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{{short description|Russian mathematician}}
{{Infobox scientist
{{Infobox scientist
| name = Victor Gershevich Kac
| name = Victor Gershevich Kac
| image =
| image =
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| image_size =
| alt =
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| birth_date = {{Birth date and age|1943|12|19}}
| birth_date = {{Birth date and age|1943|12|19}}
| birth_place = [[Buguruslan]], Orenburg Oblast, Russia
| birth_place = [[Buguruslan]], [[Orenburg Oblast]], [[Russian SFSR]]
| death_date =
| death_date =
| death_place =
| death_place =
| resting_place =
| resting_place =
| resting_place_coordinates =
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| residence =
| residence =
| citizenship =
| citizenship =
| nationality =
| nationality =
| fields = [[Mathematics]]
| fields = Mathematics
| workplaces = [[Massachusetts Institute of Technology|MIT]]
| workplaces = [[Massachusetts Institute of Technology|MIT]]
| alma_mater = [[Moscow State University]] <small>([[Master of Science|M.S.]])</small><br>[[Moscow State University]] <small>([[Doctor of Philosophy|Ph.D.]])</small>
| alma_mater = [[Moscow State University]] <small>([[Master of Science|MS]])</small><br>[[Moscow State University]] <small>(PhD)</small>
| thesis_title = Simple Irreducible Graded Lie Algebras of Finite Growth
| thesis_title = Simple Irreducible Graded Lie Algebras of Finite Growth
| thesis_url =
| thesis_url =
| thesis_year = 1968
| thesis_year = 1968
| doctoral_advisor = Èrnest Borisovich Vinberg<ref> Mathematics Genealogy Project: https://www.genealogy.math.ndsu.nodak.edu/id.php?id=37054</ref>
| doctoral_advisor = [[Ernest Vinberg|Èrnest Borisovich Vinberg]]<ref>Mathematics Genealogy Project: https://www.genealogy.math.ndsu.nodak.edu/id.php?id=37054</ref>
| academic_advisors =
| academic_advisors =
| doctoral_students =
| doctoral_students =
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* Classification of [[Lie superalgebras]]
* Classification of [[Lie superalgebras]]
* Kac–Weisfeiler conjectures
* Kac–Weisfeiler conjectures
* Kac determinate formula for [[Virasoro algebra]]}}
* Kac determinant formula for [[Virasoro algebra]]}}
| awards = {{Plainlist|
| awards = {{Plainlist|
* [[Sloan Research Fellowship]] (1981)
* [[Sloan Research Fellowship]] (1981)
* Medal of the [[College de France]] (1981)
* Medal of the [[Collège de France]] (1981)
* [[Guggenheim Fellowship]] (1986)
* [[Guggenheim Fellowship]] (1986)
* [[Wigner Medal]] (1996)
* [[Wigner Medal]] (1996)
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}}
}}


'''Victor Gershevich''' ('''Grigorievich''') '''Kac''' ({{lang-ru|Виктор Гершевич (Григорьевич) Кац}}; born 19 December 1943 in [[Buguruslan]], [[Russian SFSR|Russia]], [[USSR]]) is a [[USSR|Soviet]] and [[United States|American]] [[mathematician]] at [[MIT]], known for his work in [[representation theory]]. He co-discovered [[Kac–Moody algebra]]s, and used the [[Weyl character formula#Weyl.E2.80.93Kac character formula|Weyl–Kac character formula]] for them to reprove the [[Macdonald identity|Macdonald identities]]. He classified the finite-dimensional simple [[Lie superalgebra]]s, and found the [[Kac determinant formula]] for the [[Virasoro algebra]]. He is also known for the Kac–Weisfeiler conjectures with [[Boris Weisfeiler]].
'''Victor Gershevich''' ('''Grigorievich''') '''Kac''' ({{langx|ru|link=no|Виктор Гершевич (Григорьевич) Кац}}; born 19 December 1943) is a Soviet and American mathematician at [[MIT]], known for his work in [[representation theory]]. He co-discovered<ref>Stephen Berman, [[Karen Parshall]] "Victor Kac and Robert Moody — their paths to Kac–Moody-Algebras", ''Mathematical Intelligencer'', 2002, Nr.1 [https://www.academia.edu/20121772/Victor_kac_and_robert_moody_their_paths_to_kac-moody_lie_algebras]</ref> [[Kac–Moody algebra]]s, and used the [[Weyl character formula#Weyl.E2.80.93Kac character formula|Weyl–Kac character formula]] for them to reprove the [[Macdonald identities]]. He classified the finite-dimensional simple [[Lie superalgebra]]s, and found the [[Kac determinant formula]] for the [[Virasoro algebra]]. He is also known for the Kac–Weisfeiler conjectures with [[Boris Weisfeiler]].


==Biography==
==Biography==
Kac studied mathematics at [[Moscow State University]], receiving his M.S. in 1965 and his Ph.D. in 1968.<ref> Victor Kac, A Biographical Interview: http://dynkincollection.library.cornell.edu/sites/default/files/Victor%20Kac%20%28RI-ED%29.pdf</ref> From 1968 to 1976, he held a teaching position at the [[Moscow Institute of Electronic Machine Building]]. He left the [[Soviet Union]] in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a [[Sloan Fellowship]] in 1981 and a [[Guggenheim Fellowship]] in 1986 and the Medal of the [[College de France]] (1981). He received the [[Wigner Medal]] (1996) "in recognition of work on affine [[Lie algebras]] that has had wide influence in theoretical physics". In 1978 he was an Invited Speaker (''Highest weight representations of infinite dimensional Lie algebras'') at the ICM in [[Helsinki]]. Kac was a plenary speaker at the 1988 AMS centennial conference. In 2002 he gave a plenary lecture, ''Classification of Supersymmetries'', at the [[International Congress of Mathematicians|ICM]] in [[Beijing]].
Kac studied mathematics at [[Moscow State University]], receiving his MS in 1965 and his PhD in 1968.<ref>Victor Kac, A Biographical Interview: http://dynkincollection.library.cornell.edu/sites/default/files/Victor%20Kac%20%28RI-ED%29.pdf</ref> From 1968 to 1976, he held a teaching position at the [[Moscow Institute of Electronic Machine Building]] (MIEM). He left the [[Soviet Union]] in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a [[Sloan Fellowship]] and the Medal of the [[Collège de France]], both in 1981, and a [[Guggenheim Fellowship]] in 1986. He received the [[Wigner Medal]] (1996) "in recognition of work on affine [[Lie algebras]] that has had wide influence in [[theoretical physics]]". In 1978 he was an invited speaker (''Highest weight representations of infinite dimensional Lie algebras'') at the [[International Congress of Mathematicians]] (ICM) in [[Helsinki]]. Kac was a plenary speaker at the 1988 [[American Mathematical Society]] centennial conference. In 2002 he gave a plenary lecture, ''Classification of Supersymmetries'', at the ICM in Beijing.


Kac is a Fellow of the [[American Mathematical Society]],<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref> an Honorary member of the [[Moscow Mathematical Society]], Fellow of the [[American Academy of Arts and Sciences]] and a Member of the [[National Academy of Sciences]].
Kac is a Fellow of the [[American Mathematical Society]],<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref> an honorary member of the [[Moscow Mathematical Society]], Fellow of the [[American Academy of Arts and Sciences]] and a Member of the [[National Academy of Sciences]].


The research of Victor Kac primarily concerns [[representation theory]] and [[mathematical physics]]. His work appears in mathematics and physics and in the development of [[quantum field theory]], [[string theory]] and the theory of [[integrable systems]].
The research of Victor Kac primarily concerns [[representation theory]] and [[mathematical physics]]. His work appears in mathematics and physics and in the development of [[quantum field theory]], [[string theory]] and the theory of [[integrable systems]].


⚫
Kac has published 13 books and over 200 articles in mathematics and physics journals and is listed as an [[ISI highly cited researcher]].<ref>{{cite web|title=List of ISI highly cited researchers|url=http://highlycited.com}}</ref> Victor Kac was awarded the 2015 AMS [[Leroy P. Steele Prize]] for Lifetime Achievement.<ref>[http://www.ams.org/news?news_id=2462 2015 AMS Steele Prizes]</ref><ref>{{Cite web |title=American Mathematical Society :: Homepage |url=https://www.ams.org/home/page#sthash.3WHgu32P.dpuf |access-date=2024-11-12 |website=American Mathematical Society |language=en}}</ref>
⚫
==Kac-Moody algebra==
⚫
"Almost simultaneously in 1967, Victor Kac in the USSR and [[Robert Moody]] in Canada developed what was to become [[Kac-Moody algebra]]. Kac and Moody noticed that if [[Wilhelm Killing]]'s conditions were relaxed, it was still possible to associate to the [[Cartan matrix]] a Lie algebra which, necessarily, would be infinite dimensional." - A.J. Coleman<ref>Coleman, A. John, "The Greatest Mathematical Paper of All Time," ''[http://www.math.umd.edu/~jda/744/coleman.pdf The Mathematical Intelligencer],'' vol. 11, no. 3, pp.&nbsp;29–38.</ref>


⚫
He was married with [[Michèle Vergne]]<ref>[https://smf.emath.fr/download/pdf/170853 La Gazette des Mathématiciens 165], retrieved 2021-04-22.</ref> and they have a daughter, Marianne Kac-Vergne, who is a professor of American civilization at the university of Picardie. His brother [[Boris Katz]] is a principal research scientist at MIT.<ref>{{cite news| url=http://www.boston.com/news/globe/obituaries/articles/2006/10/04/clara_katz_soviet_migr_saved_ailing_granddaughter/ | work=The Boston Globe | first=Gloria | last=Negri | title=Clara Katz; Soviet émigré saved ailing granddaughter | date=4 October 2006}}</ref>
⚫
Kac has published 13 books and over 200 articles in mathematics and physics journals and is listed as an [[ISI highly cited researcher]].<ref>{{cite web|title=List of ISI highly cited researchers|url=http://highlycited.com}}</ref> Victor Kac was awarded the 2015 AMS [[Leroy P. Steele Prize]] for Lifetime Achievement.<ref>[http://www.ams.org/news?news_id=2462 2015 AMS Steele Prizes]</ref>


⚫
==Kac–Moody algebra==
⚫
His brother [[Boris Katz]] is a principal research scientist at MIT.<ref>{{cite news| url=http://www.boston.com/news/globe/obituaries/articles/2006/10/04/clara_katz_soviet_migr_saved_ailing_granddaughter/ | work=The Boston Globe | first=Gloria | last=Negri | title=Clara Katz; Soviet émigré saved ailing granddaughter | date=4 October 2006}}</ref>
⚫
"Almost simultaneously in 1967, Victor Kac in the USSR and [[Robert Moody]] in Canada developed what was to become [[Kac–Moody algebra]]. Kac and Moody noticed that if [[Wilhelm Killing]]'s conditions were relaxed, it was still possible to associate to the [[Cartan matrix]] a Lie algebra which, necessarily, would be infinite dimensional." – A.J. Coleman<ref>Coleman, A. John, "The Greatest Mathematical Paper of All Time", ''[https://www.math.umd.edu/~jda/744/coleman.pdf The Mathematical Intelligencer],'' vol. 11, no. 3, pp.&nbsp;29–38.</ref>


==Bibliography==
==Bibliography==
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|publisher=Cambridge University Press
|publisher=Cambridge University Press
|edition=3rd
|edition=3rd
|origyear=1985
|orig-year=1985
|year=1994
|year=1994
|isbn=0-521-46693-8
|isbn=0-521-46693-8
|url=https://books.google.com/books?id=kuEjSb9teJwC&lpg=PP1&ots=wzuwH7Nn98&dq=Infinite-Dimensional%20Lie%20Algebras&pg=PP1#v=onepage&q&f=false
|url=https://books.google.com/books?id=kuEjSb9teJwC&q=Infinite-Dimensional%20Lie%20Algebras&pg=PP1
}}
}}


*{{Cite book|url=https://www.worldcat.org/oclc/840277997|title=Infinite Dimensional Groups with Applications|last=V.|first=Kac,|date=1985|publisher=Springer New York|isbn=9781461211044|location=New York, NY|oclc=840277997}}
*{{Cite book|title=Infinite Dimensional Groups with Applications|first=V.|last=Kac|date=1985|publisher=Springer|location= New York|isbn=9781461211044 |oclc=840277997}}
⚫
*{{cite journal|last=Seligman|first= George B.|author-link=George Seligman|title=Review: ''Infinite-dimensional Lie algebras'', by Victor G. Kac, 2nd edition|journal=Bull. Amer. Math. Soc. (N.S.)|year=1987|pages=144–149|url=http://www.ams.org/journals/bull/1987-16-01/S0273-0979-1987-15492-9/S0273-0979-1987-15492-9.pdf|doi=10.1090/S0273-0979-1987-15492-9|volume=16|doi-access=free}}

⚫
*{{Cite book|title=Bombay lectures on highest weight representations of infinite-dimensional Lie algebras|last1=Kac|first1=Victor G.|date=1987|publisher=World Scientific|last2=Raina|first2= A. K.|isbn=9971503956|location=Singapore|oclc=18475755}}
⚫
*{{cite journal|author=Seligman, George B.|authorlink=George Seligman|title=Review: ''Infinite-dimensional Lie algebras'', by Victor G. Kac, 2nd edition|journal=Bull. Amer. Math. Soc. (N.S.)|year=1987|pages=144–149|url=http://www.ams.org/journals/bull/1987-16-01/S0273-0979-1987-15492-9/S0273-0979-1987-15492-9.pdf|doi=10.1090/S0273-0979-1987-15492-9|volume=16}}

⚫
*{{Cite book|url=https://www.worldcat.org/oclc/18475755|title=Bombay lectures on highest weight representations of infinite dimensional lie algebras|last=1943-|first=Kac, Victor G.,|date=1987|publisher=World Scientific|others=Raina, A. K.|isbn=9971503956|location=Singapore|oclc=18475755}}

*{{cite book
*{{cite book
|title=Vertex Algebras for Beginners (University Lecture Series, No 10)
|title=Vertex Algebras for Beginners (University Lecture Series, No 10)
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|isbn=0-8218-0643-2
|isbn=0-8218-0643-2
}}
}}
⚫
*{{Cite book|title=Quantum calculus|last1=Kac|first1= Victor G.|date=2002|publisher=Springer|last2=Cheung| first2 = Pokman|isbn=0387953418|location=New York|oclc=47243954}}

⚫
*{{Cite book|url=https://www.worldcat.org/oclc/47243954|title=Quantum calculus|last=1943-|first=Kac, Victor G.,|date=2002|publisher=Springer|others=Cheung, Pokman.|isbn=0387953418|location=New York|oclc=47243954}}

*{{cite book
*{{cite book
|title=Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras
|title=Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras
|volume=29
|first=Victor G.
|first1=Victor G.
|last=Kac
|last1=Kac
|first2=A. K.
|last2=Raina
|publisher=World Scientific Publishing
|publisher=World Scientific Publishing
|edition=2nd
|edition=2nd
|year=2013
|year=2013
|isbn=978-981-4522-18-2
|isbn=978-981-4522-18-2
|url=http://www.worldscientific.com/worldscibooks/10.1142/8882
|doi=10.1142/8882
|series=Advanced Series in Mathematical Physics
}}
}}


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[[Category:1943 births]]
[[Category:1943 births]]
[[Category:Living people]]
[[Category:Living people]]
[[Category:American mathematicians]]
[[Category:People from Buguruslan]]
[[Category:20th-century American mathematicians]]
[[Category:Russian mathematicians]]
[[Category:Russian mathematicians]]
[[Category:Soviet mathematicians]]
[[Category:Soviet mathematicians]]
[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:American people of Russian-Jewish descent]]
[[Category:American people of Russian-Jewish descent]]
[[Category:Guggenheim Fellows]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:ISI highly cited researchers]]
[[Category:Moscow State University alumni]]
[[Category:Moscow State University alumni]]
[[Category:21st-century American mathematicians]]

Latest revision as of 10:33, 12 November 2024

Victor Gershevich Kac
Born (1943-12-19) December 19, 1943 (age 80)
Buguruslan, Orenburg Oblast, Russian SFSR
Alma materMoscow State University (MS)
Moscow State University (PhD)
Known for
Awards
Scientific career
FieldsMathematics
InstitutionsMIT
Thesis Simple Irreducible Graded Lie Algebras of Finite Growth  (1968)
Doctoral advisorÈrnest Borisovich Vinberg[1]

Victor Gershevich (Grigorievich) Kac (Russian: Виктор Гершевич (Григорьевич) Кац; born 19 December 1943) is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discovered[2] Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler.

Biography

[edit]

Kac studied mathematics at Moscow State University, receiving his MS in 1965 and his PhD in 1968.[3] From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Machine Building (MIEM). He left the Soviet Union in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship and the Medal of the Collège de France, both in 1981, and a Guggenheim Fellowship in 1986. He received the Wigner Medal (1996) "in recognition of work on affine Lie algebras that has had wide influence in theoretical physics". In 1978 he was an invited speaker (Highest weight representations of infinite dimensional Lie algebras) at the International Congress of Mathematicians (ICM) in Helsinki. Kac was a plenary speaker at the 1988 American Mathematical Society centennial conference. In 2002 he gave a plenary lecture, Classification of Supersymmetries, at the ICM in Beijing.

Kac is a Fellow of the American Mathematical Society,[4] an honorary member of the Moscow Mathematical Society, Fellow of the American Academy of Arts and Sciences and a Member of the National Academy of Sciences.

The research of Victor Kac primarily concerns representation theory and mathematical physics. His work appears in mathematics and physics and in the development of quantum field theory, string theory and the theory of integrable systems.

Kac has published 13 books and over 200 articles in mathematics and physics journals and is listed as an ISI highly cited researcher.[5] Victor Kac was awarded the 2015 AMS Leroy P. Steele Prize for Lifetime Achievement.[6][7]

He was married with Michèle Vergne[8] and they have a daughter, Marianne Kac-Vergne, who is a professor of American civilization at the university of Picardie. His brother Boris Katz is a principal research scientist at MIT.[9]

Kac–Moody algebra

[edit]

"Almost simultaneously in 1967, Victor Kac in the USSR and Robert Moody in Canada developed what was to become Kac–Moody algebra. Kac and Moody noticed that if Wilhelm Killing's conditions were relaxed, it was still possible to associate to the Cartan matrix a Lie algebra which, necessarily, would be infinite dimensional." – A.J. Coleman[10]

Bibliography

[edit]
  • Kac, Victor G. (1994) [1985]. Infinite-Dimensional Lie Algebras (3rd ed.). Cambridge University Press. ISBN 0-521-46693-8.

References

[edit]
  1. ^ Mathematics Genealogy Project: https://www.genealogy.math.ndsu.nodak.edu/id.php?id=37054
  2. ^ Stephen Berman, Karen Parshall "Victor Kac and Robert Moody — their paths to Kac–Moody-Algebras", Mathematical Intelligencer, 2002, Nr.1 [1]
  3. ^ Victor Kac, A Biographical Interview: http://dynkincollection.library.cornell.edu/sites/default/files/Victor%20Kac%20%28RI-ED%29.pdf
  4. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
  5. ^ "List of ISI highly cited researchers".
  6. ^ 2015 AMS Steele Prizes
  7. ^ "American Mathematical Society :: Homepage". American Mathematical Society. Retrieved 2024-11-12.
  8. ^ La Gazette des Mathématiciens 165, retrieved 2021-04-22.
  9. ^ Negri, Gloria (4 October 2006). "Clara Katz; Soviet émigré saved ailing granddaughter". The Boston Globe.
  10. ^ Coleman, A. John, "The Greatest Mathematical Paper of All Time", The Mathematical Intelligencer, vol. 11, no. 3, pp. 29–38.
[edit]
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