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Claire Voisin
Claire Voisin (born 4 March 1962) is a French mathematician known for her work in algebraic geometry. She is a member of the French Academy of Sciences and held the chair of algebraic geometry at the Collège de France from 2015 to 2020. Work She is noted for her work in algebraic geometry particularly as it pertains to variations of Hodge structures and mirror symmetry, and has written several books on Hodge theory. In 2002, Voisin proved that the generalization of the Hodge conjecture for compact Kähler varieties is false. The Hodge conjecture is one of the seven Clay Mathematics Institute Millennium Prize Problems which were selected in 2000, each having a prize of one million US dollars. Voisin won the European Mathematical Society Prize in 1992 and the Servant Prize awarded by the Academy of Sciences in 1996. She received the Sophie Germain Prize in 2003 and the Clay Research Award in 2008 for her disproof of the Kodaira conjecture on deformations of compact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint-Leu-la-Forêt
Saint-Leu-la-Forêt () is a commune in the Val-d'Oise department, in the northwestern outer suburbs of Paris, France. It is located from the centre of Paris. In 2021, it had a population of 15,979. History In 1806, the commune of Saint-Leu-la-Forêt merged with the neighboring commune of Taverny, resulting in the creation of the commune of ''Saint-Leu-Taverny''. In 1821, the commune of ''Saint-Leu-Taverny'' was demerged. Thus, Saint-Leu-la-Forêt and Taverny were both restored as separate communes. Population Transport Saint-Leu-la-Forêt is served by Saint-Leu-la-Forêt station on the Transilien Paris-Nord suburban rail line. Cultural connections * Louis Henri Joseph de Bourbon (1756-1830), the last Prince of Condé, was found dead, probably by suicide, at the Château de Saint-Leu on 27 August 1830. * Louis Bonaparte brother to Napoleon I and father to Napoleon III, is buried at Saint-Leu-la-Forêt. * Wanda Landowska's villa in Saint-Leu-la-Forêt became a center for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BBVA Foundation Frontiers Of Knowledge Award
The BBVA Foundation Frontiers of Knowledge Awards () are an international award programme recognizing significant contributions in the areas of scientific research and cultural creation. The categories that make up the Frontiers of Knowledge Awards respond to the knowledge map of the present age. As well as the fundamental knowledge that is at their core, they address developments in information and communication technologies, and interactions between biology and medicine, ecology and conservation biology, climate change, economics, humanities and social sciences, and, finally, contemporary musical creation and performance. Specific categories are reserved for developing knowledge fields of critical relevance to confront central challenges of the 21st century, as in the case of the two environmental awards. The awards were established in 2008, with the first set of winners receiving their prizes in 2009. The BBVA Foundation – belonging to financial group BBVA – is partnered in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford's Theorem On Special Divisors
In mathematics, Clifford's theorem on special divisors is a result of on algebraic curves, showing the constraints on special linear systems on a curve ''C''. Statement A divisor on a Riemann surface ''C'' is a formal sum \textstyle D = \sum_P m_P P of points ''P'' on ''C'' with integer coefficients. One considers a divisor as a set of constraints on meromorphic functions in the function field of ''C,'' defining L(D) as the vector space of functions having poles only at points of ''D'' with positive coefficient, ''at most as bad'' as the coefficient indicates, and having zeros at points of ''D'' with negative coefficient, with ''at least'' that multiplicity. The dimension of L(D) is finite, and denoted \ell(D). The linear system of divisors attached to ''D'' is the corresponding projective space of dimension \ell(D)-1. The other significant invariant of ''D'' is its degree ''d'', which is the sum of all its coefficients. A divisor is called '' special'' if ''ℓ''(''K'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manifolds
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 self-crossing curves such as a figure 8. 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 p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kähler Manifold
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähler in 1933. The terminology has been fixed by André Weil. Kähler geometry refers to the study of Kähler manifolds, their geometry and topology, as well as the study of structures and constructions that can be performed on Kähler manifolds, such as the existence of special connections like Hermitian Yang–Mills connections, or special metrics such as Kähler–Einstein metrics. Every smooth complex projective variety is a Kähler manifold. Hodge theory is a central part of algebraic geometry, proved using Kähler metrics. Definitions Since Kähler manifolds are equipped with several compatible structures, they can be described from different points of vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kunihiko Kodaira
was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese national to receive this honour. Early life and education Kodaira was born in Tokyo. He graduated from the University of Tokyo in 1938 with a degree in mathematics and also graduated from the physics department at the University of Tokyo in 1941. During the war years he worked in isolation, but was able to master Hodge theory as it then stood. He obtained his PhD from the University of Tokyo in 1949, with a thesis entitled ''Harmonic fields in Riemannian manifolds''. He was involved in cryptographic work from about 1944, while holding an academic post in Tokyo. Institute for Advanced Study and Princeton University In 1949 he travelled to the Institute for Advanced Study in Princeton, New Jersey at the invitation of Hermann Weyl. He ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sophie Germain
Marie-Sophie Germain (; 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library, including ones by Euler, and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss (under the pseudonym of Monsieur Le Blanc). One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred. On 27 June 1831, she died from breast cancer. At the centenary of her life, a stree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Millennium Prize Problems
The Millennium Prize Problems are seven well-known complex mathematics, mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the Millennium Meeting held on May 24, 2000. Thus, on the official website of the Clay Mathematics Institute, these seven problems are officially called the Millennium Problems. To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture. The Clay Institute awarded the monetary prize to Russian mathematician Grigori Perelman in 2010. However, he declined the award as it w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's scientific activities are managed from the President's office in Oxford, United Kingdom. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the sponsorship of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI. While the institute is best known for its Millennium Prize Problems, it carries out a wide range of activities, including conferences, workshops, summer schools, and a postdoctoral program supporting Clay Research Fellows. Governance The institute is run according to a standard structure comprising a scientific advisory committee that decides on grant-awarding and research proposals, and a board of directors that overs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kähler Manifolds
Kähler may refer to: People *Birgit Kähler (born 1970), German high jumper * Erich Kähler (1906–2000), German mathematician * Heinz Kähler (1905–1974), German art historian and archaeologist *Luise Kähler (1869–1955), German trade union leader and politician * Martin Kähler (1835–1912), German theologian * Otto Kähler (1894–1967), German admiral *Wilhelmine Kähler (1864–1941), German politician Other * Kähler Keramik, a Danish ceramics manufacturer *Kähler manifold In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnol ..., an important geometric complex manifold See also * Kahler (other) {{disambiguation, surname Occupational surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hodge Conjecture
In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties. In simple terms, the Hodge conjecture asserts that the basic topological information like the number of holes in certain geometric spaces, complex algebraic varieties, can be understood by studying the possible nice shapes sitting inside those spaces, which look like zero sets of polynomial equations. The latter objects can be studied using algebra and the calculus of analytic functions, and this allows one to indirectly understand the broad shape and structure of often higher-dimensional spaces which can not be otherwise easily visualized. More specifically, the conjecture states that certain de Rham cohomology classes are algebraic; that is, they are sums of Poincaré duals of the homology classes of subvarieties. It was formulated by the Scottish mathematician Willi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mirror Symmetry (string Theory)
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometry, geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
