Symplectic manifolds : Going to infinity and coming back  Version PDF