Goro Shimura
Encyclopedia
is a Japan
ese mathematician
, and currently a professor emeritus of mathematics
(former Michael Henry Strater Chair) at Princeton University
.
Shimura was a colleague and a friend of Yutaka Taniyama
. They wrote a book (the first book treatment) on the complex multiplication of abelian varieties
, an area which in collaboration they had opened up.
Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication and modular form
s to higher dimensions (amongst other results). This work (and other developments it provoked) provided some of the 'raw data' later incorporated into the Langlands program
. It equally brought out the concept, in general, of Shimura variety
; which is the higher-dimensional equivalent of modular curve
. Even to define in general a Shimura variety is quite a formidable task: they bear, roughly speaking, the same relation to general Hodge structure
s as modular curves do to elliptic curve
s.
Shimura himself has described his approach as 'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms. He also argues for a 'romantic' approach, something he finds lacking in the younger generation of mathematician. The central 'Shimura variety' concept has been tamed (by application of Lie group
and algebraic group
theory, and the extraction of the concept 'parametrises interesting family of Hodge structures' by reference to the algebraic geometry
theory of 'motives
', which is still largely conjectural). In that sense his work is now "mainstream-for-Princeton"; but this assimilation (through David Mumford
, Pierre Deligne
and others) hardly includes all of the content.
He is known to a wider public through the important modularity theorem (previously known as the Taniyama-Shimura conjecture before being proven in the 1990s); Kenneth Ribet has shown that the famous Fermat's last theorem
follows from a special case of this theorem. Shimura dryly commented that his first reaction on hearing of Wiles
's proof of the semistable case of the theorem was 'I told you so'.
Among many honors and awards, Shimura received the Cole Prize
for number theory in 1976 and the Steele Prize for lifetime achievement in 1996, both from the American Mathematical Society
. His Collected Works have been published, in five volumes.
His hobbies are shogi
problems of extreme length and collecting Imari porcelain
. The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain is a non-fiction work by Goro Shimura published by Ten Speed Press
in 2008.
}
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese 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 currently a professor emeritus of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
(former Michael Henry Strater Chair) 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....
.
Shimura was a colleague and a friend of Yutaka Taniyama
Yutaka Taniyama
Yutaka Taniyama was a Japanese mathematician known for the Taniyama-Shimura conjecture.-Contribution:...
. They wrote a book (the first book treatment) on the complex multiplication of abelian varieties
Abelian variety of CM-type
In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End. The terminology here is from complex multiplication theory, which was developed for elliptic curves in the nineteenth century...
, an area which in collaboration they had opened up.
Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication and modular form
Modular form
In mathematics, a modular form is a analytic function on the upper half-plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections...
s to higher dimensions (amongst other results). This work (and other developments it provoked) provided some of the 'raw data' later incorporated into the Langlands program
Langlands program
The Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It was proposed by ....
. It equally brought out the concept, in general, of Shimura variety
Shimura variety
In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. The term "Shimura variety" applies to the higher-dimensional case, in the case of...
; which is the higher-dimensional equivalent of modular curve
Modular curve
In number theory and algebraic geometry, a modular curve Y is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL...
. Even to define in general a Shimura variety is quite a formidable task: they bear, roughly speaking, the same relation to general Hodge structure
Hodge structure
In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold...
s as modular curves do to elliptic curve
Elliptic curve
In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...
s.
Shimura himself has described his approach as 'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms. He also argues for a 'romantic' approach, something he finds lacking in the younger generation of mathematician. The central 'Shimura variety' concept has been tamed (by application of Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
and algebraic group
Algebraic group
In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety...
theory, and the extraction of the concept 'parametrises interesting family of Hodge structures' by reference to the 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...
theory of 'motives
Motive (algebraic geometry)
In algebraic geometry, a motive denotes 'some essential part of an algebraic variety'. To date, pure motives have been defined, while conjectural mixed motives have not. Pure motives are triples , where X is a smooth projective variety, p : X ⊢ X is an idempotent correspondence, and m an integer...
', which is still largely conjectural). In that sense his work is now "mainstream-for-Princeton"; but this assimilation (through David Mumford
David Mumford
David Bryant Mumford is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science...
, Pierre Deligne
Pierre Deligne
- See also :* Deligne conjecture* Deligne–Mumford moduli space of curves* Deligne–Mumford stacks* Deligne cohomology* Fourier–Deligne transform* Langlands–Deligne local constant- External links :...
and others) hardly includes all of the content.
He is known to a wider public through the important modularity theorem (previously known as the Taniyama-Shimura conjecture before being proven in the 1990s); Kenneth Ribet has shown that the famous Fermat's last theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
follows from a special case of this theorem. Shimura dryly commented that his first reaction on hearing of Wiles
Andrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
's proof of the semistable case of the theorem was 'I told you so'.
Among many honors and awards, Shimura received the Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of 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 theory. The prize is named after Frank Nelson Cole, who...
for number theory in 1976 and the Steele Prize for lifetime achievement in 1996, both from 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...
. His Collected Works have been published, in five volumes.
His hobbies are shogi
Shogi
, also known as Japanese chess, is a two-player board game in the same family as Western chess, chaturanga, and Chinese Xiangqi, and is the most popular of a family of chess variants native to Japan...
problems of extreme length and collecting Imari porcelain
Imari porcelain
Imari porcelain is the name for Japanese porcelain wares made in the town of Arita, in the former Hizen Province, northwestern Kyūshū. They were exported to Europe extensively from the port of Imari, Saga between latter half of 17th century and former half of 18 th century, Japanese as well as the...
. The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain is a non-fiction work by Goro Shimura published by Ten Speed Press
Ten Speed Press
Ten Speed Press is a publishing house founded in Berkeley, California in 1970. Philip Wood, founder and publisher, began his career with Barnes & Noble in 1962 and in 1965 at Penguin books...
in 2008.
Non-fiction
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