Efim Isaakovich Zelmanov (russian: Ефи́м Исаа́кович Зе́льманов; born 7 September 1955 in

Khabarovsk Khabarovsk ( rus, Хабaровск, a=Хабаровск.ogg, r=Habárovsk, p=xɐˈbarəfsk) is the largest city and the administrative centre of Khabarovsk Krai, Russia,Law #109 located from the China–Russia border, at the confluence of th ...

) is a

Russian-American Russian Americans ( rus, русские американцы, r=russkiye amerikantsy, p= ˈruskʲɪje ɐmʲɪrʲɪˈkant͡sɨ) are Americans of full or partial Russian ancestry. The term can apply to recent Russian immigrants to the United State ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, known for his work on combinatorial problems in

nonassociative algebra A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative. That is, an algebraic structure ''A'' is a non-associative algebra over a field ''K'' if ...

and

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

, including his solution of the restricted Burnside problem. He was awarded a Fields Medal 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 ...

Zürich , neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon , twintowns = Kunming, San Francisco Zürich () i ...

in 1994. Zelmanov was born into a

Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""T ...

ish family in

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

(now in

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eigh ...

). He entered

Novosibirsk State University Novosibirsk State University is a public research university located in Novosibirsk, Russia. The university was founded in 1958, on the principles of integration of education and science, early involvement of students with research activities an ...

in 1972, when he was 17 years old. He obtained a doctoral degree at

in 1980, and a higher degree at

Leningrad State University Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...

in 1985. He had a position in Novosibirsk until 1987, when he left the Soviet Union. Zelmanov and Hunter in Lincoln

In 1990 he moved to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., federal district, five ma ...

, becoming a professor at the

University of Wisconsin–Madison A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which ...

. He was at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

in 1994/5, then at

Yale University Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...

. In 2011, he became a professor at the

University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...

and a Distinguished Professor at the Korea Institute for Advanced Study. In 2022, he moved to the

People's Republic of China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's List of countries and dependencies by population, most populous country, with a Population of China, population exceeding 1.4 billion, sli ...

and joined the Southern University of Science and Technology in Shenzhen, China. He served as a chair professor and the scientific director of the SUSTech International Center for Mathematics. Zelmanov was elected a member of the U.S. National Academy of Sciences in 2001, becoming, at the age of 47, the youngest member of the mathematics section of the academy. He is also an elected member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, ...

(1996) and a foreign member of the Korean Academy of Science and Engineering and of the Spanish Royal Academy of Sciences. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

. Zelmanov gave invited talks at the

in Warsaw (1983), Kyoto (1990) and Zurich (1994). He delivered the 2004 Turán Memorial Lectures. He was awarded Honorary Doctor degrees from the

University of Alberta The University of Alberta, also known as U of A or UAlberta, is a public research university located in Edmonton, Alberta, Canada. It was founded in 1908 by Alexander Cameron Rutherford,"A Gentleman of Strathcona – Alexander Cameron Ruth ...

, Canada (2011),

Taras Shevchenko National University of Kyiv Kyiv University or Shevchenko University or officially the Taras Shevchenko National University of Kyiv ( uk, Київський національний університет імені Тараса Шевченка), colloquially known as KNU ...

, Ukraine (2012), the Universidad Internacional Menéndez Pelayo in Santander, Spain (2015) and the

University of Lincoln , mottoeng = Freedom through wisdom , established = 1861 – Hull School of Art1905 – Endsleigh College1976 – Hull College1992 – University of Humberside1996 – University of Lincolnshire and Humberside2001 � ...

, UK (2016). Zelmanov's early work was on

Jordan algebra In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: # xy = yx (commutative law) # (xy)(xx) = x(y(xx)) (). The product of two elements ''x'' and ''y'' in a Jordan al ...

s in the case of infinite dimensions. He was able to show that Glennie's identity in a certain sense generates all identities that hold. He then showed that the

Engel identity The Engel identity, named after Friedrich Engel, is a mathematical equation that is satisfied by all elements of a Lie ring, in the case of an Engel Lie ring, or by all the elements of a group, in the case of an Engel group. The Engel identity ...

for

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi iden ...

s implies

nilpotence In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree), such that x^n=0. The term was introduced by Benjamin Peirce in the context of his work on the cla ...

, in the case of infinite dimensions.

Notable publications

* Zelʹmanov, E.I. Solution of the restricted Burnside problem for groups of odd exponent. Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), no. 1, 42–59, 221. English translation in Math. USSR-Izv. 36 (1991), no. 1, 41–60. doi:10.1070/IM1991v036n01ABEH001946 * Zelʹmanov, E.I. Solution of the restricted Burnside problem for 2-groups. Mat. Sb. 182 (1991), no. 4, 568–592. English translation in Math. USSR-Sb. 72 (1992), no. 2, 543–565. doi:10.1070/SM1992v072n02ABEH001272

References

External links

* *
The Work of Efim Zelmanov (Fields Medal 1994)
b
Kapil Hari Paranjape
{{DEFAULTSORT:Zelmanov, Efim 1955 births Living people People from Khabarovsk Russian Jews American people of Russian-Jewish descent 20th-century Russian mathematicians 21st-century Russian mathematicians Algebraists Fields Medalists Jewish American scientists Members of the United States National Academy of Sciences Soviet mathematicians University of California, San Diego faculty Fellows of the American Mathematical Society Novosibirsk State University alumni 21st-century American Jews