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{{Short description|Russian American mathematician (born 1955)}}
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{{Infobox scientist
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{{Infobox Scientist
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| image =
| caption =
| name = Alexander Merkurjev
| name = Alexander Merkurjev
| residence = [[USA]]
| native_name = Aleksandr Sergeyevich Merkurjev
| birth_date = {{birth date and age|1955|9|25}}
| image = Alexander Merkurjev.jpg
| birth_place =
| image_size =
| nationality =
| alt =
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| caption =
| birth_date = {{birth date and age|1955|09|25|mf=y}}
| birth_place = [[Saint Petersburg]], [[Soviet Union|USSR]]
| field = [[Mathematics]]
| field = [[Mathematics]]
| work_institutions = [[University of California Los Angeles]]
| work_institutions = [[University of California Los Angeles]]
| alma_mater = [[Leningrad University]]
| alma_mater = [[Leningrad University]]
| doctoral_advisor = Anatoli Jakovlev
| doctoral_advisor = Anatoli Yakovlev
| doctoral_students = Nikita Karpenko
| doctoral_students =
| known_for = Merkurjev-Suslin theorem, book of involutions, [[essential dimension]]
| known_for = [[Merkurjev–Suslin theorem]], cohomological invariants, canonical dimension, book of involutions, [[essential dimension]]
| prizes = [[Cole Prize|Cole Prize in Algebra]] (2012)<br />[[Petersburg Mathematical Society]] Prize (1982)<br />[[Humboldt Prize]] (1995)
| prizes =
| religion =
| footnotes =
}}
}}

'''Alexander Merkurjev''' ({{lang-ru|Александр Сергеевич Меркурьев}}) is a [[Russia]]n-born American mathematician, who has made major contributions to the field of [[algebra]]. Currently Merkurjev is a professor at the [[University of California, Los Angeles]].
'''Aleksandr Sergeyevich Merkurjev''' ({{langx|ru|Алекса́ндр Сергее́вич Мерку́рьев}}, born September 25, 1955<ref>Listed in the [http://catalog.loc.gov/ Library of Congress Online Catalog]</ref>) is a Russian-American mathematician, who has made major contributions to the field of [[algebra]]. Currently Merkurjev is a professor at the [[University of California, Los Angeles]].


==Work==
==Work==
Merkurjev's work focuses on [[algebraic group]]s, [[quadratic form]]s, [[Galois cohomology]], [[algebraic K-theory]] and [[central simple algebra]]s. In the early 1980's Merkurjev proved a fundamental result about the structure of central simple algebras of [[period]] dividing 2, which relates the 2-torsion of the [[Brauer group]] with [[Milnor K-theory]]<ref>{{cite web|title=On the norm residue symbol of degree 2|author=A. Merkurjev|publisher=''Dokl. Akad. Nauk SSSR'', 261|date=1981|pages=542–547
Merkurjev's work focuses on [[algebraic group]]s, [[quadratic form]]s, [[Galois cohomology]], [[algebraic K-theory]] and [[central simple algebra]]s. In the early 1980s Merkurjev proved a fundamental result about the structure of central simple algebras of [[periodic group|period]] dividing 2, which relates the 2-torsion of the [[Brauer group]] with [[Milnor K-theory]].<ref>{{cite journal|title=On the norm residue symbol of degree 2|author=A. Merkurjev|journal=Dokl. Akad. Nauk SSSR |volume=261|year=1981|pages=542–547 (English trans. Soviet Math. Dokl. 24 (1982), pp.1546–1551)}}</ref> In subsequent work with [[Andrei Suslin|Suslin]] this was extended to higher torsion as the [[Merkurjev–Suslin theorem]]. The full statement of the [[norm residue isomorphism theorem]] (also known as the Bloch-Kato conjecture) was proven by [[Vladimir Voevodsky|Voevodsky]].
(English trans. Soviet Math. Dokl. 24 (1982), pp.1546–1551)}}</ref>. In subsequent work with [[Andrei Suslin|Suslin]] this was extended to higher torsion. More recently these results were generalized in the [[norm residue isomorphism theorem]] (previously known as Bloch-Kato conjecture), proven in full generality by [[Markus Rost|Rost]] and [[Vladimir Voevodsky|Voevodsky]].


In the late 1990's Merkurjev gave the most general approach to the notion of [[essential dimension]], introduced by [[Joe Buhler|Buhler]] and [[Zinovy Reichstein|Reichstein]], and made fundamental contributions to that field. In particular Merkurjev determined the essential p-dimension of central simple algebras of degree <math>p^2</math> (for a prime p)<ref>{{cite web|url=http://www.ams.org/journals/jams/2010-23-03/S0894-0347-10-00661-2/home.html|title=Essential p-dimension of PGL(p^2)|author=A. Merkurjev|date=2010|publisher=[[Journal of the american mathematical society|JAMS]], 23|pages=693-712}}</ref> and, in joint work with [[Nikita Karpenko|Karpenko]], the essential dimension of finite p-groups.<ref>{{cite web|url=http://www.springerlink.com/content/xng8qx13546t8618/|title=Essential dimension of finite p-groups|publisher=[[Inventiones Mathematicae]], 172, no. 3|author=N. Karpenko, A. Merkurjev| date=2008|pages=491--508}}</ref>.
In the late 1990s Merkurjev gave the most general approach to the notion of [[essential dimension]], introduced by [[Joe Buhler|Buhler]] and [[Zinovy Reichstein|Reichstein]], and made fundamental contributions to that field. In particular Merkurjev determined the essential p-dimension of central simple algebras of degree <math>p^2</math> (for a prime p) and, in joint work with [[Nikita Karpenko|Karpenko]], the essential dimension of finite ''p''-groups.<ref>{{cite journal|url=https://www.ams.org/journals/jams/2010-23-03/S0894-0347-10-00661-2/home.html|title=Essential p-dimension of PGL(p^2)|author=A. Merkurjev|journal=Journal of the American Mathematical Society |year=2010|volume=23 |issue=3 |publisher=[[Journal of the American Mathematical Society|JAMS]], 23|pages=693–712|doi=10.1090/S0894-0347-10-00661-2 |doi-access=free}}</ref><ref>{{cite journal|title=Essential dimension of finite ''p''-groups|journal=[[Inventiones Mathematicae]]|author=N. Karpenko|author2=A. Merkurjev| year=2008|pages=491–508|doi=10.1007/s00222-007-0106-6|volume=172|issue=3|bibcode=2008InMat.172..491K |citeseerx = 10.1.1.72.8045|s2cid=14306605}}</ref>


==Awards and Distinctions==
==Awards==
In 1982 Merkurjev won the Young Mathematician Prize of the [[Petersburg Mathematical Society]] for his work on algebraic K-theory. <ref>{{cite web|url=http://www.mathsoc.spb.ru/mol_mat.html|title=Young mathematician prize of the [[Petersburg Mathematical Society]]}}</ref> Later in 1995 he won the [[Humboldt Prize]]. Merkurjev gave a plenary talk at the 2nd [[European Congress of Mathematics]] in [[Budapest, Hungary]], 1996.<ref>{{cite web|url=http://www.emis.de/ECM2/talks.html|title=Speakers and talks at the 2nd European Congress of Mathematics}}</ref>
Merkurjev won the Young Mathematician Prize of the [[Petersburg Mathematical Society]] for his work on algebraic K-theory.<ref>{{cite web|url=http://www.mathsoc.spb.ru/mol_mat.html|title=Young mathematician prize of the Petersburg Mathematical Society}}</ref> In 1986 he was an [[list of International Congresses of Mathematicians Plenary and Invited Speakers|invited speaker at the International Congress of Mathematicians]] in [[Berkeley, California]], and his talk was entitled "Milnor K-theory and Galois cohomology".<ref>{{cite web|url=http://www.mathunion.org/ICM/ICM1986.1/|title=Proceedings of the International Congress of Mathematicians, August 3-11, 1986|publisher=International Mathematical Union|access-date=2011-05-30|archive-date=2014-02-02|archive-url=https://web.archive.org/web/20140202102209/http://www.mathunion.org/ICM/ICM1986.1/|url-status=dead}} Merkurjev's talk: [http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0389.0393.ocr.pdf Milnor K-theory and Galois cohomology] {{Webarchive|url=https://web.archive.org/web/20160303191822/http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0389.0393.ocr.pdf |date=2016-03-03 }}.</ref> In 1995 he won the [[Humboldt Prize]], an international prize awarded to renowned scholars. Merkurjev gave a plenary talk at the second [[European Congress of Mathematics]] in [[Budapest, Hungary]] in 1996.<ref>{{cite web|url=http://www.emis.de/ECM2/talks.html|title=Speakers and talks at the second European Congress of Mathematics}}</ref>
In 2012 he won the [[Cole Prize]] in Algebra for his work on the essential dimension of groups.<ref>{{cite web|url=https://www.ams.org/notices/201204/rtx120400567p.pdf|title=2012 Cole Prize in Algebra}}</ref>


In 2015 a special volume of ''Documenta Mathematica'' was published in honor of Merkurjev's sixtieth birthday.<ref>{{cite web|url=
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== References ==
https://www.math.uni-bielefeld.de/documenta/vol-merkurjev/vol-merkurjev.html
<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags which will then appear here automatically -->
|title=Extra volume of Documenta Mathematica (2015) in honour of A. Merkurjev|editor=P. Balmer |editor-link=Paul Balmer|editor2=V. Chernousov|editor3=I. Fesenko|editor3-link=Ivan Fesenko|editor4=E. Friedlander|editor4-link=Eric Friedlander|editor5=S. Garibaldi|editor5-link=Skip Garibaldi|editor6=Z. Reichstein|editor7=U. Rehmann|editor6-link=Zinovy Reichstein}}</ref>
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{{Reflist}}


== Bibliography==
==Bibliography==
* with Max-Albert Knus, [[Markus Rost]], Jean-Pierre Tignol: The book of involutions, American Mathematical Society 1998.
* with Skip Garibaldi, [[Jean-Pierre Serre]]: Cohomological Invariants in Galois Cohomology, American Mathematical Society 2003.
* with Richard Elman, Nikita Karpenko: Algebraic and geometric theory of quadratic forms, American Mathematical Society 2008.


===Books===
* Max-Albert Knus, Alexander Merkurjev, [[Markus Rost]], [[Jean-Pierre Tignol]]: The book of involutions, American Mathematical Society 1998. {{ISBN|0-8218-0904-0}}<ref>{{cite journal|author=Springer, T. A.|author-link=T. A. Springer|title=Review: ''The book of involutions'', by M.-A. Knus, A. Merkurjev, M. Rost, and J.-P. Tignol (with a preface by J. Tits)|journal=Bull. Amer. Math. Soc. (N.S.)|year=1999|volume=36|issue=3|pages=383–388|url=https://www.ams.org/journals/bull/1999-36-03/S0273-0979-99-00780-6/S0273-0979-99-00780-6.pdf|doi=10.1090/S0273-0979-99-00780-6|doi-access=free}}</ref>
* [[Skip Garibaldi]], [[Jean-Pierre Serre]], Alexander Merkurjev: Cohomological Invariants in Galois Cohomology, American Mathematical Society 2003. {{ISBN|0-8218-3287-5}}<ref>{{cite journal|author=Swallow, John|title=Review: ''Cohomological invariants in Galois cohomology'', by Skip Garibaldi, Alexander Merkurjev, and Jean-Pierre Serre|journal=Bull. Amer. Math. Soc. (N.S.)|year=2005|volume=42|issue=1|pages=93–98|url=https://www.ams.org/journals/bull/2005-42-01/S0273-0979-04-01033-X/S0273-0979-04-01033-X.pdf|doi=10.1090/S0273-0979-04-01033-X|doi-access=free}}</ref>
* [[Richard Elman (mathematician)|Richard Elman]], Nikita Karpenko, Alexander Merkurjev: Algebraic and geometric theory of quadratic forms, American Mathematical Society 2008. {{ISBN|978-0-8218-4329-1}}<ref>{{cite web|author=Zaldivar, Felipe|title=Review: ''The Algebraic and Geometric Theory of Quadratic Forms''|website=MAA Reviews|date=2008|url=http://www.maa.org/publications/maa-reviews/the-algebraic-and-geometric-theory-of-quadratic-forms}}</ref>


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==References==
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== External links ==
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{{Reflist}}
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*[http://www.math.ucla.edu/~merkurev/ Alexander Merkurjev - personal webpage at UCLA]

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*{{MathGenealogy|id=59531}}
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==External links==
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* [https://www.math.ucla.edu/~merkurev/ Alexander Merkurjev - personal webpage at UCLA]
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* {{MathGenealogy|id=59531}}
* {{IMO results |id=10249 }}

{{Authority control}}


{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME = Merkurjev, Alexander
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION =
| DATE OF BIRTH = September 25, 1955
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
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<!--- Categories --->
{{DEFAULTSORT:Merkurjev, Alexander}}
{{DEFAULTSORT:Merkurjev, Alexander}}
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<!--- Categories --->
[[Category:1950 births]]
[[Category:1955 births]]
[[Category:Living people]]
[[Category:Living people]]
[[Category:American mathematicians]]
[[Category:University of California, Los Angeles faculty]]
[[Category:University of California, Los Angeles faculty]]
[[Category:20th-century mathematicians]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Algebraists]]
[[Category:Algebraists]]
[[Category:International Mathematical Olympiad participants]]

Latest revision as of 22:18, 29 October 2024

Alexander Merkurjev
Aleksandr Sergeyevich Merkurjev
Born (1955-09-25) September 25, 1955 (age 69)
Saint Petersburg, USSR
Alma materLeningrad University
Known forMerkurjev–Suslin theorem, cohomological invariants, canonical dimension, book of involutions, essential dimension
AwardsCole Prize in Algebra (2012)
Petersburg Mathematical Society Prize (1982)
Humboldt Prize (1995)
Scientific career
FieldsMathematics
InstitutionsUniversity of California Los Angeles
Doctoral advisorAnatoli Yakovlev

Aleksandr Sergeyevich Merkurjev (Russian: Алекса́ндр Сергее́вич Мерку́рьев, born September 25, 1955[1]) is a Russian-American mathematician, who has made major contributions to the field of algebra. Currently Merkurjev is a professor at the University of California, Los Angeles.

Work

[edit]

Merkurjev's work focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K-theory and central simple algebras. In the early 1980s Merkurjev proved a fundamental result about the structure of central simple algebras of period dividing 2, which relates the 2-torsion of the Brauer group with Milnor K-theory.[2] In subsequent work with Suslin this was extended to higher torsion as the Merkurjev–Suslin theorem. The full statement of the norm residue isomorphism theorem (also known as the Bloch-Kato conjecture) was proven by Voevodsky.

In the late 1990s Merkurjev gave the most general approach to the notion of essential dimension, introduced by Buhler and Reichstein, and made fundamental contributions to that field. In particular Merkurjev determined the essential p-dimension of central simple algebras of degree (for a prime p) and, in joint work with Karpenko, the essential dimension of finite p-groups.[3][4]

Awards

[edit]

Merkurjev won the Young Mathematician Prize of the Petersburg Mathematical Society for his work on algebraic K-theory.[5] In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley, California, and his talk was entitled "Milnor K-theory and Galois cohomology".[6] In 1995 he won the Humboldt Prize, an international prize awarded to renowned scholars. Merkurjev gave a plenary talk at the second European Congress of Mathematics in Budapest, Hungary in 1996.[7] In 2012 he won the Cole Prize in Algebra for his work on the essential dimension of groups.[8]

In 2015 a special volume of Documenta Mathematica was published in honor of Merkurjev's sixtieth birthday.[9]

Bibliography

[edit]

Books

[edit]
  • Max-Albert Knus, Alexander Merkurjev, Markus Rost, Jean-Pierre Tignol: The book of involutions, American Mathematical Society 1998. ISBN 0-8218-0904-0[10]
  • Skip Garibaldi, Jean-Pierre Serre, Alexander Merkurjev: Cohomological Invariants in Galois Cohomology, American Mathematical Society 2003. ISBN 0-8218-3287-5[11]
  • Richard Elman, Nikita Karpenko, Alexander Merkurjev: Algebraic and geometric theory of quadratic forms, American Mathematical Society 2008. ISBN 978-0-8218-4329-1[12]

References

[edit]
  1. ^ Listed in the Library of Congress Online Catalog
  2. ^ A. Merkurjev (1981). "On the norm residue symbol of degree 2". Dokl. Akad. Nauk SSSR. 261: 542–547 (English trans. Soviet Math. Dokl. 24 (1982), pp.1546–1551).
  3. ^ A. Merkurjev (2010). "Essential p-dimension of PGL(p^2)". Journal of the American Mathematical Society. 23 (3). JAMS, 23: 693–712. doi:10.1090/S0894-0347-10-00661-2.
  4. ^ N. Karpenko; A. Merkurjev (2008). "Essential dimension of finite p-groups". Inventiones Mathematicae. 172 (3): 491–508. Bibcode:2008InMat.172..491K. CiteSeerX 10.1.1.72.8045. doi:10.1007/s00222-007-0106-6. S2CID 14306605.
  5. ^ "Young mathematician prize of the Petersburg Mathematical Society".
  6. ^ "Proceedings of the International Congress of Mathematicians, August 3-11, 1986". International Mathematical Union. Archived from the original on 2014-02-02. Retrieved 2011-05-30. Merkurjev's talk: Milnor K-theory and Galois cohomology Archived 2016-03-03 at the Wayback Machine.
  7. ^ "Speakers and talks at the second European Congress of Mathematics".
  8. ^ "2012 Cole Prize in Algebra" (PDF).
  9. ^ P. Balmer; V. Chernousov; I. Fesenko; E. Friedlander; S. Garibaldi; Z. Reichstein; U. Rehmann (eds.). "Extra volume of Documenta Mathematica (2015) in honour of A. Merkurjev".
  10. ^ Springer, T. A. (1999). "Review: The book of involutions, by M.-A. Knus, A. Merkurjev, M. Rost, and J.-P. Tignol (with a preface by J. Tits)" (PDF). Bull. Amer. Math. Soc. (N.S.). 36 (3): 383–388. doi:10.1090/S0273-0979-99-00780-6.
  11. ^ Swallow, John (2005). "Review: Cohomological invariants in Galois cohomology, by Skip Garibaldi, Alexander Merkurjev, and Jean-Pierre Serre" (PDF). Bull. Amer. Math. Soc. (N.S.). 42 (1): 93–98. doi:10.1090/S0273-0979-04-01033-X.
  12. ^ Zaldivar, Felipe (2008). "Review: The Algebraic and Geometric Theory of Quadratic Forms". MAA Reviews.
[edit]
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