GROMOV, MIKHAEL / Mathematics / Researchers

International Center for Scientific Research


Mathematics / GROMOV, MIKHAEL


Permanent Professor, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France.

Research interests

Gromov\'s work concerns geometry and topology of partial differential equations, Riemannian, sub-Riemannian and sympletic geometry, asymptotic theory of infinite groups and geometro-combinatorial aspects of probability.

Prizes and awards

Kyoto Prize in Basic Sciences, 2002;
Balzan Prize, 1999;
Leroy P. Steele Prize for a Seminal Contribution to Research American Mathematical Society, 1997;
Lobatchewski Medal, 1997;
Wolf Prize, 1993;
Honorary Doctorate, University of Geneva, 1992;
Elie Cartan Prize, French Academy of Sciences, 1984;
Oswald Veblen Prize in Geometry, American Mathematical Society, 1981;
Moscow Mathematical Society Prize, 1971.

Affiliations: Academy of Science, American Academy of Arts and Sciences, French Academy of Sciences.


Isometrical immersions, hyperbolic geometry and Burago\'s isoperimetric inequality, preprint SUNY. (2002).

Local and global in Geometry, Preprint IHES. (2002).

Small cancellation, unfolded hyperbolicity, and transversal measures, to appear in a volume dedicated to Andre Haefliger. (2002).

Isoperimetry of waists and concentration of maps, Preprint IHES. (2002).

Random walk in random groups, IHES (2001).
CAT(kappa)-space: construction and concentration (to Victor Abramovich Zalgaller), preprint IHES, January 2001.

(with Carbone) Mathematical slices of molecular biology, Numero special La Gazette des Mathematiciens, 88:11-80, Societe Mathematique de France (2001).

(with Carbone) Functional labels and syntactic entropy on DNA strings and proteins, IHES 2001.

Mesoscopic curvature and hyperbolicity, Proceedings of the International Congress on Differential Geometry 2000, to appear in Contemporary Mathematics series.

Interview: Mikhael Gromov 1, 213, Development of Mathematics 1950-2000, edited by Jean-Paul pier, Boston, MA, Birkhauser (2000).

Pattern formation in Biology, Vision and Dynamics, (with A. Carbone and P. Prusinkiewicz) publiblished by World Scientific Publishing Co. Pte. Ltd (2000).

Spaces and questions, GAFA, Geom. Funct. Anal., Special Volume (2000), 118-161.

Endomorphisms of symbolic algebraic varieties, J. Europ. Math. Soc. (1999), 109-197.

Topological invariants of dynamical systems and spaces of harmonic maps, Math. Phys. Anal. and Geom. 00 : 1-93 (1999).

Metric structures for Riemannian and non-Riemannian spaces, Birkhauser (1999).

Quantitative homotopy theory, Rossi, Hugo (ed.), Prospects in mathematics. Invited talk on the occasion of the 250(th) anniversary of Princeton University. Papers from the conference, Princeton, NJ, USA, March 17-21, 1996.

Providence, NJ, USA, American Mathematical Society, 45-49 (1999).

Lagrangian Intersection theory: Finite dimensiona approach, Amer. Math. Soc. Transl. (2) 186 (1998), 27-118.

Possible trends in mathematics in coming decades, Notices AMS 45 : 7 (1998), 846-847.

Holomorphic L2 - functions on coverings of pseudo-convex coverings (with G. Henkin and M. Shubin), GAFA 8 (1998), 552-585.

Lagrangian intersections and the stable Morse theory. (with Y. Eliashberg) Boll. Unione Mat. Ital., VII. Ser., B 11 Suppl.(1997), 289-326.

Systoles and intersystolic inequalities, Seminaires et Congres Soc. Math. France 1 (1996), 291-362.

Erratum to: \"Von Neumann spectra near zero\" (with M. Shubin) Geom. Anal. Funct. Anal. 5 (1995), 729.

L(2) holomorphic functions on pseudo-convex coverings. (with G. Henkin, M. Shubin)in Operator theory for complex and hypercomplex analysis.

Ramirez de Arellano ed. Proc. conf., Mexico City, Mexico, December 12--17, 1994 Amer. Math. Soc. Contemp. Math. 212 (1998), 81-94.

The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets (with M. Shubin) Inventiones Math. 117 (1994), 165-180.
Metric Invariants of Kahler manifolds, Proc. Workshop on J. Differential Geom. and Topology, Alghero, Italy 20-26 June, 1992 Caddeo, Tricerri ed. World Sci. (1993), 90-117.

Geometric reflections on the Novikov conjecture, Lecture notes taken by J. Rosenberg, Oberwolfach (1993) a paraitre dans Proc. Conference on the Novikov Conjecture.

The Riemann-Roch theorem for elliptic operators (with M. Shubin) I.M. Gelfand Seminar. Part 1: Papers of the Gelfand seminar in funct. anal. Moscow Univ., Russia, September 1993. Gelfand, S. ed. et al., translated from Adv. Sov. Math. 16 (1993), 211-241 Amer. Math. Soc., Providence.

Asymptotic invariants of infinite groups. Geometric group theory. Volume 2 Proc. Symp. Sussex Univ., Brighton, July 14-19, 1991 Lond. Math. Soc. Lecture Notes 182 Niblo and Roller ed., Cambridge Univ. Press, Cambridge(1993), 1-295.

Group cohomology with Lipschitz control and higher signatures (with A. Connes, H. Moscovici) Geom. Anal. Funct. Anal. 3 (1993), 1-78.

Positive curvature, macroscopic dimension, spectral gaps and higher signatures. in Functional analysis on the eve of the 21st century, Gindikin, Simon (ed.) et al. Volume II. In honor of the eightieth birthday of I. M. Gelfand. Proc. conf. Rutgers Univ., New Brunswick, NJ, USA, October 24-27, 1993. Prog. Math. 132 (1996), 1-213, Birkhauser, Basel.

Stability and pinching, Seminari di Geometria, Ferri Ed., Bologna (1992), 55-99.

Nilpotent structures and invariant metric on collapsed manifolds, (with J. Cheeger, K. Fukaya), J. Amer. Math. Soc. 5 (1992), 327-372.

Carnot-Caratheodory spaces seen from within. Proc. Journees nonholonomes: geometrie sous-riemannienne, theorie du controle, robotique, Paris, France, June 30--July 1, 1992 A. Bellaiche ed., Prog. Math. 144 (1996), 79-323, Birkhauser, Basel.

A.D. Alexandrov\'s spaces with curvature bounded from below, (with Y. Burago and G. Perel\'man) in Russ. Math. Surv. 47 2 (1992), 1-58.

Embeddings of Stein manifolds, (with Y. Eliashberg) Ann. Math. 136 (1992), 123-135.

The Riemann-Roch theorem for general elliptic operators, (with M. Shubin) C R Acad. Sci. Paris 314 (1992), 363-367.

Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, (with R. Schoen), Publ. Math. IHES 76 (1992), 165-246.

Spectral geometry of semi-algebraic sets, in Ann. Inst. Fourier 42 (1992), 249-274.

Chopping Riemannian manifolds (with J. Cheeger) J. Differential Geom. 52 (1991), 85-94.

Lectures on the transformation groups: geometry and dynamics, (with G. d\'Ambra) J. Differential Geom. Suppl. 1 (1991), 19-111.

Foliated plateau problem, parts I, II, Geom. Anal. Functional Anal. 1(1991), 14-79 ; idem 1 (1991), 253-320.

Convex symplectic manifolds, (with Y. Eliashberg) Proc. Symp. Pure Math. 52 (1991), Part 2, 135-162.

Sign and geometric meaning of curvature, Rend. Semin. Mat. Fis. Milano 61 (1991), 9-123.

Rigidity of Lattices : an Introduction, (with P. Pansu) Lect. Notes in Math. Springer-Verlag 1504 (1991), 39-138.

Von Neumann spectra near zero, (with M. Shubin) Geom. Anal. Functional Anal. 1 (1991), 375-404..
Near cohomology of Hilbert complexes, (with M. Shubin) preprint ETH 1991.

Kahler hyperbolicity and L(2)-Hodge theory, J. Differential Geom. 33 (1991), 263-292.

Cell division and hyperbolic geometry, prepublication IHES 1990.

Convex sets and Kahler manifolds, in Advances in J. Differential Geom., F. Tricerri ed., World Sci., Singapore. (1990), 1-38.

Collapsing Riemannian manifolds II, (with J. Cheeger), J. Differential Geom. 32 (1990), 269-298.

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