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Ahmed Abbes
Ahmed Abbes (born 24 May 1970) is a Tunisian-French mathematician and a at the Institut des Hautes Études Scientifiques (IHÉS). He is known for his work in arithmetic geometry. Early life and education Abbes was born on 24 May 1970 in Sfax, Tunisia. Abbes received a bronze medal in 1988 and a silver medal in 1989 at the International Mathematical Olympiad while representing Tunisia. Abbes has both French and Tunisian citizenship. Abbes studied at the École Normale Supérieure from 1990 to 1994 and then received his doctorate from Paris-Sud University in 1995 under the supervision of Lucien Szpiro, with the thesis ''Théorie d'Arakelov et courbes modulaires'' on Arakelov theory and modular curves. At Paris-Sud, Michel Raynaud was one of his mentors. Abbes received his habilitation in 2003. Career Abbes was a post-doctoral researcher at the Institut des Hautes Études Scientifiques (IHÉS) from 1995 to 1996 and was also a post-doctoral researcher at the Max Planck Institut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chargé De Recherche
Chargé () is a commune in the Indre-et-Loire department Department may refer to: * Departmentalization, division of a larger organization into parts with specific responsibility Government and military *Department (administrative division), a geographical and administrative division within a country, ... in central France. Chargé is a small town near Amboise. The Rock 'in Chargé festival has revitalized the village sinc2006 Population The inhabitants are called ''Chargéens''. See also * Communes of the Indre-et-Loire department References Communes of Indre-et-Loire {{IndreLoire-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1970 Births
Events January * January 1 – Unix time epoch reached at 00:00:00 UTC. * January 5 – The 7.1 Tonghai earthquake shakes Tonghai County, Yunnan province, China, with a maximum Mercalli intensity of X (''Extreme''). Between 10,000 and 14,621 were killed and 26,783 were injured. * January 14 – Biafra capitulates, ending the Nigerian Civil War. * January 15 – After a 32-month fight for independence from Nigeria, Biafran forces under Philip Effiong formally surrender to General Yakubu Gowon. February * February 1 – The Benavídez rail disaster near Buenos Aires, Argentina, kills 236. * February 10 – An avalanche at Val-d'Isère, France, kills 41 tourists. * February 11 – '' Ohsumi'', Japan's first satellite, is launched on a Lambda-4 rocket. * February 22 – Guyana becomes a Republic within the Commonwealth of Nations. March * March 1 – Rhodesia severs its last tie with the United Kingdom, declaring itself a republic. * March 4 — All 57 m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Sfax
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Geometers
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today. History The prehistory of arithmetic is limited to a small number of artifacts, which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tunisian Mathematicians
Tunisian may refer to: * Someone or something connected to Tunisia *Tunisian Arabic *Tunisian people *Tunisian cuisine * Tunisian culture Tunisian culture is a product of more than three thousand years of history and an important multi-ethnic influx. Ancient Tunisia was a major civilization crossing through history; different cultures, civilizations and multiple successive dynast ... {{Disambig Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-adic Hodge Theory
In mathematics, ''p''-adic Hodge theory is a theory that provides a way to classify and study ''p''-adic Galois representations of characteristic 0 local fields with residual characteristic ''p'' (such as Q''p''). The theory has its beginnings in Jean-Pierre Serre and John Tate's study of Tate modules of abelian varieties and the notion of Hodge–Tate representation. Hodge–Tate representations are related to certain decompositions of ''p''-adic cohomology theories analogous to the Hodge decomposition, hence the name ''p''-adic Hodge theory. Further developments were inspired by properties of ''p''-adic Galois representations arising from the étale cohomology of varieties. Jean-Marc Fontaine introduced many of the basic concepts of the field. General classification of ''p''-adic representations Let ''K'' be a local field with residue field ''k'' of characteristic ''p''. In this article, a ''p-adic representation'' of ''K'' (or of ''GK'', the absolute Galois group of ''K'') wil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonabelian Hodge Correspondence
In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold. The theorem can be considered a vast generalisation of the Narasimhan–Seshadri theorem which defines a correspondence between stable vector bundles and unitary representations of the fundamental group of a compact Riemann surface. In fact the Narasimhan–Seshadri theorem may be obtained as a special case of the nonabelian Hodge correspondence by setting the Higgs field to zero. History It was proven by M. S. Narasimhan and C. S. Seshadri in 1965 that stable vector bundles on a compact Riemann surface correspond to irreducible projective unitary representations of the fundamental group. This theorem was phrased in a new light in the work of Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-adic Field
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two -adic numbers are considered to be close when their difference is divisible by a high power of : the higher the power, the closer they are. This property enables -adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles. These numbers were first described by Kurt Hensel in 1897, though, with hindsight, some of Ernst Kummer's earlier work can be interpreted as implicitly using -adic numbers.Translator's introductionpage 35 "Indeed, with hindsight it becomes apparent that a discret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Field
In algebra, a field ''k'' is perfect if any one of the following equivalent conditions holds: * Every irreducible polynomial over ''k'' has distinct roots. * Every irreducible polynomial over ''k'' is separable. * Every finite extension of ''k'' is separable. * Every algebraic extension of ''k'' is separable. * Either ''k'' has characteristic 0, or, when ''k'' has characteristic , every element of ''k'' is a ''p''th power. * Either ''k'' has characteristic 0, or, when ''k'' has characteristic , the Frobenius endomorphism is an automorphism of ''k''. * The separable closure of ''k'' is algebraically closed. * Every reduced commutative ''k''-algebra ''A'' is a separable algebra; i.e., A \otimes_k F is reduced for every field extension ''F''/''k''. (see below) Otherwise, ''k'' is called imperfect. In particular, all fields of characteristic zero and all finite fields are perfect. Perfect fields are significant because Galois theory over these fields becomes simpler, since the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could be the ring of continuous functions defined on that open set. Such data is well behaved in that it can be restricted to smaller open sets, and also the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original open set (intuitively, every piece of data is the sum of its parts). The field of mathematics that studies sheaves is called sheaf theory. Sheaves are understood conceptually as general and abstract objects. Their correct definition is rather technical. They are specifically defined as sheaves of sets or as sheaves of rings, for example, depending on the type of data assigned to the open sets. There are also maps (or morphisms) from one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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