Victor Gershevich (Grigorievich) Kac (russian: 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 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 In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string the ...

for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with

Boris Weisfeiler Boris Weisfeiler (born 19 April 1941 – disappeared 4-5 January 1985) was a Soviet-born mathematician and professor at Penn State University who lived in the United States before disappearing in Chile in 1985. Declassified US documents sugges ...

Biography

Kac studied mathematics at Moscow State University, receiving his MS in 1965 and his PhD in 1968. 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 Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

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 The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

(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, an Honorary member of the

Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society wa ...

, Fellow of the American Academy of Arts and Sciences and a Member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

. 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 In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...

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 The Institute for Scientific Information (ISI) was an academic publishing service, founded by Eugene Garfield in Philadelphia in 1956. ISI offered scientometric and bibliographic database services. Its specialty was citation indexing and analys ...

. Victor Kac was awarded the 2015 AMS Leroy P. Steele Prize for Lifetime Achievement. He was married with

Michèle Vergne Michèle Vergne (born August 29, 1943, in L’Isle-Adam, Val d´Oise) is a French mathematician, specializing in analysis and representation theory. Life and work Michèle Vergne studied from 1962 to 1966 at the École Normal Supérieure de ...

and they have a daughter, Marianne Kac-Vergne, who is a professor of American civilization at the university of Picardie. His brother

Boris Katz Boris Katz (born October 5, 1947) is a principal American research scientist (computer scientist) at the MIT Computer Science and Artificial Intelligence Laboratory at the Massachusetts Institute of Technology in Cambridge and head of the Labora ...

is a principal research scientist at MIT.

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. ColemanColeman, A. John, "The Greatest Mathematical Paper of All Time",
The Mathematical Intelligencer
'' vol. 11, no. 3, pp. 29–38.

Bibliography

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References

External links

* *Victor Kac, A Biographical Interview

{{DEFAULTSORT:Kac, Victor 1943 births Living people People from Buguruslan 20th-century American mathematicians Russian mathematicians Soviet mathematicians Fellows of the American Academy of Arts and Sciences American people of Russian-Jewish descent Fellows of the American Mathematical Society Moscow State University alumni 21st-century American mathematicians