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in both. Unlike general lattices, which are defined by their properties, arithmetic lattices are defined by a construction. Therefore, these results of
Margulis pave a way for classification of lattices. Arithmeticity turned out to be closely related to another remarkable property of lattices
405:, and was later able to travel freely, though he still worked in the Institute of Problems of Information Transmission, a research institute rather than a university. In 1991, Margulis accepted a professorial position at
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767:. With a survey by Richard Sharp: Periodic orbits of hyperbolic flows. Translated from the Russian by Valentina Vladimirovna Szulikowska. Springer-Verlag, Berlin, 2004. vi+139 pp.
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and diophantine approximation. This was a question that had been open for half a century, on which considerable progress had been made by the
649:.) While certain rigidity phenomena had already been known, the approach of Margulis was at the same time novel, powerful, and very elegant.
902:
884:
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Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators
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1222:
824:. (Russian) Problemy Peredachi Informatsii 24 (1988), no. 1, 51–60; translation in Problems Inform. Transmission 24 (1988), no. 1, 39–46
347:
710:
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805:. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 193–215, Math. Soc. Japan, Tokyo, 1991
545:
1084:
2613:
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713:; but to reduce the number of variables to the point of getting the best-possible results, the more structural methods from
486:) that a certain simple-minded way of constructing subgroups of semisimple Lie groups produces examples of lattices, called
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793:. Fields Medallists' lectures, 272–327, World Sci. Ser. 20th Century Math., 5, World Sci. Publ., River Edge, NJ, 1997
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287:
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are semisimple algebraic groups over a local field without compact factors and whose split rank is at least two and
454:"For pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics."
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Dynamical and ergodic properties of subgroup actions on homogeneous spaces with applications to number theory
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proved decisive. He has formulated a further program of research in the same direction, that includes the
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in 2020, becoming the fifth mathematician to receive the three prizes. In 1991, he joined the faculty of
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against Jewish mathematicians in the Soviet Union. His position improved, and in 1979 he visited
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1089:, by G. A. Margulis, with a survey "Periodic orbits of hyperbolic flows", by Richard Sharp"
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Arithmeticity of the irreducible lattices in the semisimple groups of rank greater than
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from 1975 clarified an area of classical conjectures about the characterisation of
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1006:"Abel Prize in Mathematics Shared by 2 Trailblazers of Probability and Dynamics"
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for his contributions to theory of lattices and applications to ergodic theory,
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2005:
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679:≥ 4, which was also independently and almost simultaneously obtained by
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92:
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Kolata, GB (1978). "Anti-Semitism
Alleged in Soviet Mathematics".
683:, follows from a construction of a certain dense subgroup of the
854:. (Russian) Funkcional. Anal. i Prilozen. 9 (1975), no. 1, 35–44
852:
Arithmeticity of nonuniform lattices in weakly noncompact groups
402:
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with a homomorphism between the algebraic groups themselves.
540:
in it is arithmetic, i.e. can be obtained in this way. Thus
524:
entries. Margulis proved that under suitable assumptions on
629:
between the lattices agrees on a finite index subgroup of
2599:
Members of the United States
National Academy of Sciences
617:
are irreducible lattices in them, then any homomorphism
923:. Yale University Office of Public Affairs. 2005-02-23.
921:"Yale's Margulis Wins 2005 Wolf Prize for Mathematics"
992:
List of
Fellows of the American Mathematical Society
701:
In 1986, Margulis gave a complete resolution of the
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466:and the questions of rigidity and arithmeticity of
346:. At age 16 in 1962 he won the silver medal at the
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125:
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60:
32:
2664:International Mathematical Olympiad participants
742:Ergebnisse der Mathematik und ihrer Grenzgebiete
1087:On some aspects of the theory of Anosov systems
765:On some aspects of the theory of Anosov systems
694:, which was later generalized in the theory of
597:. The name derives from the following variant:
2609:Institute for Advanced Study visiting scholars
664:is the only normalized rotationally invariant
490:. It is analogous to considering the subgroup
2130:
1790:
1252:
214:On some aspects of the theory of Anosov flows
8:
2604:Fellows of the American Mathematical Society
1137:The work of Gregori Aleksandrovitch Margulis
980:Notices of the American Mathematical Society
393:in 1978, but was not permitted to travel to
1044:Discrete subgroups of semisimple Lie groups
842:, Monatsh. Math. 90 (1980), no. 3, 233–235
737:Discrete subgroups of semisimple Lie groups
416:in 2001. In 2012 he became a fellow of the
2137:
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2115:
1797:
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860:, Russian Math. Surveys 29 (1974) 107–165
830:1, Invent. Math. 76 (1984), no. 1, 93–120
49:
29:
2624:American people of Russian-Jewish descent
1144:(Helsinki, 1978). Vol. 1. Helsinki:
1107:
1064:
560:, i.e. they agree on subgroups of finite
397:to accept it in person, allegedly due to
858:Arithmetic properties of discrete groups
690:Margulis gave the first construction of
1208:MacTutor History of Mathematics Archive
977:National Academy of Sciences Elections.
876:
350:. He received his PhD in 1970 from the
294:, and the introduction of methods from
478:. It had been known since the 1950s (
412:Margulis was elected a member of the
7:
2644:Wolf Prize in Mathematics laureates
2594:21st-century Russian mathematicians
1223:International Mathematical Olympiad
348:International Mathematical Olympiad
585:into the group of real invertible
265:Григо́рий Алекса́ндрович Маргу́лис
25:
520:) that consists of matrices with
462:Margulis's early work dealt with
414:U.S. National Academy of Sciences
2567:
1758:
1749:
1748:
1066:10.1090/s0273-0979-1992-00306-3
982:, vol. 48 (2001), no. 7, p. 722
840:Some remarks on invariant means
675:. The affirmative solution for
446:In 2020, Margulis received the
423:In 2005, Margulis received the
279:; born February 24, 1946) is a
257:Grigory Aleksandrovich Margulis
2634:Moscow State University alumni
711:Hardy–Littlewood circle method
593:matrices extends to the whole
1:
1232:Mathematics Genealogy Project
1109:10.1090/S0273-0979-05-01051-7
1096:Bull. Amer. Math. Soc. (N.S.)
1053:Bull. Amer. Math. Soc. (N.S.)
1004:Chang, Kenneth (2020-03-18).
956:10.1126/science.202.4373.1167
418:American Mathematical Society
1146:Academia Scientiarum Fennica
532:greater or equal than two),
318:, where he is currently the
267:, first name often given as
2669:Dynamical systems theorists
472:semisimple algebraic groups
2695:
2649:Mathematicians from Moscow
1219:Grigory Margulis's results
748:, Berlin, 1991. x+388 pp.
458:Mathematical contributions
322:Professor of Mathematics.
2563:
2147:Wolf Prize in Mathematics
1813:
1744:
1274:
666:finitely additive measure
358:under the supervision of
308:Wolf Prize in Mathematics
300:diophantine approximation
264:
250:
179:
130:Diophantine approximation
48:
39:
1876:S. R. Srinivasa Varadhan
1213:University of St Andrews
565:discovered by Margulis.
528:(no compact factors and
368:Kazhdan–Margulis theorem
40:
2639:Yale University faculty
994:, retrieved 2013-02-02.
687:that has property (T).
577:roughly means that any
354:, starting research in
352:Moscow State University
330:Margulis was born to a
107:Moscow State University
2574:Mathematics portal
2297:Ilya Piatetski-Shapiro
660:that asks whether the
536:(irreducible) lattice
474:of higher rank over a
464:Kazhdan's property (T)
286:known for his work on
2614:Soviet mathematicians
2507:Jean-François Le Gall
1140:. Proceedings of the
725:Selected publications
719:Littlewood conjecture
429:representation theory
376:superrigidity theorem
141:Arithmeticity theorem
138:Superrigidity theorem
27:Russian mathematician
2674:Abel Prize laureates
2424:Phillip A. Griffiths
2262:Friedrich Hirzebruch
1977:John Forbes Nash Jr.
1199:Robertson, Edmund F.
1046:, by G. A. Margulis"
791:Oppenheim conjecture
703:Oppenheim conjecture
652:Margulis solved the
507:special linear group
382:amongst lattices in
370:, a basic result on
320:Erastus L. De Forest
148:Oppenheim conjecture
2497:Alexander Beilinson
1197:O'Connor, John J.;
948:1978Sci...202.1167B
942:(4373): 1167–1170.
673:-dimensional sphere
488:arithmetic lattices
389:He was awarded the
302:. He was awarded a
241:Emmanuel Breuillard
2679:Russian scientists
2528:Simon K. Donaldson
2455:Michael Aschbacher
2414:Hillel Furstenberg
2042:Hillel Furstenberg
1764:Mathematics portal
1203:"Grigory Margulis"
1148:. pp. 57–63.
1010:The New York Times
903:"Gregory Margulis"
885:"Gregory Margulis"
548:with the subgroup
452:Hillel Furstenberg
362:. Early work with
2581:
2580:
2544:Ingrid Daubechies
2501:Vladimir Drinfeld
2491:Charles Fefferman
2374:Jean-Pierre Serre
2222:Shiing-Shen Chern
2196:Andrey Kolmogorov
2145:Laureates of the
2112:
2111:
1823:Jean-Pierre Serre
1772:
1771:
1038:Zimmer, Robert J.
658:Ruziewicz problem
380:arithmetic groups
336:Lithuanian Jewish
254:
253:
237:Doctoral students
181:Scientific career
163:Lobachevsky Prize
71:February 24, 1946
42:Григорий Маргулис
16:(Redirected from
2686:
2629:Fields Medalists
2572:
2571:
2532:Yakov Eliashberg
2428:David B. Mumford
2400:Grigory Margulis
2329:Robert Langlands
2307:John G. Thompson
2303:Lennart Carleson
2272:Alberto Calderón
2242:Samuel Eilenberg
2232:Kunihiko Kodaira
2139:
2132:
2125:
2116:
2100:Michel Talagrand
2047:Grigory Margulis
2018:Robert Langlands
1888:John G. Thompson
1864:Lennart Carleson
1799:
1792:
1785:
1776:
1762:
1752:
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1268:Fields Medalists
1261:
1254:
1247:
1238:
1228:Grigory Margulis
1215:
1179:
1174:. Archived from
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905:. Archived from
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893:
892:
887:. Archived from
881:
696:Ramanujan graphs
685:orthogonal group
662:Lebesgue measure
645:is known as the
310:in 2005, and an
281:Russian-American
266:
226:Doctoral advisor
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74:
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68:
55:Margulis in 2006
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43:
34:Grigory Margulis
30:
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18:Gregori Margulis
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2445:Dennis Sullivan
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2030:Karen Uhlenbeck
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1982:Louis Nirenberg
1969:
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1941:Endre Szemerédi
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707:quadratic forms
692:expander graphs
681:Dennis Sullivan
647:strong rigidity
637:(The case when
460:
407:Yale University
372:discrete groups
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316:Yale University
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201:Yale University
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1191:External links
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1188:
1187:
1178:on 2013-02-12.
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1115:
1102:(2): 257–261.
1081:Parry, William
1072:
1059:(1): 198–202.
1029:
996:
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909:on 2016-09-11.
894:
891:on 2016-09-11.
875:
874:
872:
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849:
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812:
800:
786:
783:
782:
781:
762:
731:
728:
726:
723:
635:
634:
569:for a lattice
484:Harish-Chandra
459:
456:
441:measure theory
356:ergodic theory
327:
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296:ergodic theory
252:
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2659:Living people
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2485:
2482:
2479:
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2470:
2469:Michael Artin
2466:
2465:George Mostow
2463:
2460:
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2450:
2446:
2443:
2442:
2440:
2436:
2429:
2425:
2421:
2418:
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2411:
2410:Stephen Smale
2408:
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2391:
2388:
2385:
2381:
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2375:
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2349:László Lovász
2347:
2344:
2340:
2339:Joseph Keller
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2240:
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2210:
2207:
2206:Oscar Zariski
2203:
2200:
2197:
2193:
2190:
2189:
2187:
2183:
2176:
2172:
2169:
2166:
2162:
2159:
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2128:
2126:
2121:
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2097:
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2077:
2073:
2072:
2070:
2065:
2064:Avi Wigderson
2062:
2060:
2059:László Lovász
2056:
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2019:
2015:
2014:
2012:
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1717:Duminil-Copin
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1636:Lindenstrauss
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1155:951-41-0352-1
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773:3-540-40121-0
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754:3-540-12179-X
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608:
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600:
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588:
584:
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576:
572:
568:
567:Superrigidity
563:
559:
555:
551:
547:
546:commensurable
543:
539:
535:
531:
527:
523:
519:
515:
511:
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489:
485:
481:
477:
473:
469:
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457:
455:
453:
450:jointly with
449:
444:
442:
438:
437:combinatorics
434:
433:number theory
430:
426:
421:
419:
415:
410:
408:
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396:
392:
387:
385:
381:
377:
373:
369:
366:produced the
365:
364:David Kazhdan
361:
357:
353:
349:
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341:
337:
333:
325:
323:
321:
317:
313:
309:
305:
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284:mathematician
282:
278:
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108:
105:
101:
98:
94:
91:
87:
83:
79:
73:(age 78)
63:
59:
52:
47:
38:
31:
19:
2619:Russian Jews
2565:
2475:Peter Sarnak
2399:
2333:Andrew Wiles
2323:Jürgen Moser
2317:Jacques Tits
2246:Atle Selberg
2202:Lars Ahlfors
2192:Henri Cartan
2046:
1994:Andrew Wiles
1893:Jacques Tits
1449:
1379:Grothendieck
1206:
1183:Fields Medal
1180:
1176:the original
1136:
1099:
1095:
1086:
1075:
1056:
1052:
1043:
1032:
1021:. Retrieved
1009:
999:
987:
972:
939:
935:
929:
915:
907:the original
897:
889:the original
879:
857:
851:
839:
827:
821:
802:
790:
764:
736:
715:group theory
700:
689:
676:
670:
651:
638:
636:
630:
626:
622:
618:
614:
610:
606:
602:
594:
590:
586:
582:
579:homomorphism
574:
570:
566:
557:
553:
549:
541:
537:
533:
525:
521:
517:
513:
509:
499:
495:
491:
487:
461:
445:
422:
411:
399:antisemitism
391:Fields Medal
388:
344:Soviet Union
329:
304:Fields Medal
276:
272:
268:
256:
255:
212:
197:Institutions
180:
158:Fields Medal
82:Soviet Union
2654:1946 births
2276:John Milnor
2098:2024
2086:2023
2074:2022
2057:2021
2040:2020
2028:2019
2016:2018
2004:2017
1992:2016
1975:2015
1965:Yakov Sinai
1963:2014
1951:2013
1939:2012
1929:John Milnor
1927:2011
1915:2010
1903:2009
1886:2008
1874:2007
1862:2006
1850:2005
1833:2004
1821:2003
1715:2022
1688:2018
1661:2014
1634:2010
1607:2006
1590:2002
1563:1998
1536:1994
1509:1990
1487:1986
1465:1982
1438:1978
1421:1974
1394:1970
1367:1966
1350:1962
1333:1958
1316:1954
1299:1950
1282:1936
643:isomorphism
476:local field
360:Yakov Sinai
338:descent in
306:in 1978, a
231:Yakov Sinai
191:Mathematics
89:Nationality
2588:Categories
2554:Adi Shamir
2390:Mikio Sato
2370:Raoul Bott
2252:Kiyosi Itô
2226:Paul Erdős
2216:Mark Krein
2175:André Weil
2171:Jean Leray
2006:Yves Meyer
1806:Abel Prize
1678:Mirzakhani
1575:Kontsevich
1172:0426.22011
1132:Olli Lehto
1023:2020-03-18
871:References
744:(3) , 17.
530:split rank
448:Abel Prize
425:Wolf Prize
384:Lie groups
334:family of
312:Abel Prize
292:Lie groups
173:Abel Prize
168:Wolf Prize
134:Lie groups
67:1946-02-24
2550:Noga Alon
2416:(2006/07)
2396:(2002/03)
2394:John Tate
2345:(1996/97)
2335:(1995/96)
2325:(1994/95)
2256:Peter Lax
2238:(1984/85)
2236:Hans Lewy
2228:(1983/84)
1917:John Tate
1852:Peter Lax
1808:laureates
1732:Viazovska
1705:Venkatesh
1597:Voevodsky
1592:Lafforgue
1565:Borcherds
1489:Donaldson
1445:Fefferman
1352:Hörmander
1185:citation.
1085:"Review:
1042:"Review:
1018:0362-4331
502:) of the
326:Biography
103:Education
1754:Category
1668:Bhargava
1614:Perelman
1609:Okounkov
1580:McMullen
1553:Zelmanov
1538:Bourgain
1511:Drinfeld
1499:Freedman
1494:Faltings
1472:Thurston
1450:Margulis
1423:Bombieri
1411:Thompson
1401:Hironaka
1301:Schwartz
1130:(1980).
1083:(2005).
1040:(1992).
964:17735390
785:Lectures
468:lattices
395:Helsinki
288:lattices
97:American
1727:Maynard
1700:Scholze
1695:Figalli
1651:Villani
1646:Smirnov
1455:Quillen
1440:Deligne
1428:Mumford
1406:Novikov
1318:Kodaira
1306:Selberg
1289:Douglas
1284:Ahlfors
1230:at the
1164:0562596
1134:(ed.).
1128:J. Tits
944:Bibcode
936:Science
865:0463353
847:0596890
835:0739627
810:1159213
798:1622909
779:2035655
760:1090825
668:on the
522:integer
332:Russian
277:Gregori
273:Grigori
269:Gregory
261:Russian
170:(2005)
165:(1996)
160:(1978)
93:Russian
2556:(2024)
2546:(2023)
2540:(2022)
2534:(2020)
2513:(2019)
2503:(2018)
2493:(2017)
2483:(2015)
2477:(2014)
2471:(2013)
2461:(2012)
2451:(2010)
2430:(2008)
2406:(2005)
2386:(2001)
2376:(2000)
2355:(1999)
2319:(1993)
2309:(1992)
2299:(1990)
2278:(1989)
2268:(1988)
2258:(1987)
2248:(1986)
2218:(1982)
2208:(1981)
2198:(1980)
2177:(1979)
2167:(1978)
1690:Birkar
1673:Hairer
1624:Werner
1570:Gowers
1548:Yoccoz
1526:Witten
1467:Connes
1369:Atiyah
1357:Milnor
1170:
1162:
1152:
1016:
962:
816:Papers
771:
752:
654:Banach
641:is an
439:, and
374:. His
340:Moscow
245:Hee Oh
219:(1970)
217:
208:Thesis
187:Fields
175:(2020)
154:Awards
78:Moscow
2521:2020s
2438:2010s
2363:2000s
2286:1990s
2185:1980s
2154:1970s
1663:Avila
1543:Lions
1516:Jones
1396:Baker
1384:Smale
1374:Cohen
1323:Serre
1181:1978
1092:(PDF)
1049:(PDF)
730:Books
562:index
556:) of
480:Borel
298:into
1521:Mori
1340:Thom
1335:Roth
1150:ISBN
1014:ISSN
960:PMID
769:ISBN
750:ISBN
613:and
605:and
504:real
403:Bonn
61:Born
1722:Huh
1641:Ngô
1619:Tao
1477:Yau
1221:at
1168:Zbl
1142:ICM
1104:doi
1061:doi
952:doi
940:202
705:on
607:G'
601:If
581:of
573:in
544:is
534:any
470:in
290:in
275:or
119:PhD
2590::
2552:/
2530:/
2509:/
2499:/
2489:/
2467:/
2457:/
2447:/
2426:/
2422:/
2412:/
2402:/
2392:/
2382:/
2372:/
2351:/
2341:/
2331:/
2315:/
2305:/
2295:/
2274:/
2264:/
2254:/
2244:/
2234:/
2224:/
2214:/
2204:/
2194:/
2173:/
2163:/
1211:,
1205:,
1201:,
1166:.
1160:MR
1158:.
1100:42
1098:.
1094:.
1057:27
1055:.
1051:.
1012:.
1008:.
958:.
950:.
938:.
862:MR
844:MR
832:MR
807:MR
795:MR
776:MR
757:MR
740:,
721:.
698:.
625:→
621::
589:×
510:SL
492:SL
482:,
443:.
435:,
431:,
420:.
409:.
386:.
342:,
271:,
263::
117:,
115:MS
113:,
111:BS
95:,
80:,
69:)
2138:e
2131:t
2124:v
1798:e
1791:t
1784:v
1260:e
1253:t
1246:v
1112:.
1106::
1069:.
1063::
1026:.
966:.
954::
946::
677:n
671:n
656:–
639:f
631:Γ
627:Γ
623:Γ
619:f
615:Γ
611:Γ
603:G
595:G
591:n
587:n
583:Γ
575:G
571:Γ
558:G
554:Z
552:(
550:G
542:Γ
538:Γ
526:G
518:R
516:,
514:n
512:(
500:Z
498:,
496:n
494:(
259:(
121:)
109:(
65:(
20:)
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