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Colette Moeglin
Colette Moeglin (born 1953) is a French mathematician, working in the field of automorphic forms, a topic at the intersection of number theory and representation theory. Career and distinctions Moeglin is a Directeur de recherche at the Centre national de la recherche scientifique and is currently working at the Institut de mathématiques de Jussieu. She was a speaker at the 1990 International Congress of Mathematicians, on decomposition into distinguished subspaces of certain spaces of square-integral automorphic forms. She was a recipient of the Jaffé prize of the French Academy of Sciences in 2004, "for her work, most notably on the topics of enveloping algebras of Lie algebras, automorphic forms and the classification of square-integrable representations of reductive classical p-adic groups by their cuspidal representations". She was the chief editor of the ''Journal of the Institute of Mathematics of Jussieu'' from 2002 to 2006. She became a member of the Academia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms. More generally, one can use the adelic approach as a way of dealing with the whole family of congruence subgroups at once. From this point of view, an automorphic form over the group ''G''(A''F''), for an algebraic group ''G'' and an algebraic number field ''F'', is a complex-valued function on ''G''(A''F'') that is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eisenstein Series
Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series can be generalized in the theory of automorphic forms. Eisenstein series for the modular group Let be a complex number with strictly positive imaginary part. Define the holomorphic Eisenstein series of weight , where is an integer, by the following series: :G_(\tau) = \sum_ \frac. This series absolutely converges to a holomorphic function of in the upper half-plane and its Fourier expansion given below shows that it extends to a holomorphic function at . It is a remarkable fact that the Eisenstein series is a modular form. Indeed, the key property is its -invariance. Explicitly if and then :G_ \left( \frac \right) = (c\tau +d)^ G_(\tau) Relation to modular invariants The modular invariants and of an elliptic curve are given by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century French Mathematicians
The 1st century was the century spanning AD 1 (Roman numerals, I) through AD 100 (Roman numerals, C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or History by period, historical period. The 1st century also saw the Christianity in the 1st century, appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Union
The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports the International Congress of Mathematicians. Its members are national mathematics organizations from more than 80 countries. The objectives of the International Mathematical Union (IMU) are: promoting international cooperation in mathematics, supporting and assisting the International Congress of Mathematicians (ICM) and other international scientific meetings/conferences, acknowledging outstanding research contributions to mathematics through the awarding of scientific prizes, and encouraging and supporting other international mathematical activities, considered likely to contribute to the development of mathematical science in any of its aspects, whether pure, applied, or educational. The IMU was established in 1920, but dissolved in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bourbaki Seminar
Bourbaki(s) may refer to : Persons and science * Charles-Denis Bourbaki (1816–1897), French general, son of Constantin Denis Bourbaki * Colonel Constantin Denis Bourbaki (1787–1827), officer in the Greek War of Independence and serving in the French military * Nicolas Bourbaki, the collective pseudonym of a group of French mathematicians ** Séminaire Nicolas Bourbaki and its follow-ups *** Séminaire Nicolas Bourbaki (1950–1959) *** Séminaire Nicolas Bourbaki (1960–1969) ** Bourbaki–Witt theorem ** Bourbaki–Alaoglu theorem ** Jacobson–Bourbaki theorem * Nikolaos Bourbakis, computer scientist Other * A place in Algeria, now known as Khemisti, near Aïn-Tourcia and the site of ancient city and former bishopric Columnata Khemisti is a town and commune in Tissemsilt Province in northern Algeria. It was called Bourbaki when Algeria was a colony of France. History In Roman times, it was called Columnata and belonged to the Roman province of Mauretania C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Arthur (mathematician)
James Greig Arthur (born May 18, 1944) is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He is a Mossman Chair and University Professor at the University of Toronto Department of Mathematics. Education and career Born in Hamilton, Ontario, Arthur graduated from Upper Canada College in 1962, received a BSc from the University of Toronto in 1966, and a MSc from the same institution in 1967. He received his PhD from Yale University in 1970. He was a student of Robert Langlands; his dissertation was ''Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One''. Arthur taught at Yale from 1970 until 1976. He joined the faculty of Duke University in 1976. He has been a professor at the University of Toronto since 1978. He was four times a visiting scholar at the Institute for Advanced Study between 1976 and 2002. Contributions Arthur is known for the Arthur–Selberg trace formula, generalizing t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gan–Gross–Prasad Conjecture
In mathematics, the Gan–Gross–Prasad conjecture is a restriction problem in the representation theory of real or p-adic Lie groups posed by Gan Wee Teck, Benedict Gross, and Dipendra Prasad. The problem originated from a conjecture of Gross and Prasad for special orthogonal groups but was later generalized to include all four classical groups. In the cases considered, it is known that the multiplicity of the restrictions is at most one and the conjecture describes when the multiplicity is precisely one. Motivation A motivating example is the following classical branching problem in the theory of compact Lie groups. Let \pi be an irreducible finite dimensional representation of the compact unitary group U(n), and consider its restriction to the naturally embedded subgroup U(n-1). It is known that this restriction is multiplicity-free, but one may ask precisely which irreducible representations of U(n-1) occur in the restriction. By the Cartan–Weyl theory of highest we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Howe Correspondence
In mathematics, the theta correspondence or Howe correspondence is a mathematical relation between representations of two groups of a reductive dual pair. The local theta correspondence relates irreducible admissible representations over a local field, while the global theta correspondence relates irreducible automorphic representations over a global field. The theta correspondence was introduced by Roger Howe in . Its name arose due to its origin in André Weil's representation theoretical formulation of the theory of theta series in . The Shimura correspondence as constructed by Jean-Loup Waldspurger in and may be viewed as an instance of the theta correspondence. Statement Setup Let F be a local or a global field, not of characteristic 2. Let W be a symplectic vector space over F, and Sp(W) the symplectic group. Fix a reductive dual pair (G,H) in Sp(W). There is a classification of reductive dual pairs. Local theta correspondence F is now a local field. Fix a non-trivia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marie-France Vignéras
Marie-France Vignéras (born 1946) is a French mathematician. She is a Professor Emeritus of the Institut de Mathématiques de Jussieu in Paris. She is known for her proof published in 1980 of the existence of isospectral non-isometric Riemann surfaces. Such surfaces show that one cannot hear the shape of a hyperbolic drum. Another highlight of her work is the establishment of the mod-l local Langlands correspondence for GL(n) in 2000. Her current work concerns the p-adic Langlands program. Early life and education Born in 1946, Vignéras was the daughter of Janine Mocudé and Robert Vignéras (sea captain and pilot in the port of Dakar). She spent her childhood in Senegal, and did her high school studies at the lycée Van-Vollenhoven in Dakar. She moved to the University of Bordeaux after receiving her baccalauréat in Senegal. She received the agrégation de mathématiques in 1969 and the doctorat d'Etat in 1974; her thesis was written under the direction of Jacques Martinet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adelic Algebraic Group
In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group ''G'' over a number field ''K'', and the adele ring ''A'' = ''A''(''K'') of ''K''. It consists of the points of ''G'' having values in ''A''; the definition of the appropriate topology is straightforward only in case ''G'' is a linear algebraic group. In the case of ''G'' being an abelian variety, it presents a technical obstacle, though it is known that the concept is potentially useful in connection with Tamagawa numbers. Adelic algebraic groups are widely used in number theory, particularly for the theory of automorphic representations, and the arithmetic of quadratic forms. In case ''G'' is a linear algebraic group, it is an affine algebraic variety in affine ''N''-space. The topology on the adelic algebraic group G(A) is taken to be the subspace topology in ''A''''N'', the Cartesian product of ''N'' copies of the adele ring. In this case, G(A) is a topological group ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
