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Pierre Cartier (mathematician)
Pierre Émile Cartier (born 10 June 1932) is a French mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory. He studied at the École Normale Supérieure in Paris under Henri Cartan and André Weil. Since his 1958 thesis on algebraic geometry he has worked in a number of fields. He is known for the introduction of the Cartier operator in algebraic geometry in characteristic ''p'', and for work on duality of abelian varieties and on formal groups. He is the eponym of Cartier divisors and Cartier duality. From 1961 to 1971 he was a professor at the University of Strasbourg. In 1970 he was an Invited Speaker at the International Congress of Mathematicians in Nice. He was awarded the 1978 Prize Ampère of the French Academy of Sciences. In 2012 he became a fellow of the American Mathematical Society. Publications ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sedan, Ardennes
Sedan () is a commune in the Ardennes department and Grand Est region of north-eastern France. It is also the chef-lieu (administrative centre) of the arrondissement of the same name. Location The town is situated about 200 km from Paris, 85 km north-east of Reims, and 10 km south of the border with Belgium. The historic centre occupies a peninsula formed by a bend in the river Meuse. Sedan station has rail connections to Charleville-Mézières, Reims and Longwy. The A34 autoroute links Sedan with Charleville-Mézières and Reims. History Sedan was founded in 1424. In the 16th century Sédan was an asylum for Protestant refugees from the Wars of Religion. Until 1651, the Principality of Sedan belonged to the La Tour d'Auvergne family. It was at that time a sovereign principality. Their representative, Marshal Turenne, was born at Sedan on 11 September 1611. With help from the Holy Roman Empire, it defeated France at the Battle of La Marfée. Immediately after i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics). Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. Classical mechanics The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry (physics), symmetry and conservation law, con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cédric Villani
Cédric Patrice Thierry Villani (; born 5 October 1973) is a French politician and mathematician working primarily on partial differential equations, Riemannian geometry and mathematical physics. He was awarded the Fields Medal in 2010, and he was the director of Sorbonne University's Institut Henri Poincaré from 2009 to 2017. As of September 2022, he is a professor at Institut des Hautes Études Scientifiques. Villani has given two lectures at the Royal Institution, the first titled 'Birth of a Theorem'. The English translation of his book ''Théorème vivant'' (''Living Theorem'') has the same title. In the book he describes the links between his research on kinetic theory and the one of the mathematician Carlo Cercignani: Villani, in fact, proved the so-called Cercignani's conjecture. His second lecture at the Royal Institution is titled 'The Extraordinary Theorems of John Nash'. Villani was elected as the deputy for Essonne's 5th constituency in the National Assembly, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Academy Of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefront of scientific developments in Europe in the 17th and 18th centuries, and is one of the earliest Academy of Sciences, Academies of Sciences. Currently headed by Patrick Flandrin (President of the Academy), it is one of the five Academies of the Institut de France. History The Academy of Sciences traces its origin to Colbert's plan to create a general academy. He chose a small group of scholars who met on 22 December 1666 in the King's library, near the present-day Bibliothèque nationale de France, Bibliothèque Nationals, and thereafter held twice-weekly working meetings there in the two rooms assigned to the group. The first 30 years of the Academy's existence were relatively informal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly 1 millionDemographia: World Urban Areas , Demographia.com, April 2016 on an area of . Located on the , the southeastern coast of France on the , at the foot of the |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartier Duality
In mathematics, Cartier duality is an analogue of Pontryagin duality for commutative group schemes. It was introduced by . Definition using characters Given any finite flat commutative group scheme ''G'' over ''S'', its Cartier dual is the group of characters, defined as the functor that takes any ''S''-scheme ''T'' to the abelian group of group scheme homomorphisms from the base change G_T to \mathbf_ and any map of ''S''-schemes to the canonical map of character groups. This functor is representable by a finite flat ''S''-group scheme, and Cartier duality forms an additive involutive antiequivalence from the category of finite flat commutative ''S''-group schemes to itself. If ''G'' is a constant commutative group scheme, then its Cartier dual is the diagonalizable group ''D''(''G''), and vice versa. If ''S'' is affine, then the duality functor is given by the duality of the Hopf algebras of functions. Definition using Hopf algebras A finite commutative group scheme over a fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Group
In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations. Formal groups are intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology. Definitions A one-dimensional formal group law over a commutative ring ''R'' is a power series ''F''(''x'',''y'') with coefficients in ''R'', such that # ''F''(''x'',''y'') = ''x'' + ''y'' + terms of higher degree # ''F''(''x'', ''F''(''y'',''z'')) = ''F''(''F''(''x'',''y''), ''z'') (associativity). The simplest example is the additive formal group law ''F''(''x'', ''y'') = ''x'' + ''y''. The idea of the definition is that ''F'' should be something like the formal power series expansion of the product of a Lie group, where we choose coordinates so that the id ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Varieties
In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined ''over'' that field. Historically the first abelian varieties to be studied were those defined over the field of complex numbers. Such abelian varieties turn out to be exactly those complex tori that can be embedded into a complex projective space. Abelian varieties defined over algebraic number fields are a special case, which is important also from the viewpoint of number theory. Localization techniques lead naturally from abe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartier Operator
Cartier may refer to: People * Cartier (surname), a surname (including a list of people with the name) * Cartier Martin (born 1984), American basketball player Places * Cartier Island, an island north-west of Australia that is part of Australia's Northern Territory * Rural Municipality of Cartier, Manitoba * Cartier, Ontario, a small town in Northern Ontario * Cartier (electoral district), Quebec * Mount Cartier, a mountain in British Columbia Transportation * Cartier Railway, Quebec, Canada * Cartier station (Montreal Metro), a subway station in Laval, Quebec, Canada * Cartier station (Ontario), a train station in Cartier, Ontario, Canada * De Cartier (Charleroi Metro), a subway station in Charleroi, Belgium Other uses * Cartier (jeweler), a French jewellery and watch manufacturer * Cartier Field, Indiana * Cartier (typeface) ** Cartier Book * HMCS ''Cartier'', a surveying ship * "Cartier", a song by Bazzi from the album ''Cosmic'' See also * Port-Cartier, Quebec * Cartier Ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thesis
A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: DocumentationPresentation of theses and similar documents International Organization for Standardization, Geneva, 1986. In some contexts, the word "thesis" or a cognate is used for part of a bachelor's or master's course, while "dissertation" is normally applied to a doctorate. This is the typical arrangement in American English. In other contexts, such as within most institutions of the United Kingdom and Republic of Ireland, the reverse is true. The term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, and the required minimum study period may thus vary significantly in d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
