Institute of Mathematical Sciences in New York since 1996. He adopted French citizenship in 1992. Work Gromov's style of geometry often features a "coarse" or "soft" viewpoint, analyzing asymptotic or large-scale properties. He is also interested in mathematical biology, the structure of the brain and the thinking process, and the way scientific ideas evolve. Motivated by Nash and Kuiper's isometric embedding theorems and the results on immersions by Morris Hirsch and Stephen Smale, Gromov introduced the h-principle in various formulations. Modeled upon the special case of the Hirsch–Smale theory, he introduced and developed the general theory of microflexible sheaves, proving that they satisfy an h-principle on open manifolds. As a consequence (among other results) he was able to establish the existence of positively curved and negatively curved Riemannian metrics on any open manifold whatsoever. His result is in counterpoint to the well-known topological restrictions (such as the Cheeger–Gromoll soul theorem or Cartan–Hadamard theorem) on geodesically complete Riemannian manifolds of positive or negative curvature. After this initial work, he developed further h-principles partly in collaboration with Yakov Eliashberg, including work building upon Nash and Kuiper's theorem and the Nash–Moser implicit function theorem. There are many applications of his results, including topological conditions for the existence of exact Lagrangian immersions and similar objects in symplectic and contact geometry. His well-known book Partial Differential Relations collects most of his work on these problems. Later, he applied his methods to complex geometry, proving certain instances of the Oka principle on deformation of continuous maps to holomorphic maps. His work initiated a renewed study of the Oka–Grauert theory, which had been introduced in the 1950s. Gromov and Vitali Milman gave a formulation of the concentration of measure phenomena. They defined a "Lévy family" as a sequence of normalized metric measure spaces in which any asymptotically nonvanishing sequence of sets can be metrically thickened to include almost every point. This closely mimics the phenomena of the law of large numbers, and in fact the law of large numbers can be put into the framework of Lévy families. Gromov and Milman developed the basic theory of Lévy families and identified a number of examples, most importantly coming from sequences of Riemannian manifolds in which the lower bound of the Ricci curvature or the first eigenvalue of the Laplace–Beltrami operator diverge to infinity. They also highlighted a feature of Lévy families in which any sequence of continuous functions