词条 | Mikhail Leonidovich Gromov |
释义 |
| name = Mikhail Leonidovich Gromov | image = Gromov Mikhail Leonidovich.jpg | image_size = | caption = Mikhail Gromov in 2009 | birth_date = {{birth date and age|1943|12|23|df=y}} | birth_place = Boksitogorsk, Russian SFSR, Soviet Union | death_date = | death_place = | residence = France | nationality = Russian and French and American | alma_mater = Leningrad State University (PhD) | doctoral_advisor = Vladimir Rokhlin | doctoral_students = François Labourie Pierre Pansu Mikhail Katz | known_for = Geometry | field = Mathematics | work_institutions = Institut des Hautes Études Scientifiques New York University | prizes = {{no wrap|Oswald Veblen Prize in Geometry (1981) Wolf Prize (1993) Kyoto Prize (2002) Nemmers Prize in Mathematics (2004) Bolyai Prize (2005) Abel Prize (2009)}} }} Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; {{lang-ru|link=no|Михаи́л Леони́дович Гро́мов}}; born 23 December 1943), is an American-French-Russian mathematician known for work in geometry, analysis and group theory. He is a permanent member of IHÉS in France and a Professor of Mathematics at New York University. Gromov has won several prizes, including the Abel Prize in 2009 "for his revolutionary contributions to geometry". BiographyMikhail Gromov was born on 23 December 1943 in Boksitogorsk, Soviet Union. His father Leonid Gromov and his Jewish[1] mother Lea Rabinovitz[2][3] were pathologists.[4] His mother was the cousin of chess-player Mikhail Botvinnik, as well as of the mathematician Isaak Moiseevich Rabinovich. [5] Gromov was born during World War II, and his mother, who worked as a medical doctor in the Soviet Army, had to leave the front line in order to give birth to him.[6] When Gromov was nine years old,[7] his mother gave him the book The Enjoyment of Mathematics by Hans Rademacher and Otto Toeplitz, a book that piqued his curiosity and had a great influence on him.[6] Gromov studied mathematics at Leningrad State University where he obtained a master's degree in 1965, a Doctorate in 1969 and defended his Postdoctoral Thesis in 1973. His thesis advisor was Vladimir Rokhlin.[7] Gromov married in 1967. In 1970, invited to give a presentation at the International Congress of Mathematicians in France, he was not allowed to leave the USSR. Still, his lecture was published in the conference proceedings.[10] Disagreeing with the Soviet system, he had been thinking of emigrating since the age of 14. In the early 1970s he ceased publication, hoping that this would help his application to move to Israel.[8][9] He changed his last name to that of his mother.[8] When the request was granted in 1974, he moved directly to New York where a position had been arranged for him at Stony Brook.[10] In 1981 he left Stony Brook to join the faculty of University of Paris VI and in 1982 he became a permanent professor at the Institut des Hautes Études Scientifiques (IHES) where he remains today. At the same time, he has held professorships at the University of Maryland, College Park from 1991 to 1996, and at the Courant Institute of Mathematical Sciences since 1996.[3] He adopted French citizenship in 1992.[11] WorkGromov's style of geometry often features a "coarse" or "soft" viewpoint, analyzing asymptotic or large-scale properties. Motivated by Nash and Kuiper's C1 embedding theorem and Stephen Smale's early results,[17] Gromov introduced in 1973 the notion of [https://www.encyclopediaofmath.org/index.php/Convex_integration convex integration] and the h-principle, a very general way to solve underdetermined partial differential equations and the basis for a geometric theory of these equations. In the 1980s, Gromov introduced the Gromov–Hausdorff metric, a measure of the difference between two compact metric spaces. In this context he proved Gromov's compactness theorem, stating that the set of compact Riemannian manifolds with Ricci curvature ≥ c and diameter ≤ D is relatively compact in the Gromov–Hausdorff metric. The possible limit points of sequences of such manifolds are Alexandrov spaces of curvature ≥ c, a class of metric spaces studied in detail by Burago, Gromov and Perelman in 1992. Gromov was also the first to study the space of all possible Riemannian structures on a given manifold. Gromov introduced geometric group theory, the study of infinite groups via the geometry of their Cayley graphs and their word metric. In 1981 he proved Gromov's theorem on groups of polynomial growth: a finitely generated group has polynomial growth (a geometric property) if and only if it is virtually nilpotent (an algebraic property). The proof uses the Gromov–Hausdorff metric mentioned above. Along with Eliyahu Rips he introduced the notion of hyperbolic groups. Gromov founded the field of symplectic topology by introducing the theory of pseudoholomorphic curves. This led to Gromov–Witten invariants which are used in string theory and to his non-squeezing theorem. Gromov is also interested in mathematical biology,[12] the structure of the brain and the thinking process, and the way scientific ideas evolve.[10] Prizes and honorsPrizes
Honors
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Books and other publications
Notes1. ^{{cite book |author=Masha Gessen|title=Perfect Rigour: A Genius and the Mathematical Breakthrough of a Lifetime|publisher=Icon Books Ltd |year=2011 |pages= |isbn=}} 2. ^{{cite book|title=The International Who's Who, 1997–98|url=https://books.google.com/books?id=4XNtwLEbl7wC|year=1997|publisher=Europa Publications|isbn=978-1-85743-022-6|pages=591}} 3. ^1 {{MacTutor Biography|id=Gromov}} 4. ^Gromov, Mikhail. "A Few Recollections", in {{cite book|author1=Helge Holden|author2=Ragni Piene|title=The Abel Prize 2008–2012|url=https://books.google.com/books?id=tEprnQEACAAJ|date=3 February 2014|publisher=Springer Berlin Heidelberg|isbn=978-3-642-39448-5|pages=129–137}} (also available on Gromov's homepage: link) 5. ^Воспоминания Владимира Рабиновича (генеалогия семьи М. Громова по материнской линии. Лия Александровна Рабинович также приходится двоюродной сестрой известному рижскому математику, историку математики и популяризатору науки Исааку Моисеевичу Рабиновичу (род. 1911), автору книг «Математик Пирс Боль из Риги» (совместно с А. Д. Мышкисом и с приложением комментария М. М. Ботвинника «О шахматной игре П. Г. Боля», 1965), «Строптивая производная» (1968) и др. Троюродный брат М. Громова — известный латвийский адвокат и общественный деятель Александр Жанович Бергман (польск., род. 1925). 6. ^1 Newsletter of the European Mathematical Society, No. 73, September 2009, p. 19 7. ^http://cims.nyu.edu/newsletters/Spring2009.pdf 8. ^1 2 {{Cite news|url=http://www.lemonde.fr/planete/article/2009/03/26/mikhail-gromov-le-genie-qui-venait-du-froid_1172835_3244.html|title=Mikhaïl Gromov, le génie qui venait du froid|last=Foucart|first=Stéphane|date=2009-03-26|work=|newspaper=Le Monde.fr|language=fr|issn=1950-6244|via=}} 9. ^{{Cite book|url=https://books.google.com/books?id=BoUFAQAAIAAJ&q=Vivre+savant+sous+le+communisme&dq=Vivre+savant+sous+le+communisme&hl=en&sa=X&ved=0ahUKEwjU3Yue6K3PAhWr6oMKHbZQAlMQ6AEIHjAA|title=Vivre savant sous le communisme|last=Ripka|first=Georges|date=2002-01-01|publisher=Belin|isbn=9782701130538|language=fr}} 10. ^1 2 {{cite web|url=https://www.simonsfoundation.org/science_lives_video/science-lives-mikhail-gromov/|title=Science Lives: Mikhail Gromov|last=Roberts|first=Siobhan|authorlink=Siobhan Roberts|date=December 22, 2014|website=|publisher=Simons Foundation|access-date=|work=}} 11. ^{{cite web|title=Mikhail Leonidovich Gromov|work=abelprize.no|date=|url=http://www.abelprize.no/c53859/binfil/download.php?tid=53784}} 12. ^1 {{citation|url=http://www.ams.org/notices/201003/rtx100300391p.pdf|title=Interview with Mikhail Gromov|journal=Notices of the AMS|date=March 2010|volume=57|issue=3|pages=391–403}}. 13. ^Gromov Receives Nemmers Prize 14. ^Abel Prize for 2009, Laureates 2009 15. ^Professor Mikhail Gromov ForMemRS | Royal Society 16. ^Mikhaël Gromov — Membre de l’Académie des sciences 17. ^{{cite journal|author=Toledo, Domingo|title=Review: Geometric group theory, Vol. 2: Asymptotic invariants of infinite groups, by M. Gromov|journal=Bull. Amer. Math. Soc. (N.S.)|year=1996|volume=33|issue=3|pages=395–398|doi=10.1090/s0273-0979-96-00669-6|url=http://www.ams.org/journals/bull/1996-33-03/S0273-0979-96-00669-6/S0273-0979-96-00669-6.pdf}} 18. ^{{cite journal|author=Grove, Karsten|title=Review: Metric structures for Riemannian and non-Riemannian spaces, by M. Gromov|journal=Bull. Amer. Math. Soc. (N.S.)|year=2001|volume=38|issue=3|pages=353–363|url=http://www.ams.org/journals/bull/2001-38-03/S0273-0979-01-00904-1/S0273-0979-01-00904-1.pdf|doi=10.1090/s0273-0979-01-00904-1}} 19. ^{{cite journal|author=McDuff, Dusa|authorlink=Dusa McDuff|title=Review: Partial differential relations, by Mikhael Gromov|journal=Bull. Amer. Math. Soc. (N.S.)|year=1988|volume=18|issue=2|pages=214–220|url=http://www.ams.org/journals/bull/1988-18-02/S0273-0979-1988-15654-6/S0273-0979-1988-15654-6.pdf|doi=10.1090/s0273-0979-1988-15654-6}} 20. ^{{cite journal|author=Heintze, Ernst|title=Review: Manifolds of nonpositive curvature, by W. Ballmann, M. Gromov & V. Schroeder|journal=Bull. Amer. Math. Soc. (N.S.)|year=1987|volume=17|issue=2|pages=376–380|doi=10.1090/s0273-0979-1987-15603-5|url=http://www.ams.org/journals/bull/1987-17-02/S0273-0979-1987-15603-5/S0273-0979-1987-15603-5.pdf}} References{{refbegin}}
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23 : 1943 births|Living people|People from Boksitogorsk|Russian people of Jewish descent|Russian emigrants to France|Members of the United States National Academy of Sciences|Foreign Members of the Russian Academy of Sciences|Kyoto laureates in Basic Sciences|Differential geometers|Russian mathematicians|20th-century French mathematicians|21st-century French mathematicians|French people of Russian-Jewish descent|Group theorists|New York University faculty|Wolf Prize in Mathematics laureates|Geometers|Members of the French Academy of Sciences|Members of the Norwegian Academy of Science and Letters|Abel Prize laureates|Foreign Members of the Royal Society|ISI highly cited researchers|Soviet mathematicians |
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