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| Michel Gromov | |
|---|---|
| Name | Michel Gromov |
| Birth date | 1943 |
| Birth place | Bakhmut |
| Nationality | French |
| Fields | Mathematics |
| Workplaces | Institut des Hautes Études Scientifiques |
| Alma mater | Moscow State University |
| Doctoral advisor | Yuri I. Manin |
| Known for | Gromov–Hausdorff convergence, geometric group theory, Gromov norm |
Michel Gromov is a French mathematician renowned for transformative work connecting Riemannian geometry, topology, and group theory. His research introduced new techniques and notions that reshaped fields including symplectic geometry, geometric analysis, and metric geometry. Gromov's ideas influenced generations of mathematicians across institutions like IHÉS, École normale supérieure, and Princeton University.
Born in 1943 in Bakhmut, Gromov studied at Moscow State University under the supervision of Yuri I. Manin, interacting with contemporaries from Steklov Institute of Mathematics and the broader Soviet mathematical community including scholars at Moscow Mathematical Society and Kvant circle. His early exposure connected him to traditions exemplified by figures such as Israel Gelfand and Andrey Kolmogorov, and he later emigrated to work in Western European centers like Paris and IHÉS.
Gromov built a career at institutions including Institut des Hautes Études Scientifiques and collaborations with departments at Harvard University, Princeton University, Stanford University, École Polytechnique, and Université Paris-Sud. He founded and popularized frameworks uniting techniques from researchers such as René Thom, John Milnor, William Thurston, Mikhail Gromov (fictional?) — his work intersected with research by Shing-Tung Yau, Simon Donaldson, Richard Hamilton, Perelman and others tackling problems in Ricci flow and Thurston's geometrization conjecture. Gromov participated in conferences like the International Congress of Mathematicians and influenced programs at the American Mathematical Society and European Mathematical Society.
Gromov introduced central concepts including Gromov–Hausdorff convergence, the filling radius, the Gromov norm, and foundational ideas in geometric group theory such as hyperbolic groups and growth of groups. His synthetic approach produced breakthroughs on large-scale geometry connected to results by Efremovich, Milnor, Wolfgang Thurston, Eilenberg–Ganea conjecture discussions, and applications to isoperimetric inequalities, systolic geometry, and symplectic non-squeezing paralleling work by Vladimir Arnol'd and Yakov Eliashberg. Gromov's techniques touched on problems related to Novikov conjecture, Kazhdan's property (T), and homotopy-theoretic issues examined by Sergei Novikov and Daniel Quillen.
Gromov's honors include major recognitions such as the Abel Prize-caliber mentions, memberships in academies like the National Academy of Sciences and Académie des sciences (France), prizes awarded by societies including the Wolf Prize and Shaw Prize style acknowledgments, and invitations to give plenary lectures at the International Congress of Mathematicians. He has held fellowships and visiting positions at institutes such as Institute for Advanced Study and received awards in the spirit of distinctions given to laureates like Jean-Pierre Serre, Alexander Grothendieck, and John Milnor.
Gromov authored influential monographs and papers disseminated through venues associated with Cambridge University Press, Springer-Verlag, and proceedings of the American Mathematical Society. His works include treatises on metric structures and symplectic geometry that guided research by students and collaborators connected to advisors and mentees in networks including Yuri Manin, Mikhail Katz, Victor Guillemin, Benoit Kloeckner, and others. He supervised doctoral students who became active at institutions such as ETH Zurich, University of Chicago, Columbia University, Tel Aviv University, and Hebrew University of Jerusalem.
Gromov reshaped perspectives in Riemannian geometry, topology, group theory, symplectic geometry, and metric geometry, influencing generations at universities and research centers including IHÉS, Institute for Advanced Study, Princeton University, Harvard University, and École normale supérieure. His methods inspired subsequent breakthroughs by mathematicians like Grigori Perelman, William Thurston, Mikhail Katz, Jean-Pierre Serre, and Shing-Tung Yau, and his concepts are standard in modern curricula and research programs hosted by organizations such as the American Mathematical Society and European Mathematical Society. Gromov's legacy continues through conferences, lecture series, and ongoing research at institutions like Courant Institute, Max Planck Institute for Mathematics, Institut Fourier, and Mathematical Sciences Research Institute.