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{{Infobox scientist
|name              = Grigory Margulis
|image            = Grigory Margulis.jpg
|image_size        = 250px
|caption          = Grigory Margulis
|birth_date        = {{birth date and age|1946|02|24|mf=yes}}
|birth_place      = [[Moscow]], [[Soviet Union]]
|death_date        =
|death_place      =
|nationality      = [[Russia]]n
|field            = [[Mathematics]]
|work_institutions = [[Yale University]]
|alma_mater        = [[Moscow State University]]
|doctoral_advisor = [[Yakov Sinai]]
|doctoral_students = [[Emmanuel Breuillard]]<br>[[Bengt Karlsson]]<br>[[Dmitry Kleinbock]]<br>[[Hee Oh]]
|known_for        = [[Diophantine approximation]]<br>[[Lie group]]s<br>[[Superrigidity theorem]]<br>[[Arithmeticity theorem]]<br>[[Expander graphs]]<br>[[Oppenheim conjecture]]
|prizes            = [[Fields Medal]] <small>(1978)</small><br>{{nowrap|[[Wolf Prize in Mathematics]] <small>(2005)</small>}}<br>[[Medal of the Collège de France]]<br>[[Alexander von Humboldt Prize]]<br>[[Lobachevsky International Prize]]
}}
'''Gregori Aleksandrovich Margulis''' ({{lang-ru|Григо́рий Алекса́ндрович Маргу́лис}}, first name often given as '''Gregory''', '''Grigori''' or '''Grigory'''; born February 24, 1946) is a [[Russia]]n [[mathematician]] known for his work on [[lattice (discrete subgroup)|lattices]] in [[Lie group]]s, and the introduction of methods from [[ergodic theory]] into [[diophantine approximation]]. He was awarded a [[Fields Medal]] in 1978 and a [[Wolf Prize]] [[Wolf Prize in Mathematics|in Mathematics]] in 2005, becoming the seventh mathematician to receive both prizes.  In 1991, he joined the faculty of [[Yale University]], where he is currently the Erastus L. DeForest Professor of Mathematics.<ref name="YOPA_2005_02_23">{{cite web|url=http://opa.yale.edu/news/article.aspx?id=4312|title=Yale's Margulis Wins 2005 Wolf Prize for Mathematics|date=2005-02-23|publisher=Yale University Office of Public Affairs}}</ref>
 
== Short biography ==
Margulis was born in [[Moscow]], [[Soviet Union]]. He received his PhD in 1970 from the [[Moscow State University]], starting research in [[ergodic theory]] under the supervision of [[Yakov Sinai]].  Early work with [[David Kazhdan]] produced the [[Kazhdan's property (T)|Kazhdan–Margulis theorem]], a basic result on [[discrete group]]s. His [[superrigidity theorem]] from 1975 clarified an area of classical conjectures about the characterisation of [[arithmetic group]]s amongst lattices in [[Lie groups]].
 
He was awarded the [[Fields Medal]] in 1978, but was not permitted to travel to [[Helsinki]] to accept in person. His position improved, and in 1979 he visited [[Bonn]], 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 [[Yale University]].
 
Margulis was elected a member of the [[United States National Academy of Sciences|U.S. National Academy of Sciences]] in 2001.<ref>[http://www.ams.org/notices/200107/people.pdf National Academy of Sciences Elections.] [[Notices of the American Mathematical Society]], vol. 48 (2001), no. 7, p. 722</ref> In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-02-02.</ref>
 
In 2005, Margulis received the [[Wolf Prize]] for his contributions to theory of lattices and applications to ergodic theory, [[representation theory]], [[number theory]], [[combinatorics]], and [[measure theory]].
 
== Mathematical contributions ==
 
Early work of Margulis dealt with [[Kazhdan's property (T)]] and the questions of rigidity and arithmeticity of [[lattice (discrete subgroup)|lattices]] in [[semisimple algebraic group]]s of higher rank over a [[local field]]. It had been known since the 1950s ([[Armand Borel|Borel]], [[Harish-Chandra]]) that a certain simple-minded way of constructing subgroups of semisimple Lie groups produces examples of lattices, called ''arithmetic lattices''. It is analogous to considering the subgroup ''SL''(''n'','''Z''') of the [[real numbers|real]] [[special linear group]] ''SL''(''n'','''R''') that consists of matrices with ''integer'' entries. Margulis proved that under suitable assumptions on ''G'' (no compact factors and [[split rank]] greater or equal than two), ''any'' (irreducible) lattice ''Γ'' in it is arithmetic, i.e. can be obtained in this way. Thus ''Γ'' is [[commensurability (mathematics)|commensurable]] with the subgroup ''G''('''Z''') of ''G'', i.e. they agree on subgroups of finite [[Index of a subgroup|index]] 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 discovered by Margulis. ''Superrigidity'' for a lattice ''Γ'' in ''G'' roughly means that any [[group representation|homomorphism]] of ''Γ'' into the group of real invertible ''n'' × ''n'' matrices extends to the whole ''G''. The name derives from the following variant:
 
: If ''G'' and ''G' '', semisimple algebraic groups over a local field without compact factors and whose split rank is at least two and ''Γ'' and ''Γ''<sup><math>'</math></sup> are irreducible lattices in them, then any homomorphism ''f'': ''Γ'' → ''Γ''<sup><math>'</math></sup> between the lattices agrees on a finite index subgroup of ''Γ'' with a homomorphism between the algebraic groups themselves.
 
(The case when ''f'' is an [[isomorphism]] is known as the [[strong rigidity]].) While certain rigidity phenomena had already been known, the approach of Margulis was at the same time novel, powerful, and very elegant.
 
Margulis solved the long-standing [[Banach]]–[[Ruziewicz problem]] that asks whether the [[Lebesgue measure]] is the only normalized rotationally invariant [[Banach measure|finitely additive measure]] on the [[n-sphere|''n''-dimensional sphere]]. The affirmative solution for ''n'' ≥ 4, which was also independently and almost simultaneously obtained by [[Dennis Sullivan]], follows from a construction of a certain dense subgroup of the [[orthogonal group]] that has property (T).
 
Margulis gave the first construction of [[expander graph]]s, which was later generalized in the theory of [[Ramanujan graph]]s.
 
In 1986, Margulis completed the proof of the [[Oppenheim conjecture]]  on [[quadratic form]]s and diophantine approximation. This was a question that had been open for half a century, on which considerable progress had been made by the [[Hardy-Littlewood circle method]]; but to reduce the number of variables to the point of getting the best-possible results, the more structural methods from [[group theory]] proved decisive. He has formulated a further program of research in the same direction, that includes the [[Littlewood conjecture]].
 
== Selected publications ==
 
=== Books ===
 
* [http://books.google.com/books/about/Discrete_Subgroups_of_Semisimple_Lie_Gro.html?id=V9z2cjHOhVoC ''Discrete subgroups of semisimple Lie groups''], [[Ergebnisse der Mathematik und ihrer Grenzgebiete]] (3) [Results in Mathematics and Related Areas (3)], 17. [[Springer-Verlag]], Berlin, 1991. x+388 pp.&nbsp;ISBN 3-540-12179-X {{MR|1090825}}<ref>{{cite journal|author=Zimmer, Robert J.|authorlink=Robert Zimmer|title=Review: ''Discrete subgroups of semisimple Lie groups'', by G. A. Margulis|journal=Bull. Amer. Math. Soc. (N.S.)|year=1992|volume=27|issue=1|pages=198–202|url=http://www.ams.org/journals/bull/1992-27-01/S0273-0979-1992-00306-3/S0273-0979-1992-00306-3.pdf}}</ref>
* ''On some aspects of the theory of Anosov systems''. With a survey by Richard Sharp: Periodic orbits of hyperbolic flows. Translated from the Russian by Valentina Vladimirovna Szulikowska. [[Springer Monographs in Mathematics]]. Springer-Verlag, Berlin, 2004. vi+139 pp.&nbsp;ISBN 3-540-40121-0 {{MR|2035655}}<ref>{{cite journal|author=Parry, William|authorlink=Bill Parry (mathematician)|title=Review: ''On some aspects of the theory of Anosov systems'', by G. A. Margulis, with a survey "Periodic orbits of hyperbolic flows", by Richard Sharp|journal=Bull. Amer. Math. Soc. (N.S.)|year=2005|volume=42|issue=2|pages=257–261|url=http://www.ams.org/journals/bull/2005-42-02/S0273-0979-05-01051-7/S0273-0979-05-01051-7.pdf}}</ref>
 
=== Lectures ===
* ''Oppenheim conjecture''.  Fields Medallists' lectures,  272–327, World Sci. Ser. 20th Century Math., 5, World Sci. Publ., River Edge, NJ, 1997 {{MR|1622909}}
* ''Dynamical and ergodic properties of subgroup actions on homogeneous spaces with applications to number theory''.  Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990),  193–215, Math. Soc. Japan, Tokyo, 1991 {{MR|1159213}}
 
=== Papers ===
* ''Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators''.  (Russian)  Problemy Peredachi Informatsii  24  (1988),  no. 1, 51–60; translation in Problems Inform. Transmission 24 (1988), no. 1, 39–46
* ''Arithmeticity of the irreducible lattices in the semisimple groups of rank greater than'' 1, Invent. Math. 76 (1984), no. 1, 93–120 {{MR|0739627}}
* ''Some remarks on invariant means'', Monatsh. Math. 90 (1980), no. 3, 233–235 {{MR|0596890}}
* ''Arithmeticity of nonuniform lattices in weakly noncompact groups''.  (Russian) Funkcional. Anal. i Prilozen. 9 (1975), no. 1, 35–44
* ''Arithmetic properties of discrete groups'',  Russian Math. Surveys 29 (1974) 107–165 {{MR|0463353}}
 
== References ==
{{reflist}}
 
== Further reading ==
* {{ cite conference | author=J. Tits | authorlink=Jacques Tits | title=The work of Gregori Aleksandrovitch Margulis | url=http://imu2.zib.de/ICM/ICM1978.1/ | pages=57–63 | editor=Olli Lehto (ed.) | booktitle=Proceedings of the [[International Congress of Mathematicians|ICM]] (Helsinki, 1978) | volume=1 | year=1980 | publisher=[[Finnish Academy of Science and Letters|Academia Scientiarum Fennica]] | location=Helsinki | isbn=951-41-0352-1 | mr=562596 | zbl = 0426.22011 }} ''1978 [[Fields Medal]] citation.''
 
== External links ==
* {{MacTutor Biography|id=Margulis}}
* {{IMO results |id=9834}}
* {{MathGenealogy |id=15062}}
 
{{Fields medalists}}
{{Wolf Prize in Mathematics}}
 
{{Authority control |VIAF=24699676 |LCCN=n/90/711576}}
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              =Margulis, Grigory
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Russian mathematician
| DATE OF BIRTH    =February 24, 1946
| PLACE OF BIRTH    = [[Moscow]], [[Russia]]
| DATE OF DEATH    =
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Margulis, Grigory}}
[[Category:21st-century mathematicians]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Soviet mathematicians]]
[[Category:Russian mathematicians]]
[[Category:Fields Medalists]]
[[Category:Moscow State University alumni]]
[[Category:Yale University faculty]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:People from Moscow]]
[[Category:1946 births]]
[[Category:Living people]]
[[Category:Alexander von Humboldt Fellows]]
[[Category:International Mathematical Olympiad participants]]

Revision as of 10:20, 21 January 2014

Template:BLP sources Template:Infobox scientist Gregori Aleksandrovich Margulis (My name is Jordan (41 years old) and my hobbies are Microscopy and Canoeing.

Check out my weblog Hostgator Review, first name often given as Gregory, Grigori or Grigory; born February 24, 1946) is a Russian mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978 and a Wolf Prize in Mathematics in 2005, becoming the seventh mathematician to receive both prizes. In 1991, he joined the faculty of Yale University, where he is currently the Erastus L. DeForest Professor of Mathematics.[1]

Short biography

Margulis was born in Moscow, Soviet Union. He received his PhD in 1970 from the Moscow State University, starting research in ergodic theory under the supervision of Yakov Sinai. Early work with David Kazhdan produced the Kazhdan–Margulis theorem, a basic result on discrete groups. His superrigidity theorem from 1975 clarified an area of classical conjectures about the characterisation of arithmetic groups amongst lattices in Lie groups.

He was awarded the Fields Medal in 1978, but was not permitted to travel to Helsinki to accept in person. His position improved, and in 1979 he visited Bonn, 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 Yale University.

Margulis was elected a member of the U.S. National Academy of Sciences in 2001.[2] In 2012 he became a fellow of the American Mathematical Society.[3]

In 2005, Margulis received the Wolf Prize for his contributions to theory of lattices and applications to ergodic theory, representation theory, number theory, combinatorics, and measure theory.

Mathematical contributions

Early work of Margulis dealt with Kazhdan's property (T) and the questions of rigidity and arithmeticity of lattices in semisimple algebraic groups of higher rank over a local field. It had been known since the 1950s (Borel, Harish-Chandra) that a certain simple-minded way of constructing subgroups of semisimple Lie groups produces examples of lattices, called arithmetic lattices. It is analogous to considering the subgroup SL(n,Z) of the real special linear group SL(n,R) that consists of matrices with integer entries. Margulis proved that under suitable assumptions on G (no compact factors and split rank greater or equal than two), any (irreducible) lattice Γ in it is arithmetic, i.e. can be obtained in this way. Thus Γ is commensurable with the subgroup G(Z) of G, i.e. they agree on subgroups of finite index 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 discovered by Margulis. Superrigidity for a lattice Γ in G roughly means that any homomorphism of Γ into the group of real invertible n × n matrices extends to the whole G. The name derives from the following variant:

If G and G' , semisimple algebraic groups over a local field without compact factors and whose split rank is at least two and Γ and Γ are irreducible lattices in them, then any homomorphism f: Γ → Γ between the lattices agrees on a finite index subgroup of Γ with a homomorphism between the algebraic groups themselves.

(The case when f is an isomorphism is known as the strong rigidity.) While certain rigidity phenomena had already been known, the approach of Margulis was at the same time novel, powerful, and very elegant.

Margulis solved the long-standing Banach–Ruziewicz problem that asks whether the Lebesgue measure is the only normalized rotationally invariant finitely additive measure on the n-dimensional sphere. The affirmative solution for n ≥ 4, which was also independently and almost simultaneously obtained by Dennis Sullivan, follows from a construction of a certain dense subgroup of the orthogonal group that has property (T).

Margulis gave the first construction of expander graphs, which was later generalized in the theory of Ramanujan graphs.

In 1986, Margulis completed the proof of the Oppenheim conjecture on quadratic forms and diophantine approximation. This was a question that had been open for half a century, on which considerable progress had been made by the Hardy-Littlewood circle method; but to reduce the number of variables to the point of getting the best-possible results, the more structural methods from group theory proved decisive. He has formulated a further program of research in the same direction, that includes the Littlewood conjecture.

Selected publications

Books

Lectures

  • Oppenheim conjecture. Fields Medallists' lectures, 272–327, World Sci. Ser. 20th Century Math., 5, World Sci. Publ., River Edge, NJ, 1997 Template:MR
  • Dynamical and ergodic properties of subgroup actions on homogeneous spaces with applications to number theory. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 193–215, Math. Soc. Japan, Tokyo, 1991 Template:MR

Papers

  • Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators. (Russian) Problemy Peredachi Informatsii 24 (1988), no. 1, 51–60; translation in Problems Inform. Transmission 24 (1988), no. 1, 39–46
  • Arithmeticity of the irreducible lattices in the semisimple groups of rank greater than 1, Invent. Math. 76 (1984), no. 1, 93–120 Template:MR
  • Some remarks on invariant means, Monatsh. Math. 90 (1980), no. 3, 233–235 Template:MR
  • Arithmeticity of nonuniform lattices in weakly noncompact groups. (Russian) Funkcional. Anal. i Prilozen. 9 (1975), no. 1, 35–44
  • Arithmetic properties of discrete groups, Russian Math. Surveys 29 (1974) 107–165 Template:MR

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Further reading

  • 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

    You can view that web-site... ccleaner free download 1978 Fields Medal citation.

External links

Template:Fields medalists Template:Wolf Prize in Mathematics

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  1. ↑ Template:Cite web
  2. ↑ National Academy of Sciences Elections. Notices of the American Mathematical Society, vol. 48 (2001), no. 7, p. 722
  3. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-02-02.
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    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
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