Title: 
Contact non-squeezing at the quantum scale

Abstract:
Gromov's famous non-squeezing theorem states
that the standard symplectic ball cannot be symplectically
squeezed into the cylinder of smaller radius.
We discuss an analogue of this result in contact geometry
as well as its link to the existence of a natural partial order
on the group of contact transformations. The talk is based
on a joint work with Y. Eliashberg and S.-S. Kim.