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# Eugene Dynkin

Eugene Borisovich Dynkin (Russian: Евге́ний Бори́сович Ды́нкин; born May 11, 1924) is a Soviet and American mathematician.[1] He has made contributions to the fields of probability and algebra, especially semisimple Lie groups, Lie algebras, and Markov processes. The Dynkin diagram, the Dynkin system, and Dynkin's lemma are named for him.

Biography

Dynkin lived in Leningrad until 1935, when his family was exiled to Kazakhstan.[2] Two years later, when Dynkin was 13, his father disappeared in the Gulag.[2][1]

Moscow University

At the age of 16, in 1940, Dynkin was admitted to Moscow University. He avoided military service in World War II because of his poor eyesight, and received his M.S. in 1945 and his Ph.D. in 1948. He became an assistant professor at Moscow, but was not awarded a "chair" until 1954 because of his political undesirability. His academic progress was made difficult due to his father's fate, as well as Dynkin's Jewish origin; the special efforts of Andrey Kolmogorov, his Ph.D. supervisor, made it possible for Dynkin to progress through graduate school into a teaching position.[2]

USSR Academy of Sciences

In 1968, Dynkin was forced to transfer from the Moscow University to the Central Economic Mathematical Institute of the USSR Academy of Sciences.[1] He worked there on the theory of economic growth and economic equilibrium.

Cornell

He remained at the Institute until 1976, when he emigrated to the United States.[1] In 1977, he became a professor at Cornell University, where he remains as of 2010.[1][3]

Mathematical work

Dynkin is considered to be a rare example of a mathematician who made fundamental contributions to two very distinct areas of mathematics: algebra and probability theory.[4] The algebraic period of Dynkin's mathematical work was between 1944 and 1954, though even during this time a probabilistic theme was noticeable.[5] Indeed, Dynkin's first publication was in 1945, joinly with N. A. Dmitriev, solved a problem on the eigenvalues of stochastic matrices. This problem was raised at Kolmogorov's seminar on Markov chains, while both Dynkin and Dmitriev were undergraduates.[5]

Lie Theory

While Dynkin was a student at Moscow University, he attended Israel Gelfand's seminar on Lie groups. In 1944, Gelfand asked him to prepare a survey on the structure and classification of semisimple Lie groups, based on the papers by Hermann Weyl and Bartel Leendert van der Waerden. Dynkin found the papers difficult to read, and in an attempt to better understand the results, he invented the notion of a "simple root" in a root system. He represented the pairwise angles between these simple roots in the form of a Dynkin diagram. In this way he obtained an cleaner exposition of the classification of complex semisimple Lie algebras.[6] Of Dynkin's 1947 paper "Structure of semisimple Lie algebras", Bertram Kostant wrote:

In this paper, using only elementary mathematics, and starting with almost nothing, Dynkin, brilliantly and elegantly developed the structure and machinery of semisimple Lie algebras. What he accomplished in this paper was to take a hitherto esoteric subject, and to make it into beautiful and powerful mathematics.

—Bertram Kostant, "Selected papers", p. 363

Dynkin's 1952 influential paper "Semisimple subalgebras of semisimple Lie algebras", contained large tables and lists, and studied the subalgebras of the exceptional Lie algebras.

Probability theory

Dynkin is considered one of the founders of the modern theory of Markov processes. The results obtained by Dynkin and other participants of his seminar at Moscow University were summarized in two books. The first of these, "Theory of Markov Processes", was published in 1959, and lay the foundations of the theory.

Dynkin's one hour talk at the 1962 International Congress of Mathematicians in Stockholm, was delivered by Kolmogorov, since prior to his emigration, Dynkin was never permitted to travel to the West.[7] This talk was titled "Markov processes and problems in analysis".

Prizes and Awards

Prize of the Moscow Mathematical Society, 1951

Institute of Mathematical Statistics, Fellow, 1962

American Academy of Arts and Sciences, Fellow, 1978

National Academy of Sciences of the USA, Member, 1985[8]

American Mathematical Society, Leroy P. Steele Prize for Total Mathematical Work, 1993

Moscow Mathematical Society, Honorary Member, 1995

Doctor Honoris Causa of the Pierre and Marie Curie University (Paris 6), 1997

Doctor Honoris Causa of the University of Warwick (England), 2003

Doctor Honoris Causa of the Independent Moscow University (Russia), 2003

Publications

Dynkin, Eugene B. (2000). Yushkevich, A. A.; Seitz, G. M.; Onishchik, A. L.. eds. Selected papers of E. B. Dynkin with commentary. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-1065-1. MR1757976.

See also

Algebra

Affine Dynkin diagram

Coxeter–Dynkin diagram

Dynkin diagram (Dynkin graph)

Dynkin index

Probability

Doob–Dynkin lemma

Dynkin's formula

Dynkin system

Notes

^ a b c d e Vvedenskaya, N. D.; Dobrushin, R. L.; Onishchik, A. L.; Uspenskiĭ, V. A. (1994). "Evgeniĭ Borisovich Dynkin (on the occasion of his seventieth birthday).". Russian Math. Surveys 49 (4): 183–191. MR 1309461.

^ a b c Dynkin (2000, p. xiii)

^ In Dynkin (2000, p. xv), Dynkin states "I came to the United States from the Soviet Union in 1977".

^ Dynkin (2000, p. xi)

^ a b Dynkin (2000, p. 385)

^ Dynkin (2000, p. xiii,7)

^ Dynkin (2000, p. 388)

^ "Eugene Dynkin". NAS.

External links

Eugene Dynkin at the Mathematics Genealogy Project

O'Connor, John J.; Robertson, Edmund F., "Eugene Dynkin", MacTutor History of Mathematics archive, University of St Andrews.

Department listing at Cornell University

Personal web page

Genealogy Tree of Dynkin's School

Collection of interviews assembled by Dynkin

Lothar Collatz at the Mathematics Genealogy Project

Retrieved from "http://en.wikipedia.org/"

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