77 relations: Abel Prize, Alexander Grothendieck, Algebraic geometry, Algebraic number, Balzan Prize, Beck's monadicity theorem, Belgium, Complex geometry, Complex multiplication, Crafoord Prize, Dan Freed, David Kazhdan, David Mumford, David R. Morrison (mathematician), Deformation theory, Deligne cohomology, Deligne–Lusztig theory, Deligne–Mumford stack, Doctorate, E7½, Edward Witten, Eigenvalues and eigenvectors, Etterbeek, Fields Medal, Fourier–Deligne transform, Frobenius endomorphism, Functional equation, George Lusztig, Group of Lie type, Hochschild homology, Hodge conjecture, Hodge cycle, Hodge theory, Institut des Hautes Études Scientifiques, Institute for Advanced Study, Jean-Pierre Serre, John Morgan (mathematician), K-theory, L-function, Langlands program, Langlands–Deligne local constant, Lê Dũng Tráng, Lisa Jeffrey, Mathematician, Mathematics, Michael Rapoport, Miles Reid, Modular form, Moduli of algebraic curves, Moduli space, ..., Monodromy, Motive (algebraic geometry), NLab, Norwegian Academy of Science and Letters, Operad theory, Orsay, Paris, Pavel Etingof, Perverse sheaf, Ramanujan–Petersson conjecture, Representation theory, Riemann hypothesis, Royal Swedish Academy of Sciences, Scheme (mathematics), Shimura variety, Simple Lie group, Special values of L-functions, Stack (mathematics), String theory, Tannakian formalism, Université libre de Bruxelles, University of Paris-Sud, Weil cohomology theory, Weil conjectures, Wolf Prize, Yan Soibelman, Zariski's main theorem. Expand index (27 more) »

## Abel Prize

The Abel Prize (Abelprisen) is a Norwegian prize awarded annually by the Government of Norway to one or more outstanding mathematicians.

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## Alexander Grothendieck

Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.

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## Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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## Algebraic number

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

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## Balzan Prize

The International Balzan Prize Foundation awards four annual monetary prizes to people or organizations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the brotherhood of man.

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## Beck's monadicity theorem

In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by in about 1964.

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## Belgium

Belgium, officially the Kingdom of Belgium, is a country in Western Europe bordered by France, the Netherlands, Germany and Luxembourg.

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## Complex geometry

In mathematics, complex geometry is the study of complex manifolds and functions of several complex variables.

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## Complex multiplication

In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the tangent space at the identity element of A is a direct sum of one-dimensional modules).

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## Crafoord Prize

The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord.

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## Dan Freed

Daniel Stuart "Dan" Freed (born 17 April 1959) is an American mathematician, who specializes in global analysis and its applications to supersymmetry, string theory, and quantum field theory.

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## David Kazhdan

David Kazhdan (דוד קשדן) or Každan, Kazhdan, formerly named Dmitry Aleksandrovich Kazhdan (until he left the Soviet Union; Дми́трий Александро́вич Кажда́н), is a Soviet and Israeli mathematician known for work in representation theory.

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## David Mumford

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.

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## David R. Morrison (mathematician)

David Robert Morrison (born July 29, 1955, in Oakland, California) is an American mathematician and theoretical physicist.

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## 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.

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## Deligne cohomology

In mathematics, Deligne cohomology is the hypercohomology of the Deligne complex of a complex manifold.

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## Deligne–Lusztig theory

In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced by.

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## Deligne–Mumford stack

In algebraic geometry, a Deligne–Mumford stack is a stack F such that.

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## Doctorate

A doctorate (from Latin docere, "to teach") or doctor's degree (from Latin doctor, "teacher") or doctoral degree (from the ancient formalism licentia docendi) is an academic degree awarded by universities that is, in most countries, a research degree that qualifies the holder to teach at the university level in the degree's field, or to work in a specific profession.

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## E7½

In mathematics, the Lie algebra E7½ is a subalgebra of E8 containing E7 defined by Landsberg and Manivel in order to fill the "hole" in a dimension formula for the exceptional series E''n'' of simple Lie algebras.

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## Edward Witten

Edward Witten (born August 26, 1951) is an American theoretical physicist and professor of mathematical physics at the Institute for Advanced Study in Princeton, New Jersey.

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## Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

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## Etterbeek

Etterbeek (French:; Dutch) is one of the nineteen municipalities located in the Brussels-Capital Region of Belgium.

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## Fields Medal

The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.

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## Fourier–Deligne transform

In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ℓ-adic sheaves over the affine line.

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## Frobenius endomorphism

In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class which includes finite fields.

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## Functional equation

In mathematics, a functional equation is any equation in which the unknown represents a function.

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## George Lusztig

George Lusztig (born Gheorghe Lusztig, May 20, 1946) is a Romanian-American mathematician and Abdun Nur Professor at the Massachusetts Institute of Technology (MIT).

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## Group of Lie type

In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field.

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## Hochschild homology

In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings.

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## Hodge conjecture

In mathematics, the Hodge conjecture is a major unsolved problem in the field of algebraic geometry that relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of it.

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## Hodge cycle

In differential geometry, a Hodge cycle or Hodge class is a particular kind of homology class defined on a complex algebraic variety V, or more generally on a Kähler manifold.

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## Hodge theory

In mathematics, Hodge theory, named after W. V. D. Hodge, uses partial differential equations to study the cohomology groups of a smooth manifold M. The key tool is the Laplacian operator associated to a Riemannian metric on M. The theory was developed by Hodge in the 1930s as an extension of de Rham cohomology.

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## Institut des Hautes Études Scientifiques

The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French institute supporting advanced research in mathematics and theoretical physics.

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## Institute for Advanced Study

The Institute for Advanced Study (IAS) in Princeton, New Jersey, in the United States, is an independent, postdoctoral research center for theoretical research and intellectual inquiry founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld.

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## Jean-Pierre Serre

Jean-Pierre Serre (born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory.

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## John Morgan (mathematician)

John Willard Morgan (born March 21, 1946) is an American mathematician, with contributions to topology and geometry.

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## K-theory

In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme.

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## L-function

In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects.

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## Langlands program

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

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## Langlands–Deligne local constant

In mathematics, the Langlands–Deligne local constant (or local Artin root number up to an elementary function of s) is an elementary function associated with a representation of the Weil group of a local field.

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## Lê Dũng Tráng

Lê Dũng Tráng, (born 1947 in Saigon) is a Vietnamese-French mathematician.

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## Lisa Jeffrey

Lisa Claire Jeffrey FRSC is a Canadian mathematician, a professor of mathematics at the University of Toronto.

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## Mathematician

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

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## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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## Michael Rapoport

Michael Rapoport (born 2 October 1948) is a German mathematician.

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## Miles Reid

Miles Anthony Reid FRS (born 30 January 1948) is a mathematician who works in algebraic geometry.

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## Modular form

In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.

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## Moduli of algebraic curves

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves.

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## Moduli space

In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.

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## Monodromy

In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity.

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## Motive (algebraic geometry)

In algebraic geometry, a motive (or sometimes motif, following French usage) denotes 'some essential part of an algebraic variety'.

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## NLab

The nLab is a wiki for research-level notes, expositions and collaborative work, including original research, in mathematics, physics, and philosophy, with a focus on methods from category theory and homotopy theory.

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## Norwegian Academy of Science and Letters

The Norwegian Academy of Science and Letters (Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway.

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## Operad theory

Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity.

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## Orsay

Orsay is a commune in the Essonne department in Île-de-France in northern France.

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## Paris

Paris is the capital and most populous city of France, with an area of and a population of 2,206,488.

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## Pavel Etingof

Pavel Ilyich Etingof (Павел Ильич Этингоф; born 1969) is an American mathematician of Russian-Ukrainian origin.

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## Perverse sheaf

The mathematical term perverse sheaves refers to a certain abelian category associated to a topological space X, which may be a real or complex manifold, or a more general topologically stratified space, usually singular.

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## Ramanujan–Petersson conjecture

In mathematics, the Ramanujan conjecture, due to, states that Ramanujan's tau function given by the Fourier coefficients of the cusp form of weight where q.

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## 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.

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## Riemann hypothesis

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

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## Royal Swedish Academy of Sciences

The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden.

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## Scheme (mathematics)

In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.

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## 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 one-dimensional varieties one speaks of Shimura curves.

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## Simple Lie group

In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.

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## Special values of L-functions

In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely by the recognition that expression on the left-hand side is also L(1) where L(s) is the Dirichlet L-function for the Gaussian field.

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## Stack (mathematics)

In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets.

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## String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

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## Tannakian formalism

In mathematics, a tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C is to approximate, in some sense, the category of linear representations of an algebraic group G defined over K. A number of major applications of the theory have been made, or might be made in pursuit of some of the central conjectures of contemporary algebraic geometry and number theory.

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## Université libre de Bruxelles

The Université libre de Bruxelles (in English: Free University of Brussels), abbreviated ULB, is a French-speaking private research university in Brussels, Belgium.

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## University of Paris-Sud

University of Paris-Sud (French: Université Paris-Sud), also known as University of Paris XI, is a French university distributed among several campuses in the southern suburbs of Paris including Orsay, Cachan, Châtenay-Malabry, Sceaux and Kremlin-Bicêtre campuses.

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## Weil cohomology theory

In algebraic geometry, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles and cohomology groups.

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## Weil conjectures

In mathematics, the Weil conjectures were some highly influential proposals by on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.

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## Wolf Prize

The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people...

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## Yan Soibelman

Yakov Soibelman (Russian: Яков Семенович Сойбельман) born 15 April 1956 (Kiev, USSR) is a Russian mathematician, professor of Kansas State University (Manhattan, USA), member of the (Ukraine), founder of Manhattan Mathematical Olympiad.

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## Zariski's main theorem

In algebraic geometry, Zariski's main theorem, proved by, is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety.

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## Redirects here:

Deligne, Deligne conjecture, Deligne motive, Deligne tensor product of abelian categories, Deligne's conjecture, List of things named after Pierre Deligne, Pierre R. Deligné, Pierre Rene Deligne, Pierre René Deligne, Pierre deligne, Weight monodromy conjecture, Weight-monodromy conjecture.

## References

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