The Hofer question on intermediate symplectic capacities
  Roughly twenty five years ago Hofer asked: can the cylinder B^2(1) \times \mathbb{R}^{2(n-1)} be symplectically embedded into B^{2(n-1)}(R) \times \mathbb{R}^2 for some R>0? We show that this is the case if R \geq \sqrt{2^{n-1}+2^{n-2}-2}. We deduce that there are no intermediate capacities, between 1-capacities, first constructed by Gromov in 1985, and n-capacities, answering another question of Hofer. In 2008, Guth reached the same conclusion under the additional hypothesis that the intermediate capacities should satisfy the exhaustion property. 
Alvaro Pelayo and San Vu Ngoc
math.SG math.DS