Michael Artin
Encyclopedia
Michael Artin is an American
mathematician
and a professor emeritus in the Massachusetts Institute of Technology
mathematics department
, known for his contributions to algebraic geometry
. and also generally recognized as one of the outstanding professors in his field.
Artin was born in Hamburg
, Germany
, and brought up in Indiana
. His father was Emil Artin
, preeminent algebraist of the 20-th century. He did his undergraduate studies at Princeton University
, receiving an A.B. in 1955; he then moved to Harvard University
, where he received a Ph.D. in 1960 under the supervision of Oscar Zariski
.
In the early 1960s Artin spent time at the IHÉS in France
, contributing to the SGA4 volumes of the Séminaire de géométrie algébrique, on topos theory and étale cohomology
. His work on the problem of characterising the representable functor
s in the category of schemes has led to the Artin approximation theorem
, in local algebra. This work also gave rise to the ideas of an algebraic space
and algebraic stack, and has proved very influential in moduli theory. Additionally, he has made contributions to the deformation theory
of algebraic varieties. He is working on noncommutative ring
s, especially geometric aspects.
In 2002, Artin won the American Mathematical Society
's annual Steele Prize
for Lifetime Achievement. In 2005, he was awarded the Harvard Centennial Medal
. He is also a member of the National Academy of Sciences
and a Fellow of the American Academy of Arts and Sciences
(1969), the American Association for the Advancement of Science
, and the Society for Industrial and Applied Mathematics
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and a professor emeritus in the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
mathematics department
MIT Mathematics Department
The Department of Mathematics at the Massachusetts Institute of Technology is one of the leading mathematics departments in the USAand the world...
, known for his contributions to algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
. and also generally recognized as one of the outstanding professors in his field.
Artin was born in Hamburg
Hamburg
-History:The first historic name for the city was, according to Claudius Ptolemy's reports, Treva.But the city takes its modern name, Hamburg, from the first permanent building on the site, a castle whose construction was ordered by the Emperor Charlemagne in AD 808...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, and brought up in Indiana
Indiana
Indiana is a US state, admitted to the United States as the 19th on December 11, 1816. It is located in the Midwestern United States and Great Lakes Region. With 6,483,802 residents, the state is ranked 15th in population and 16th in population density. Indiana is ranked 38th in land area and is...
. His father was Emil Artin
Emil Artin
Emil Artin was an Austrian-American mathematician of Armenian descent.-Parents:Emil Artin was born in Vienna to parents Emma Maria, née Laura , a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent...
, preeminent algebraist of the 20-th century. He did his undergraduate studies at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, receiving an A.B. in 1955; he then moved to Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, where he received a Ph.D. in 1960 under the supervision of Oscar Zariski
Oscar Zariski
Oscar Zariski was a Russian mathematician and one of the most influential algebraic geometers of the 20th century.-Education:...
.
In the early 1960s Artin spent time at the IHÉS in France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, contributing to the SGA4 volumes of the Séminaire de géométrie algébrique, on topos theory and étale cohomology
Étale cohomology
In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures...
. His work on the problem of characterising the representable functor
Representable functor
In mathematics, particularly category theory, a representable functor is a functor of a special form from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures In mathematics, particularly category theory, a...
s in the category of schemes has led to the Artin approximation theorem
Artin approximation theorem
In mathematics, the Artin approximation theorem is a fundamental result of Michael Artin in deformation theory which implies that formal power series with coefficients in a field k are well-approximated by the algebraic functions on k....
, in local algebra. This work also gave rise to the ideas of an algebraic space
Algebraic space
In mathematics, an algebraic space is a generalization of the schemes of algebraic geometry introduced by Michael Artin for use in deformation theory...
and algebraic stack, and has proved very influential in moduli theory. Additionally, he has made contributions to the deformation theory
Deformation theory
In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or vector of small quantities. The infinitesimal conditions are therefore the result of applying the approach...
of algebraic varieties. He is working on noncommutative ring
Noncommutative ring
In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, if R is a noncommutative ring, there exists a and b in R with a·b ≠ b·a, and conversely.Noncommutative rings are ubiquitous in mathematics, and occur...
s, especially geometric aspects.
In 2002, Artin won the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
's annual Steele Prize
Leroy P. Steele Prizes
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....
for Lifetime Achievement. In 2005, he was awarded the Harvard Centennial Medal
Harvard Centennial Medal
The Harvard Centennial Medal is an honor given by the Harvard Graduate School of Arts and Sciences to recipients of graduate degrees from the School for their "contributions to society."...
. He is also a member of the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
and a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
(1969), the American Association for the Advancement of Science
American Association for the Advancement of Science
The American Association for the Advancement of Science is an international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...
, and the Society for Industrial and Applied Mathematics
Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics was founded by a small group of mathematicians from academia and industry who met in Philadelphia in 1951 to start an organization whose members would meet periodically to exchange ideas about the uses of mathematics in industry. This meeting led...
.
See also
- Artin stacks
- Artin–Mazur zeta function
- Artin–Verdier dualityArtin–Verdier dualityIn mathematics, Artin–Verdier duality is a duality theorem for constructible abelian sheaves over the spectrum of a ring of algebraic numbers, introduced by , that generalizes Tate duality.-References:...