earlier work on Yang-Mills connections, and Uhlenbeck and Jonathan Sack's work on harmonic maps. In the time since Sacks, Uhlenbeck, and Gromov's work, such bubbling phenomena has been found in a number of other geometric contexts. The corresponding compactness theorem encoding the bubbling allowed Gromov to arrive at a number of analytically deep conclusions on existence of pseudo-holomorphic curves. A particularly famous result of Gromov's, arrived at as a consequence of the existence theory and the monotonicity formula for minimal surfaces, is the "non-squeezing theorem," which provided a striking qualitative feature of symplectic geometry. Following ideas of Edward Witten, Gromov's work is also fundamental for Gromov-Witten theory, which is a widely studied topic reaching into string theory, algebraic geometry, and symplectic geometry. From a different perspective, Gromov's work was also inspirational for much of Andreas Floer's work. Yakov Eliashberg and Gromov developed some of the basic theory for symplectic notions of convexity. They introduce various specific notions of convexity, all of which are concerned with the existence of one-parameter families of diffeomorphisms which contract the symplectic form. They show that convexity is an appropriate context for an h-principle to hold for the problem of constructing certain symplectomorphisms. They also introduced analogous notions in contact geometry; the existence of convex contact structures was later studied by Emmanuel Giroux. Prizes and honors Prizes Prize of the Mathematical Society of Moscow (1971) Oswald Veblen Prize in Geometry (AMS) (1981) Prix Elie Cartan de l'Academie des Sciences de Paris (1984) Prix de l'Union des Assurances de Paris (1989) Wolf Prize in Mathematics (1993) Leroy P. Steele Prize for Seminal Contribution to Research (AMS) (1997) Lobachevsky Medal (1997) Balzan Prize for Mathematics (1999) Kyoto Prize in Mathematical Sciences (2002) Nemmers Prize in Mathematics (2004) Bolyai Prize in 2005 Abel Prize in 2009 "for his revolutionary contributions to geometry" Honors Invited speaker to International Congress of Mathematicians: 1970 (Nice), 1978 (Helsinki), 1983 (Warsaw), 1986 (Berkeley) Foreign member of the National Academy of Sciences (1989), the American Academy of Arts and Sciences (1989), the Norwegian Academy of Science and Letters, and the Royal Society (2011) Member of the French Academy of Sciences (1997) Delivered the 2007 Paul Turán Memorial Lectures. See also Cartan–Hadamard conjecture Cartan–Hadamard theorem Collapsing manifold Lévy–Gromov inequality Taubes's Gromov invariant Mostow rigidity theorem Ramsey–Dvoretzky–Milman phenomenon Systoles of surfaces Publications Books Major articles Notes References Marcel Berger, "Encounter with a Geometer, Part I", AMS Notices,