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The Abel Prize is an international award for outstanding work in mathematics, named after Niels Henrik Abel. It was first awarded in 2003 to Jean-Pierre Serre. The Norwegian Academy of Science and Letters administers the selection.^[ref]

The mathematical work behind an award is more informative than the honour alone. The 2009 award recognized Mikhail Gromov's contributions to geometry and topology, including global geometric questions whose behaviour cannot be read from local coordinates alone.^[ref] The 2021 award to László Lovász and Avi Wigderson recognized contributions connecting discrete mathematics and theoretical computer science.^[ref] The prize's scope therefore spans several mathematical traditions.

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]

By Mikhail Gromov.

Verified locator: Inventiones Mathematicae 82 (1985), 307–347; section 0.3.A, Corollary, printed page 310: symplectic ball embedding obstruction.