Mikhael Gromov

Mikhael Gromov
Name	Mikhael Gromov
Birth date	1943
Birth place	Boksitogorsk, Leningrad Oblast, Soviet Union
Fields	Mathematics, Geometry, Topology
Workplaces	Steklov Institute of Mathematics, IHÉS, Courant Institute, NYU
Alma mater	Moscow State University
Doctoral advisor	Israel Gelfand
Known for	Gromov–Hausdorff convergence, hyperbolic groups, symplectic geometry
Awards	Abel Prize, Wolf Prize in Mathematics, Crafoord Prize

Mikhael Gromov is a Russian-French mathematician noted for transformative work in geometry and topology, particularly in large-scale Riemannian geometry, geometric group theory, and symplectic topology. His research introduced foundational concepts such as the notion of almost flat manifolds and the use of metric techniques across differential geometry, algebraic topology, and analysis, influencing generations of mathematicians and institutions worldwide. Gromov's approach bridged methods from Erlangen Program-style geometric classification to analytic tools developed in the traditions of Pavel Alexandrov, Andrey Kolmogorov, and Israel Gelfand.

Early life and education

Gromov was born in Boksitogorsk in Leningrad Oblast and studied at Moscow State University under the supervision of Israel Gelfand, interacting with contemporaries from Steklov Institute of Mathematics, Moscow Mathematical Society, and the Kvant circle. During his graduate years he encountered influences from Andrey Kolmogorov, Pavel Alexandrov, Lazar Lyusternik, and the school around Nikolai Luzin, while participating in seminars connected to Steklov Institute of Mathematics and Moscow State University research groups. His early exposure to problems posed by John Milnor, Raoul Bott, and Shing-Tung Yau helped shape his interest in global Riemannian geometry and comparison techniques.

Academic career and positions

Gromov held positions at the Steklov Institute of Mathematics, spent extended periods at the Institut des Hautes Études Scientifiques (IHÉS), and held visiting appointments at institutions such as the Courant Institute of Mathematical Sciences, New York University, and Institute for Advanced Study. He collaborated with researchers affiliated with CNRS, École Normale Supérieure, Harvard University, Princeton University, and the University of California, Berkeley, and lectured at conferences organized by International Mathematical Union and European Mathematical Society. Gromov supervised students linked to IHÉS and exchanged ideas with scholars from Max-Planck-Institut für Mathematik, Mathematical Sciences Research Institute, and Clay Mathematics Institute visitors.

Major contributions and research

Gromov introduced the concept of Gromov–Hausdorff convergence, influencing studies by John Milnor, Shing-Tung Yau, Jeff Cheeger, Mikhail Gromov? — note: do not link the subject — and others in collapsing Riemannian manifolds and comparison geometry, with applications in work by G. Perelman, Richard Hamilton, and Grigori Perelman on Ricci flow. He founded geometric group theory through the notion of hyperbolic groups, impacting research by M. Bridson, A. Haefliger, Cornelia Druţu, and Mark Sapir, and connecting with problems studied by Andrei Yershov and Borisov? — please disregard. His contributions to symplectic topology, notably almost complex structures and filling techniques, influenced Yasha Eliashberg, Paul Seidel, Dusa McDuff, and Alan Weinstein. Gromov's work on systolic geometry inspired results by Michael Katz, Misha Gromov? — avoid linking, and has informed studies by C. Croke, M. Berger, and Dennis Sullivan on global invariants. He pioneered techniques applying coarse geometry to analysis, aligning with developments by Gromov? — omitted, and researchers at Institute for Advanced Study, IHÉS, and Courant Institute.

Awards and honours

Gromov received major awards including the Abel Prize, the Wolf Prize in Mathematics, the Crafoord Prize, and membership in academies such as the French Academy of Sciences and the National Academy of Sciences. He was awarded honors from organizations including the European Mathematical Society, International Mathematical Union, and national orders from France and Russia. Lectureships and prizes from institutions like IHÉS, Steklov Institute of Mathematics, Courant Institute, and the Clay Mathematics Institute recognized his influence across geometry and topology communities.

Selected publications

- "Curvature, Diameter and Betti Numbers" — influential paper cited alongside works by John Milnor, Shing-Tung Yau, and Raoul Bott in Riemannian geometry contexts. - "Groups of Polynomial Growth and Expanding Maps" — foundational text linked to studies by Mikhail Gromov? — do not link, and researchers such as Grigori Perelman and M. Gromov collaborators. - "Partial Differential Relations" — monograph that interacts with themes from Israel Gelfand, Andrey Kolmogorov, and Sergei Novikov. - Collections of lectures at IHÉS and articles in proceedings of the International Congress of Mathematicians and journals associated with American Mathematical Society and Springer.

Influence and legacy

Gromov's ideas reshaped research agendas at institutions including IHÉS, Steklov Institute of Mathematics, Courant Institute of Mathematical Sciences, and influenced programs at Harvard University, Princeton University, and University of Cambridge. His students and collaborators propagated geometric group theory, symplectic topology, and systolic geometry through work connected to European Mathematical Society conferences, International Congress of Mathematicians lectures, and research networks like MSRI and Clay Mathematics Institute. The techniques he introduced continue to inform contemporary research by figures such as Grigori Perelman, Yasha Eliashberg, Dusa McDuff, M. Bridson, and Cornelia Druţu, and remain central to modern studies in differential geometry, algebraic topology, and mathematical analysis.

Category:Russian mathematicians Category:Geometers Category:Topologists Category:Abel Prize winners