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Goro Shimura, the Glossary

was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry.^[1]

61 relations: Alice Silverberg, André Weil, Andrew Wiles, Annals of Mathematics, Arithmetic geometry, Asahi Prize, Automorphic form, Automorphic L-function, Bill Casselman, Class field theory, Cohomology, Cole Prize, Complex multiplication, Complex multiplication of abelian varieties, Cusp form, Don Blasius, Eichler–Shimura congruence relation, Eichler–Shimura isomorphism, Emeritus, Fermat's Last Theorem, Galois module, Guggenheim Fellowship, Hamamatsu, Hecke operator, Hilbert's twelfth problem, Imari ware, Institute for Advanced Study, Iwanami Shoten, Japan, Ken Ribet, Langlands program, Leroy P. Steele Prize, Local zeta function, Martin Eichler, Mathematician, Mathematics, Melvin Hochster, Modular curve, Modular form, Modularity theorem, Motivic L-function, New Jersey, Number theory, Osaka University, PBS, Pierre Deligne, Princeton University, Princeton, New Jersey, Ribet's theorem, Robert Rumely, ... Expand index (11 more) »
People from Hamamatsu

Alice Silverberg

Alice Silverberg (born 1958) is professor of Mathematics and Computer Science at the University of California, Irvine.

See Goro Shimura and Alice Silverberg

André Weil

André Weil (6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry.

See Goro Shimura and André Weil

Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. Goro Shimura and Andrew Wiles are Institute for Advanced Study visiting scholars.

See Goro Shimura and Andrew Wiles

Annals of Mathematics

The Annals of Mathematics is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.

See Goro Shimura and Annals of Mathematics

Arithmetic geometry

In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory.

See Goro Shimura and Arithmetic geometry

Asahi Prize

The, established in 1929, is an award presented by the Japanese newspaper Asahi Shimbun and Asahi Shimbun Foundation to honor individuals and groups that have made outstanding accomplishments in the fields of arts and academics and have greatly contributed to the development and progress of Japanese culture and society at large.

See Goro Shimura and Asahi Prize

Automorphic form

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group.

See Goro Shimura and Automorphic form

Automorphic L-function

In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive group G over a global field and a finite-dimensional complex representation r of the Langlands dual group LG of G, generalizing the Dirichlet L-series of a Dirichlet character and the Mellin transform of a modular form.

See Goro Shimura and Automorphic L-function

Bill Casselman

William Allen Casselman (born November 27, 1941) is an American Canadian mathematician who works in representation theory and automorphic forms. Goro Shimura and Bill Casselman are Institute for Advanced Study visiting scholars.

See Goro Shimura and Bill Casselman

Class field theory

In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field.

See Goro Shimura and Class field theory

Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex.

See Goro Shimura and Cohomology

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 theory.

See Goro Shimura and Cole Prize

Complex multiplication

In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers.

See Goro Shimura and Complex multiplication

Complex multiplication of abelian varieties

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).

See Goro Shimura and Complex multiplication of abelian varieties

Cusp form

In number theory, a branch of mathematics, a cusp form is a particular kind of modular form with a zero constant coefficient in the Fourier series expansion.

See Goro Shimura and Cusp form

Don Blasius

Don Malcolm Blasius (born 5 September 1950 in Paterson, New Jersey) is an American mathematician.

See Goro Shimura and Don Blasius

Eichler–Shimura congruence relation

In number theory, the Eichler–Shimura congruence relation expresses the local ''L''-function of a modular curve at a prime p in terms of the eigenvalues of Hecke operators.

See Goro Shimura and Eichler–Shimura congruence relation

Eichler–Shimura isomorphism

In mathematics, Eichler cohomology (also called parabolic cohomology or cuspidal cohomology) is a cohomology theory for Fuchsian groups, introduced by, that is a variation of group cohomology analogous to the image of the cohomology with compact support in the ordinary cohomology group.

See Goro Shimura and Eichler–Shimura isomorphism

Emeritus

Emeritus (female version: emerita) is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus".

See Goro Shimura and Emeritus

Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than.

See Goro Shimura and Fermat's Last Theorem

Galois module

In mathematics, a Galois module is a ''G''-module, with G being the Galois group of some extension of fields.

See Goro Shimura and Galois module

Guggenheim Fellowship

Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon and Olga Hirsh Guggenheim.

See Goro Shimura and Guggenheim Fellowship

Hamamatsu

is a city located in western Shizuoka Prefecture, Japan.

See Goro Shimura and Hamamatsu

Hecke operator

In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by, is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations.

See Goro Shimura and Hecke operator

Hilbert's twelfth problem

Hilbert's twelfth problem is the extension of the Kronecker–Weber theorem on abelian extensions of the rational numbers, to any base number field.

See Goro Shimura and Hilbert's twelfth problem

Imari ware

is a Western term for a brightly-coloured style of Japanese export porcelain made in the area of Arita, in the former Hizen Province, northwestern Kyūshū.

See Goro Shimura and Imari ware

Institute for Advanced Study

The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey.

See Goro Shimura and Institute for Advanced Study

Iwanami Shoten

is a Japanese publishing company based in Tokyo.

See Goro Shimura and Iwanami Shoten

Japan

Japan is an island country in East Asia, located in the Pacific Ocean off the northeast coast of the Asian mainland.

See Goro Shimura and Japan

Ken Ribet

Kenneth Alan Ribet (born June 28, 1948) is an American mathematician working in algebraic number theory and algebraic geometry.

See Goro Shimura and Ken Ribet

Langlands program

In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry.

See Goro Shimura and Langlands program

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.

See Goro Shimura and Leroy P. Steele Prize

Local zeta function

In number theory, the local zeta function (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as where is a non-singular -dimensional projective algebraic variety over the field with elements and is the number of points of defined over the finite field extension of.

See Goro Shimura and Local zeta function

Martin Eichler

Martin Maximilian Emil Eichler (29 March 1912 – 7 October 1992) was a German number theorist.

See Goro Shimura and Martin Eichler

Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.

See Goro Shimura and Mathematician

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Goro Shimura and Mathematics

Melvin Hochster

Melvin Hochster (born August 2, 1943) is an American mathematician working in commutative algebra.

See Goro Shimura and Melvin Hochster

Modular curve

In number theory and algebraic geometry, a modular curve Y(Γ) 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(2, Z).

See Goro Shimura and Modular curve

Modular form

In mathematics, a modular form is a (complex) analytic function on the upper half-plane, \,\mathcal\,, that satisfies.

See Goro Shimura and Modular form

Modularity theorem

The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture or modularity conjecture for elliptic curves) states that elliptic curves over the field of rational numbers are related to modular forms in a particular way.

See Goro Shimura and Modularity theorem

Motivic L-function

In mathematics, motivic L-functions are a generalization of Hasse–Weil ''L''-functions to general motives over global fields.

See Goro Shimura and Motivic L-function

New Jersey

New Jersey is a state situated within both the Mid-Atlantic and Northeastern regions of the United States.

See Goro Shimura and New Jersey

Number theory

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.

See Goro Shimura and Number theory

Osaka University

, abbreviated as OU or, is a national research university in Osaka, Japan.

See Goro Shimura and Osaka University

PBS

The Public Broadcasting Service (PBS) is an American public broadcaster and non-commercial, free-to-air television network based in Crystal City, Virginia.

See Goro Shimura and PBS

Pierre Deligne

Pierre René, Viscount Deligne (born 3 October 1944) is a Belgian mathematician.

See Goro Shimura and Pierre Deligne

Princeton University

Princeton University is a private Ivy League research university in Princeton, New Jersey.

See Goro Shimura and Princeton University

Princeton, New Jersey

Princeton is a borough in Mercer County, in the U.S. state of New Jersey.

See Goro Shimura and Princeton, New Jersey

Ribet's theorem

Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is part of number theory.

See Goro Shimura and Ribet's theorem

Robert Rumely

Robert Scott Rumely (born 1952) is a professor of mathematics at the University of Georgia who specializes in number theory and arithmetic geometry.

See Goro Shimura and Robert Rumely

Shimura correspondence

In number theory, the Shimura correspondence is a correspondence between modular forms F of half integral weight k+1/2, and modular forms f of even weight 2k, discovered by.

See Goro Shimura and Shimura correspondence

Shimura subgroup

In mathematics, the Shimura subgroup Σ(N) is a subgroup of the Jacobian of the modular curve X0(N) of level N, given by the kernel of the natural map to the Jacobian of X1(N).

See Goro Shimura and Shimura subgroup

Shimura variety

In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties are not algebraic varieties but are families of algebraic varieties.

See Goro Shimura and Shimura variety

Shimura's reciprocity law

In mathematics, Shimura's reciprocity law, introduced by, describes the action of ideles of imaginary quadratic fields on the values of modular functions at singular moduli.

See Goro Shimura and Shimura's reciprocity law

Shogi

, also known as Japanese chess, is a strategy board game for two players.

See Goro Shimura and Shogi

Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

See Goro Shimura and Springer Science+Business Media

References

[1] https://en.wikipedia.org/wiki/Goro_Shimura

Also known as Gorō Shimura, The Map of My Life.

, Shimura correspondence, Shimura subgroup, Shimura variety, Shimura's reciprocity law, Shogi, Springer Science+Business Media, Ten Speed Press, University of Tokyo, Weil conjectures, Wiles's proof of Fermat's Last Theorem, Yutaka Taniyama.

Goro Shimura, the Glossary

Table of Contents

See also

People from Hamamatsu

References