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Encyclopedia > Goro Shimura

Goro Shimura (志村 五郎, 1930 -) is a Japanese-American mathematician, and currently a professor of mathematics at Princeton University. Download high resolution version (532x702, 28 KB)Goro Shimura, date unknown. ... 1930 is a common year starting on Wednesday. ... A mathematician is a person whose area of study and research is mathematics. ... A professor is a senior teacher and researcher, usually in a college or university. ... History Main article: History of mathematics In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. ... Princeton University, located in Princeton, New Jersey, is the fourth-oldest institution of higher education in the United States. ...


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. Yutaka Taniyama (谷山 豊, November 12, 1927 – November 17, 1958) was a Japanese mathematician, best known for conjecturing the Taniyama-Shimura theorem after a meeting with André Weil, whose statement he subsequently refined in collaboration with Goro Shimura. ... 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(A). ...


Shimura then wrote a long series of important papers, extending the phenomena found in the theory of complex multiplication and modular forms 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 state in general what a Shimura variety is (should be) is quite a formidable task. A modular form is an analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. ... In mathematics, the Langlands program is a web of far-reaching and influential conjectures that connect number theory and the representation theory of certain groups. ... In mathematics, a modular curve is a Riemann surface, or corresponding algebraic curve, constructed as H/Γ where H is the upper half-plane in the complex numbers, and Γ is a Fuchsian group acting on H, with Γ a subgroup of the modular group of integral 2×2 matrices. ...


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. In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ... 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. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In algebraic geometry the idea of a motive intuitively refers to some essential part of an algebraic variety. Mathematically, the theory of motives is then the conjectural universal cohomology theory for such objects. ... David Bryant Mumford (born 11 June 1937) is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. ... Pierre Deligne (born 3 October 1944) is a Belgian mathematician. ...


He is known to a wider public through the important Taniyama-Shimura conjecture, which implied the famous Fermat's last theorem as a special case. The conjecture was finally proven in 1999. The Taniyama-Shimura theorem establishes an important connection between elliptic curves, which are objects from algebraic geometry, and modular forms, which are certain periodic holomorphic functions investigated in number theory. ... Pierre de Fermat Fermats last theorem (sometimes abbreviated as FLT and also called Fermats great theorem) is one of the most famous theorems in the history of mathematics. ... 1999 is a common year starting on Friday of the Common Era, and was designated the International Year of Older Persons by the United Nations. ...


His hobby is shogi problems of extreme length. Shogi (shōgi 将棋) is one of a family of strategic board games of which chess and xiangqi are also members, which originated from the 6th century Indian game of chaturanga or a close relative thereof. ...


He is one of the worst professors in the mathematics department. In response to a question in an undergraduate complex analysis class, he replied "I came here to teach -- I didn't come hear to answer questions".


  Results from FactBites:
 
Goro Shimura (308 words)
Shimura then wrote a long series of important papers, extending the phenomena found in the theory of complex multiplication and modular forms to higher dimensions (amongst other results).
Shimura himself has described his approach as 'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms.
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).
Goro Shimura at AllExperts (403 words)
Goro Shimura (Japanese: 志村 äº"郎 Shimura Gorō; born 1930) is a Japanese mathematician, and currently a professor emeritus of mathematics (former Michael Henry Strater Chair) at Princeton University.
Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication and modular forms to higher dimensions (amongst other results).
Even to state in general what a Shimura variety is quite a formidable task: they bear, roughly speaking, the same relation to general Hodge structures as modular curves do to elliptic curves.
  More results at FactBites »


 

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