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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 founder of catastrophe theory (later developed by Erik Christopher Zeeman). Life and career René Thom grow up in a modest family in Montbéliard, Doubs and obtained a Baccalauréat in 1940. After 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''), was w ... [...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 |
Thom Conjecture
In mathematics, a smooth algebraic curve C in the complex projective plane, of degree d, has Genus_(mathematics)#Topology, genus given by the genus–degree formula :g = (d-1)(d-2)/2. The Thom conjecture, named after French mathematician René Thom, states that if \Sigma is any smoothly embedded connected curve representing the same class in homology (mathematics), homology as C, then the genus g of \Sigma satisfies the inequality :g \geq (d-1)(d-2)/2. In particular, ''C'' is known as a ''genus minimizing representative'' of its homology class. It was first proved by Peter B. Kronheimer, Peter Kronheimer and Tomasz Mrowka in October 1994, using the then-new Seiberg–Witten invariants. Assuming that \Sigma has nonnegative self intersection number this was generalized to Kähler manifolds (an example being the complex projective plane) by John Morgan (mathematician), John Morgan, Zoltán Szabó (mathematician), Zoltán Szabó, and Clifford Taubes, also using the Seiberg–Wit ... [...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. These ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topologist
In mathematics, topology (from the Greek words , and ) is 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 a topological space, 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. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedne ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann Lecture Prize
The John von Neumann Prize (until 2019 named John von Neumann Lecture Prize) was established in 1959 with funds from IBM and other industry corporations, and is awarded for "outstanding and distinguished contributions to the field of applied mathematical sciences and for the effective communication of these ideas to the community". It is considered the highest honor bestowed by the Society for Industrial and Applied Mathematics (SIAM). The recipient receives a monetary award and presents a survey lecture at the SIAM Annual Meeting. Selection process Anybody is able to nominate a mathematician for the prize. Nominations are reviewed by a selection committee, consisting of members of SIAM who serve two-year appointments. The committee selects one recipient for the prize nine months before the SIAM Annual Meeting and forwards their nomination to SIAM's Executive Committee and Vice President for Programs. Past lecturers *1960: Lars Valerian Ahlfors *1961: Mark Kac *1962: Jean ... [...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 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 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 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 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 in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has bee ... [...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 number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive id ..., 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] |
Thom–Porteous Formula
In mathematics, the Porteous formula, or Thom–Porteous formula, or Giambelli–Thom–Porteous formula, is an expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes. Giambelli's formula In mathematics, Giambelli's formula, named after Giovanni Giambelli, expresses Schubert classes in terms of special Schubert classes, or Schur functions in terms of complete symmetric functions. It states :\displaystyle \sigma_\lambda= \det(\si ... is roughly the special case when the vector bundles are sums of line bundles over projective space. pointed out that the fundamental class must be a polynomial in the Chern classes and found this polynomial in a few special cases, and found the polynomial in general. proved a more general version, and generalized it further. Statement Given a morphism of vector bundles ''E'', ''F'' of ranks ''m'' and ''n'' over a smooth variety, its ''k''-th degeneracy lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thom's First Isotopy Lemma
In mathematics, especially in differential topology, Thom's first isotopy lemma states: given a smooth map f : M \to N between smooth manifolds and S \subset M a closed Whitney stratified subset, if f, _S is proper and f, _A is a submersion for each stratum A of S, then f, _S is a locally trivial fibration. The lemma was originally introduced by René Thom who considered the case when N = \mathbb. In that case, the lemma constructs an isotopy from the fiber f^(a) to f^(b); whence the name "isotopy lemma". The local trivializations that the lemma provide preserve the strata. However, they are generally not smooth (not even C^1). On the other hand, it is possible that local trivializations are semialgebraic if the input data is semialgebraic. The lemma is also valid for a more general stratified space such as a stratified space in the sense of Mather but still with the Whitney conditions (or some other conditions). The lemma is also valid for the stratification that satisfies Bekk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
