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René Thom
René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as the founder of catastrophe theory (later developed by Christopher Zeeman). Life and career René Thom grew up in a modest family in Montbéliard, Doubs and obtained a Baccalauréat in 1940. After the German invasion of France, his family took refuge in Switzerland and then in Lyon. In 1941 he moved to Paris to attend Lycée Saint-Louis and in 1943 he began studying mathematics at École Normale Supérieure, becoming agrégé in 1946. He received his PhD in 1951 from the University of Paris. His thesis, titled ''Espaces fibrés en sphères et carrés de Steenrod'' (''Sphere bundles and Steenrod squares' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Montbéliard
Montbéliard (; traditional ) is a town in the Doubs department in the Bourgogne-Franche-Comté region in eastern France, about from the border with Switzerland. It is one of the two subprefectures of the department. History Montbéliard is mentioned as early as 983 as . The County of Montbéliard or Mömpelgard was a feudal county of the Holy Roman Empire from 1033 to 1796. In 1283, it was granted rights under charter by Count Reginald. Its charter guaranteed the county perpetual liberties and franchises which lasted until the French Revolution in 1789. Montbéliard's original municipal institutions included the Magistracy of the Nine Bourgeois, the Corp of the Eighteen and the Notables, a Mayor, and Procurator, and appointed "Chazes", who all participated in the administration of the county as provided by the charter. Also under the 1283 charter, the Count and the people of Montbéliard were required by law to defend Montbéliard, while citizens of Montbéliard were not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thom Space
In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space. Construction of the Thom space One way to construct this space is as follows. Let :p\colon E \to B be a rank ''n'' real vector bundle over the paracompact space ''B''. Then for each point ''b'' in ''B'', the fiber E_b is an ''n''-dimensional real vector space. We can form an ''n''-sphere bundle \operatorname(E) \to B by taking the one-point compactification of each fiber and gluing them together to get the total space. Finally, from the total space \operatorname(E) we obtain the Thom space T(E) as the quotient of \operatorname(E) by ''B''; that is, by identifying all the new points to a single point \infty, which we take as the basepoint of T(E). If ''B'' is compact, then T(E) is the one-point compactification of ''E''. For ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catastrophe Theory
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation. This may lead to sudden and dramatic changes, for example the unpredictable timing and magnitude of a landslide. Catastrophe theory originated with the work of the French mathematician René Thom in the 1960s, and became very popular due to the efforts of Christopher Zeeman in the 1970s. It considers the special case where the long-run stable equilibrium can be identified as the minimum of a smooth, well-defined potential function (Lyapunov function). Small changes in certain parameters of a nonlinear system can cause equilibria to appear or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singularity Theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string. Perhaps the string will also touch itself without crossing, like an underlined "U". This is another kind of singularity. Unlike the double point, it is not ''stable'', in the sense that a small push will lift the bottom of the "U" away from the "underline". Vladimir Arnold defines the main goal of singularity theory as describing how objects depend on parameters, particularly in cases where the properties undergo sudden change under a small variation of the parameters. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topologist
Topology (from the Greek words , and ) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Françoise Thom
Françoise Thom (born 1951) is a French historian and Sovietologist, honorary lecturer in contemporary history at Paris-Sorbonne University. A specialist in post-communist Russia, she is the author of works of political analysis on the country and its leaders. Early life and education Françoise Thom was born in Strasbourg, 1951. Her parents are René Thom, a mathematician known for his theory of catastrophes and winner of the Fields Medal, and of Suzanne Helmlinger. Françoise has two siblings, Elizabeth and Christian. Thom has a degree in Russian. Career She lived for three years in the Soviet Union, then taught Russian in secondary schools in Ferney-Voltaire and Calais. She is a research associate at the Institut français de polémologie. In 1983, she defended a thesis entitled , directed by Alain Besançon at the School for Advanced Studies in the Social Sciences. She was then appointed lecturer in contemporary history at Paris-Sorbonne University. In 2011, she presented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann Lecture Prize
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope John (dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brouwer Medal
The Brouwer Medal is a triennial award presented by the Royal Dutch Mathematical Society and the Royal Netherlands Academy of Sciences. The Brouwer Metal gets its name from Dutch mathematician L. E. J. Brouwer and is the Netherlands’ most prestigious award in mathematics. Recipients *1970 René Thom *1973 Abraham Robinson *1978 Armand Borel *1981 Harry Kesten *1984 Jürgen Moser *1987 Yuri I. Manin *1990 Walter Murray Wonham, W. M. Wonham *1993 László Lovász *1996 Wolfgang Hackbusch *1999 George Lusztig *2002 Michael Aizenman *2005 Lucien Birgé *2008 Phillip Griffiths *2011 Kim Plofker *2014 John N. Mather *2017 Ken Ribet *2020 David Aldous *2023 Éva Tardos, Eva Tardos References {{International mathematical activities Dutch science and technology awards Mathematics awards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been list of prizes known as the Nobel or the highest honors of a field, described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by Academic Ranking of World Universities, ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG Observatory on Academic Ranking and Excellence, IR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dold–Thom Theorem
In algebraic topology, the Dold-Thom theorem states that the homotopy groups of the infinite symmetric product of a connected CW complex are the same as its reduced homology groups. The most common version of its proof consists of showing that the composition of the homotopy group functors with the infinite symmetric product defines a reduced homology theory. One of the main tools used in doing so are quasifibrations. The theorem has been generalised in various ways, for example by the Almgren isomorphism theorem. There are several other theorems constituting relations between homotopy and homology, for example the Hurewicz theorem. Another approach is given by stable homotopy theory. Thanks to the Freudenthal suspension theorem, one can see that the latter actually defines a homology theory. Nevertheless, none of these allow one to directly reduce homology to homotopy. This advantage of the Dold-Thom theorem makes it particularly interesting for algebraic geometry. The theorem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thom–Sebastiani Theorem
In complex analysis, a branch of mathematics, the Thom–Sebastiani Theorem states: given the germ f : (\mathbb^, 0) \to (\mathbb, 0) defined as f(z_1, z_2) = f_1(z_1) + f_2(z_2) where f_i are germs of holomorphic functions with isolated singularities, the vanishing cycle complex of f is isomorphic to the tensor product of those of f_1, f_2. Moreover, the isomorphism respects the monodromy operators in the sense: T_ \otimes T_ = T_f. The theorem was introduced by Thom and Sebastiani in 1971. Observing that the analog fails in positive characteristic In mathematics, the characteristic of a ring , often denoted , is defined to be the smallest positive number of copies of the ring's multiplicative identity () that will sum to the additive identity (). If no such number exists, the ring is said ..., Deligne suggested that, in positive characteristic, a tensor product should be replaced by a (certain) local convolution product. References * Theorems in complex analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
