George Lusztig (born ''Gheorghe Lusztig''; May 20, 1946) is an American-Romanian mathematician and Abdun Nur Professor at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

(MIT). He was a

Norbert Wiener Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher i ...

Professor in the

Department of Mathematics Department may refer to: * Departmentalization, division of a larger organization into parts with specific responsibility Government and military *Department (administrative division), a geographical and administrative division within a country, ...

from 1999 to 2009.

Education and career

Born in

Timișoara ), City of Roses ( ro, Orașul florilor), City of Parks ( ro, Orașul parcurilor) , image_map = Timisoara jud Timis.svg , map_caption = Location in Timiș County , pushpin_map = Romania#Europe , pushpin_ ...

to a

Hungarian-Jewish The history of the Jews in Hungary dates back to at least the Kingdom of Hungary, with some records even predating the Hungarian conquest of the Carpathian Basin in 895 CE by over 600 years. Written sources prove that Jewish communities lived i ...

family, he did his undergraduate studies at the

University of Bucharest The University of Bucharest ( ro, Universitatea din București), commonly known after its abbreviation UB in Romania, is a public university founded in its current form on by a decree of Prince Alexandru Ioan Cuza to convert the former Princel ...

, graduating in 1968. Later that year he left Romania for the United Kingdom, where he spent several months at the

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

and

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

. In 1969 he moved to the United States, where he went to work for two years with

Michael Atiyah Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded th ...

at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

. He received his PhD in mathematics in 1971 after completing a doctoral dissertation, titled "Novikov's higher signature and families of elliptic operators", under the supervision of William Browder and

. Lusztig worked for almost seven years at the

. His involvement at the university encompassed a Research Fellowship, (1971–72); lecturer in Mathematics, (1972–74); and Professor of Mathematics, (1974–78). In 1978, he accepted a chair at MIT.

Contributions

He is known for his work on

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

, in particular for the objects closely related to

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

s, such as finite reductive groups, Hecke algebras,

p

-adic groups,

quantum groups In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebra ...

, and

Weyl group In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections th ...

s. He essentially paved the way for modern representation theory. This has included fundamental new concepts, including the character sheaves, the Deligne–Lusztig varieties, and the

Kazhdan–Lusztig polynomial In the mathematical field of representation theory, a Kazhdan–Lusztig polynomial P_(q) is a member of a family of integral polynomials introduced by . They are indexed by pairs of elements ''y'', ''w'' of a Coxeter group ''W'', which can in part ...

Awards and honors

In 1983, Lusztig was elected as a fellow of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

. In 1985 Lusztig won the

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...

(

Algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

). He was elected to 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 ...

in 1992. He received the

Brouwer Medal The Brouwer Medal is a triennial award presented by the Royal Dutch Mathematical Society and the Royal Netherlands Academy of Sciences. The Brouwer Metal gets its name from Dutch mathematician L. E. J. Brouwer and is the Netherlands’ most prestigi ...

in 1999, the

National Order of Faithful Service The National Order of Faithful Service ( ro, Ordinul Național "Serviciul Credincios") is the second highest national order of Romania, with the Order of the Star of Romania being the highest national order. Originally it was established as the Me ...

in 2003 and the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for Lifetime Achievement in Mathematics in 2008. 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, ...

and in 2014 he received the Shaw Prize in Mathematics. In 2022, he received the Wolf Prize in Mathematics.

References

External links

*
George Lusztig's entry
in the ''

International Who's Who ''The International Who's Who'' is a Who's Who series of reference books of notable people worldwide that has been published annually since 1935. History The first edition was published in 1935 by Europa Publications. The eighth edition (1943-4 ...

''. {{DEFAULTSORT:Lusztig, George Members of the United States National Academy of Sciences 20th-century Romanian mathematicians 20th-century American mathematicians 21st-century American mathematicians Princeton University alumni Fellows of the Royal Society Brouwer Medalists Fellows of the American Mathematical Society Massachusetts Institute of Technology School of Science faculty Institute for Advanced Study visiting scholars University of Bucharest alumni Romanian Jews Romanian emigrants to the United States Scientists from Timișoara Academics of the University of Warwick 1946 births Living people International Mathematical Olympiad participants 21st-century Romanian mathematicians Recipients of the National Order of Faithful Service