Mikhail Gromov

Mikhail Gromov is a mathematician whose work connects Riemannian geometry, symplectic geometry and geometric group theory. His 1985 paper introduced powerful methods based on J-holomorphic curves and established the ball-embedding obstruction underlying the Gromov non-squeezing theorem.^[ref]

The obstruction says that a standard symplectic ball of radius $R$ cannot fit symplectically into $B^2(r)\times {\mathbb{R}}^{2n-2}$ when $R>r$. In higher dimensions the target has infinite volume, so preserving volume is weaker than preserving the symplectic form. This gives a concrete example of the global rigidity his work uncovered. His IHES profile records his permanent professorship from 1982 to 2015 and subsequent emeritus status.^[ref] He received the 2009 Abel Prize.^[ref]