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Laurent Lafforgue
Laurent Lafforgue (; born 6 November 1966) is a French mathematician. He has made outstanding contributions to Langlands' program in the fields of number theory and Mathematical analysis, analysis, and in particular proved the Langlands conjectures for the Automorphism#Automorphism group, automorphism group of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas. The mathematical proof, proof was the result of more than six years of concentrated efforts. In 2002 at the 24th International Congress of Mathematicians in Beijing, China, he received the Fields Medal together with Vladimir Voevodsky. Biography Laurent Lafforgue has two brothers, Thomas and Vincent Lafforgue, Vincent, both mathematicians. Thomas is now a teacher in a ''classe préparatoire aux grandes écoles'' at Lycée Louis le Grand in Paris and Vincent Lafforgue, Vincent a CNRS directeur de recherches at the Insti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antony, Hauts-de-Seine
Antony () is a Communes of France, commune in the southern suburbs of Paris, France, from the Kilometre Zero, centre of Paris. Antony is a subprefecture of the Hauts-de-Seine Departments of France, department and the seat of the arrondissement of Antony. Watered by the Bièvre (river), Bièvre, a tributary of the Seine, Antony is at the crossroads of important transport routes, especially the main north–south axis, which has existed for 2,000 years. Little urbanized until the early 20th century, the city grew considerably between the two wars, under Senator-Mayor (France), Mayor Auguste Mounié, from 4,000 to 20,000 inhabitants. In the early 1960s the population quickly increased from 25,000 to 50,000 to accommodate repatriated people from Algeria. Now incorporated in the Paris Metropolitan Area, it is particularly strong in education, with one of the largest private institutions in France, and in health, with the largest private establishment in Île-de-France, Île-de-France. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shtuka
In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of complex multiplication theory. A shtuka (also called F-sheaf or chtouca) is a sort of generalization of a Drinfeld module, consisting roughly of a vector bundle over a curve, together with some extra structure identifying a "Frobenius twist" of the bundle with a "modification" of it. Drinfeld modules were introduced by , who used them to prove the Langlands conjectures for GL2 of an algebraic function field in some special cases. He later invented shtukas and used shtukas of rank 2 to prove the remaining cases of the Langlands conjectures for GL2. Laurent Lafforgue proved the Langlands conjectures for GL''n'' of a function field by studying the moduli stack of shtukas of rank ''n''. "Shtuka" is a Russian word штука meaning "a single co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Université De Paris-Sud
Paris-Sud University (), also known as the University of Paris — XI (or as the Orsay Faculty of Sciences, University of Paris before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, including Orsay, Cachan, Châtenay-Malabry, Sceaux, and Kremlin-Bicêtre campuses. In 2019, the university was replaced by the Paris-Saclay University. History Paris-Sud, as the Orsay Faculty of Sciences, was originally part of the University of Paris, which was subsequently split into several universities. After World War II, the rapid growth of nuclear physics and chemistry meant that research needed more and more powerful accelerators, which required large areas. The University of Paris, the and the looked for space in the south of Paris near Orsay. Later some of the teaching activity of the Faculty of Sciences in Paris was transferred to Orsay in 1956 at the request of Irène Joliot-Curie and Frédéric Joliot-Curie. The rapid i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of Postgraduate education, graduate study and original research. The name of the degree is most often abbreviated PhD (or, at times, as Ph.D. in North American English, North America), pronounced as three separate letters ( ). The University of Oxford uses the alternative abbreviation "DPhil". PhDs are awarded for programs across the whole breadth of academic fields. Since it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and, in some cases, defend their work before a panel of other experts in the field. In many fields, the completion of a PhD is typically required for employment as a university professor, researcher, or scientist. Definition In the context o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the world. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980. More than 100 countries participate. Each country sends a team of up to six students, plus one team leader, one deputy leader, and observers. Awards are given to approximately the top-scoring 50% of the individual contestants. Teams are not officially recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more than individual scores. Question type The content ranges from extremely difficult algebra and pre-calculus problems to problems in branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of cities in the European Union by population within city limits, fourth-most populous city in the European Union and the List of cities proper by population density, 30th most densely populated city in the world in 2022. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, culture, Fashion capital, fashion, and gastronomy. Because of its leading role in the French art, arts and Science and technology in France, sciences and its early adoption of extensive street lighting, Paris became known as the City of Light in the 19th century. The City of Paris is the centre of the Île-de-France region, or Paris Region, with an official estimated population of 12,271,794 inhabitants in January 2023, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classe Préparatoire Aux Grandes écoles
The ''Classes préparatoires aux grandes écoles'' (, ''Higher school preparatory classes'', abbr. CPGE), commonly called ''classes prépas'' or ''prépas'', are part of the French post-secondary education system. They consist of two years of study (extendable to three or exceptionally four years) which act as an intensive preparatory course (or cram school) with the main goal of training students for enrolment in one of the ''grandes écoles''. Whereas enrollment in public universities in France is open to any school leaver with an adequate ''baccalauréat'', enrollment in the ''grandes écoles'' is restricted to the highest-ranked students in a separate national competitive examination. Preparation for this examination entails one of the highest student workloads in Europe (29 to 45 contact hours a week, with up to 10 hours of guided tutorials and oral exam sessions). The ''grandes écoles'' are higher education establishments (graduate schools) delivering master's degrees an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vincent Lafforgue
Vincent Lafforgue (born 20 January 1974) is a French mathematician who is active in algebraic geometry, especially in the Langlands program, and a CNRS " Directeur de Recherches" at the Institute Fourier in Grenoble. He is the younger brother of Fields Medalist Laurent Lafforgue. Awards Lafforgue was awarded the 2000 EMS Prize for his contribution to the K-theory of operator algebras: the proof of the Baum–Connes conjecture for discrete co-compact subgroups of \mathrm(3,\mathbb), \mathrm(3,\mathbb), \mathrm(3,\mathbb_p) and some other locally compact groups, and of more general objects. He participated in the International Mathematical Olympiad and wrote two perfect papers in 1990 and 1991, making him one of only three French mathematicians to win two gold medals (besides Joseph Najnudel, 1997–98, and Aurélien Fourré, 2020-21). Lafforgue was an Invited Speaker of the ICM in 2002 in Beijing, China and a Plenary Speaker of the ICM in 2018 in Rio de Janeiro, Brazil. He wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Voevodsky
Vladimir Alexandrovich Voevodsky (, ; 4 June 1966 – 30 September 2017) was a Russian-American mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. He is also known for the proof of the Milnor conjecture and motivic Bloch–Kato conjectures and for the univalent foundations of mathematics and homotopy type theory. Early life and education Vladimir Voevodsky's father, Aleksander Voevodsky, was head of the Laboratory of High Energy Leptons in the Institute for Nuclear Research at the Russian Academy of Sciences. His mother Tatyana was a chemist. Voevodsky attended Moscow State University for a while, but was expelled without a diploma for refusing to attend classes and failing academically. He received his Ph.D. in mathematics from Harvard University in 1992 after being recommended without even applying and without a formal college degree, following several independent p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
China
China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after India, representing 17.4% of the world population. China spans the equivalent of five time zones and Borders of China, borders fourteen countries by land across an area of nearly , making it the list of countries and dependencies by area, third-largest country by land area. The country is divided into 33 Province-level divisions of China, province-level divisions: 22 provinces of China, provinces, 5 autonomous regions of China, autonomous regions, 4 direct-administered municipalities of China, municipalities, and 2 semi-autonomous special administrative regions. Beijing is the country's capital, while Shanghai is List of cities in China by population, its most populous city by urban area and largest financial center. Considered one of six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
