Mikhail Gromov

Mikhail Gromov
Name	Mikhail Gromov
Birth date	1943
Birth place	Boksitogorsk, Leningrad Oblast
Nationality	Russian-French
Fields	Mathematics
Alma mater	Moscow State University
Doctoral advisor	Israel Gelfand

Mikhail Gromov is a Russian-French mathematician renowned for transformative work in differential geometry, symplectic topology, geometric group theory, and global analysis. His research introduced influential concepts and techniques that reshaped modern Riemannian geometry, influenced Alain Connes, Richard S. Hamilton, and informed developments in Perelman's work, Gromov–Witten invariants, and the study of large-scale geometry. Gromov's career spans positions at leading institutions and has been recognized by major prizes and memberships in prestigious academies.

Early life and education

Gromov was born in Boksitogorsk, Leningrad Oblast and studied at Moscow State University where he worked under Israel Gelfand and engaged with figures such as Andrei Kolmogorov, Sergei Novikov, and Yakov Sinai. During his formative years he interacted with mathematicians from the Steklov Institute of Mathematics, the Institute of Applied Mathematics, and the intellectual milieu that included Ilya Piatetski-Shapiro, Lars Ahlfors, and Mark Vishik. His early exposure to seminar culture connected him to the circles of Vadim Kaimanovich, Victor Petrov, Emanuel Dynkin, Leonid Kantorovich, and contemporaries like Grigori Perelman and Yuri Manin.

Mathematical career and positions

Gromov held positions at the Institut des Hautes Études Scientifiques (IHÉS), the Université Paris VII, and later at the Institut des Hautes Études Scientifiques and Courant Institute of Mathematical Sciences interactions, collaborating with researchers from Princeton University, Université Paris-Saclay, University of California, Berkeley, and ETH Zurich. He visited and lectured at institutions including Harvard University, Massachusetts Institute of Technology, Stanford University, University of Chicago, University of Bonn, and Max Planck Institute for Mathematics. His institutional affiliations brought him into contact with mathematicians such as Jean-Michel Bismut, Jean-Pierre Serre, Henri Cartan, Beno Eckmann, Peter Sarnak, Michael Atiyah, and Isadore Singer.

Major contributions and concepts

Gromov introduced the notion of Gromov–Hausdorff convergence, the concept of Gromov hyperbolic groups, and influential techniques like the use of filling invariants and the study of systolic inequalities influenced by Charles Loewner, Charles B. Morrey Jr., and Marston Morse. His work on symplectic geometry led to the introduction of pseudoholomorphic curves and connections to Gromov–Witten invariants, impacting research by Edward Witten, Maxim Kontsevich, Paul Seidel, Dusa McDuff, and Yakov Eliashberg. He developed large-scale geometric ideas related to coarse embeddings, asymptotic invariants, and the concept of almost flat manifolds linked to results of John Milnor, Hermann Weyl, Shing-Tung Yau, and William Thurston. Gromov's techniques intersect with the Novikov conjecture, the Atiyah–Singer index theorem, and have influenced advances in Ricci flow involving Grigori Perelman and Richard Hamilton.

Awards and recognition

Gromov has received numerous honors including the Abel Prize, the Wolf Prize in Mathematics, the Jeffery–Williams Prize, and memberships in academies such as the French Academy of Sciences, the National Academy of Sciences (United States), and the Royal Society. He has been awarded prizes and fellowships alongside laureates like Pierre Deligne, Enrico Bombieri, Jean-Pierre Serre, Alain Connes, and Andrew Wiles. Gromov's recognition extends to invitations to speak at the International Congress of Mathematicians, plenary addresses, honorary degrees from institutions including University of Cambridge, University of Oxford, ETH Zurich, and distinctions connected to organizations like the American Mathematical Society and the European Mathematical Society.

Selected publications

Gromov's influential writings include works on metric structures, symplectic topology, and group theory that have been cited alongside texts by John Milnor, Marcel Berger, Mikhael Gromov (alternate spelling prohibited), Mikhail Katz, and Victor Bangert. Notable publications are the monograph "Metric Structures for Riemannian and Non-Riemannian Spaces" which interacts with literature by Bertrand Meyer, Stephen Smale, René Thom, and papers introducing Gromov–Hausdorff convergence, hyperbolicity, and systolic geometry which converse with contributions by G. Perelman, M. Katz, J. Cheeger, Cheeger–Chern–Simons, and Shing-Tung Yau.

Influence and legacy

Gromov's methodologies reshaped the work of geometers and topologists such as William Thurston, Benson Farb, Mikhael Gromov (forbidden), Cornelia Drutu, Michel Talagrand, Boris Hasselman, and inspired interactions with physics via researchers like Edward Witten and Maxim Kontsevich. His concepts permeate contemporary research in geometric group theory, metric geometry, symplectic topology, and global analysis, influencing programs at institutions like IHÉS, Princeton University, Institute for Advanced Study, and catalyzing developments related to the Poincaré conjecture solutions, the Novikov conjecture, and modern studies in topological quantum field theory.

Category:Russian mathematicians Category:French mathematicians Category:Geometers