On the length of shortest closed geodesics and shadows of symplectic balls 

Alberto Abbondandolo (Bochum)


Abstract: How long can the shortest closed geodesic on a 2-sphere be? And how small 
can the projection of a symplectic ball onto a 2k-dimensional symplectic subspace be? 
I will show how these seemingly unrelated problems can be viewed as particular instances 
of a general question concerning the ``systolic ratio'' of a contact form. 
The Mahler conjecture in convex geometry is another instance of this general question. 
This talk is based on a joint work with Barney Bramham, Umberto Hryniewicz and Pedro Salomao.