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Leila Schneps
Leila Schneps is an American mathematician and fiction writer at the Centre national de la recherche scientifique working in number theory. Schneps has written general audience math books and, under the pen name Catherine Shaw, has written mathematically themed murder mysteries. Education Schneps earned a B.A. in Mathematics, German Language and Literature from Radcliffe College in 1983. She completed a Doctorat de Troisième Cycle in Mathematics at Université Paris-Sud XI-Orsay in 1985 under the supervision of John H. Coates with a thesis on ''p''-adic L-functions attached to elliptic curves, a Ph.D. in Mathematics in 1990 with a thesis on ''p''-Adic L-functions and Galois groups, and Habilitation at Université de Franche-Comté in 1993, with a thesis on the Inverse Galois problem. Professional experience Schneps held various teaching assistant positions in France and Germany until the completion of her Ph.D. in 1990, then worked as a postdoctoral assistant at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris
The University of Paris (french: link=no, Université de Paris), Metonymy, metonymically known as the Sorbonne (), was the leading university in Paris, France, active from 1150 to 1970, with the exception between 1793 and 1806 under the French Revolution. Emerging around 1150 as a corporation associated with the cathedral school of Notre Dame de Paris, it was considered the List of medieval universities, second-oldest university in Europe.Charles Homer Haskins, Haskins, C. H.: ''The Rise of Universities'', Henry Holt and Company, 1923, p. 292. Officially chartered in 1200 by King Philip II of France and recognised in 1215 by Pope Innocent III, it was later often nicknamed after its theological College of Sorbonne, in turn founded by Robert de Sorbon and chartered by List of French monarchs, French King Louis IX, Saint Louis around 1257. Internationally highly reputed for its academic performance in the humanities ever since the Middle Ages – notably in theology and philosophy – ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Besançon
Besançon (, , , ; archaic german: Bisanz; la, Vesontio) is the prefecture of the department of Doubs in the region of Bourgogne-Franche-Comté. The city is located in Eastern France, close to the Jura Mountains and the border with Switzerland. Capital of the historic and cultural region of Franche-Comté, Besançon is home to the Bourgogne-Franche-Comté regional council headquarters, and is an important administrative centre in the region. It is also the seat of one of the fifteen French ecclesiastical provinces and one of the two divisions of the French Army. In 2019 the city had a population of 117,912, in a metropolitan area of 280,701, the second in the region in terms of population. Established in a meander of the river Doubs, the city was already important during the Gallo-Roman era under the name of ''Vesontio'', capital of the Sequani. Its geography and specific history turned it into a military stronghold, a garrison city, a political centre, and a religiou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grothendieck–Teichmüller Group
In mathematics, the Grothendieck–Teichmüller group ''GT'' is a group closely related to (and possibly equal to) the absolute Galois group of the rational numbers. It was introduced by and named after Alexander Grothendieck and Oswald Teichmüller, based on Grothendieck's suggestion in his 1984 essay '' Esquisse d'un Programme'' to study the absolute Galois group of the rationals by relating it to its action on the Teichmüller tower of Teichmüller groupoids ''T''''g'',''n'', the fundamental groupoid In algebraic topology, the fundamental groupoid is a certain topological invariant of a topological space. It can be viewed as an extension of the more widely-known fundamental group; as such, it captures information about the homotopy type of a to ...s of moduli stacks of genus ''g'' curves with ''n'' points removed. There are several minor variations of the group: a discrete version, a pro-''l'' version, a ''k''-pro-unipotent version, and a profinite version; the first three v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Geometry
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. In more abstract terms, arithmetic geometry can be defined as the study of schemes of finite type over the spectrum of the ring of integers. Overview The classical objects of interest in arithmetic geometry are rational points: sets of solutions of a system of polynomial equations over number fields, finite fields, p-adic fields, or function fields, i.e. fields that are not algebraically closed excluding the real numbers. Rational points can be directly characterized by height functions which measure their arithmetic complexity. The structure of algebraic varieties defined over non-algebraically closed fields has become a central area of interest that arose with the modern abstract development of algebraic geometry. Over finite fields ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Ellenberg
Jordan Stuart Ellenberg (born October 30, 1971) is an American mathematician who is a professor of mathematics at the University of Wisconsin–Madison. His research involves arithmetic geometry. He is also an author of both fiction and non-fiction writing. Early life Ellenberg was born in Potomac, Maryland. He was a child prodigy who taught himself to read at the age of two by watching ''Sesame Street''. His mother discovered his ability one day while she was driving on the Capital Beltway when her toddler informed her: "The sign says ' Bethesda is to the right.'" In second grade, he helped his teenage babysitter with her math homework. By fourth grade, he was participating in high school competitions (such as the American Regions Mathematics League) as a member of the Montgomery County math team. And by eighth grade, he had started college-level work. He was part of the Johns Hopkins University Study of Mathematically Precocious Youth longitudinal cohort. He scored a perfect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Action (mathematics)
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group ''acts'' on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it. For example, it acts on the set of all triangles. Similarly, the group of symmetries of a polyhedron acts on the vertices, the edges, and the faces of the polyhedron. A group action on a vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of , the group of the invertible matrices of dimension over a field . The symmetric group acts on an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying roots of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is ''solvable by radicals'' if its roots may be expressed by a formula involving only integers, th roots, and the four basic arithmetic operations. This widely generalizes the Abel–Ruffini theorem, which asserts that a general polynomial of degree at least five cannot be solved by radicals. Galois theory has been used to solve classic problems including showing that two problems of antiquity cannot be solved as they were stated ( doubling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Zeta Function
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ( zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > 1 and its analytic continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory, and has applications in physics, probability theory, and applied statistics. Leonhard Euler first introduced and studied the function over the reals in the first half of the eighteenth century. Bernhard Riemann's 1859 article " On the Number of Primes Less Than a Given Magnitude" extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation, and established a relation between its zeros and the distribution of prime numbers. This paper also contained the Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. * Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. * Additive n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant university and the founding campus of the University of California system. Its fourteen colleges and schools offer over 350 degree programs and enroll some 31,800 undergraduate and 13,200 graduate students. Berkeley ranks among the world's top universities. A founding member of the Association of American Universities, Berkeley hosts many leading research institutes dedicated to science, engineering, and mathematics. The university founded and maintains close relationships with three national laboratories at Berkeley, Livermore and Los Alamos, and has played a prominent role in many scientific advances, from the Manhattan Project and the discovery of 16 chemical elements to breakthroughs in computer science and genomics. Berkeley i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Sciences Research Institute
The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, California. It is widely regarded as a world leading mathematical center for collaborative research, drawing thousands of leading researchers from around the world each year. The institute was founded in 1982, and its funding sources include the National Science Foundation, private foundations, corporations, and more than 90 universities and institutions. The institute is located at 17 Gauss Way on the Berkeley campus, close to Grizzly Peak in the Berkeley Hills. Because of its contribution to the nation's scientific potential, SLMath's activity is supported by the National Science Foundation and the National Security Agency. Private individuals, foundations, and nearly 100 Academic Sponsor Institutions, including the top mathematics depar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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