René Frédéric Thom was a French mathematician, who received the Fields Medal in 1958.
Hassler Whitney was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes, and geometric integration theory.
Stratification has several usages in mathematics.
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".
Sir Erik Christopher Zeeman FRS, was a British mathematician, known for his work in geometric topology and singularity theory.
Sir Oliver Simon D'Arcy Hart is a British-born American economist, currently the Lewis P. and Linda L. Geyser University Professor at Harvard University. Together with Bengt R. Holmström, he received the Nobel Memorial Prize in Economic Sciences in 2016.
Aix-Marseille University is a public research university located in the Provence region of southern France. It was founded in 1409 when Louis II of Anjou, Count of Provence, petitioned the Pisan Antipope Alexander V to establish the University of Provence, making it the fourth-oldest university in France. The institution came into its current form following a reunification of the University of Provence, the University of the Mediterranean and Paul Cézanne University. The reunification became effective on 1 January 2012, resulting in the creation of the largest university in the Francophone world, with about 80,000 students. AMU has the largest budget of any academic institution in the French-speaking world standing at €750 million. It is consistently ranked among the top 200 universities in the world and is ranked within the top 4 universities in France according to CWTS and USNWR, and 5th in the country according to ARWU.
Jean-Louis Verdier was a French mathematician who worked, under the guidance of his doctoral advisor Alexander Grothendieck, on derived categories and Verdier duality. He was a close collaborator of Grothendieck, notably contributing to SGA 4 his theory of hypercovers and anticipating the later development of étale homotopy by Michael Artin and Barry Mazur, following a suggestion he attributed to Pierre Cartier. Saul Lubkin's related theory of rigid hypercovers was later taken up by Eric Friedlander in his definition of the étale topological type.
In topology, a branch of mathematics, an abstract stratified space, or a Thom–Mather stratified space is a topological space X that has been decomposed into pieces called strata; these strata are manifolds and are required to fit together in a certain way. Thom–Mather stratified spaces provide a purely topological setting for the study of singularities analogous to the more differential-geometric theory of Whitney. They were introduced by René Thom, who showed that every Whitney stratified space was also a topologically stratified space, with the same strata. Another proof was given by John Mather in 1970, inspired by Thom's proof.
In differential topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney in 1965.
Jeremy John Gray is an English mathematician primarily interested in the history of mathematics.
In mathematics, especially in topology, a stratified space is a topological space that admits or is equipped with a stratification, a decomposition into subspaces, which are nice in some sense.
Paris-Sud University, also known as the University of Paris — XI, was a French research university distributed among several campuses in the southern suburbs of Paris, including Orsay, Cachan, Châtenay-Malabry, Sceaux, and Kremlin-Bicêtre campuses. In 2020, the university was replaced by the Paris-Saclay University.
Paris-Saclay University is a combined technological research institute and public research university based in Paris, France. Paris-Saclay was established in 2019 after the merger of four technical grandes écoles, as well as several technological institutes, engineering schools, and research facilities; giving it fifteen constituent colleges with over 48.000 students combined.
Peter Larkin Duren was an American mathematician. He specialized in mathematical analysis and was known for the monographs and textbooks he has written.
Tristan Rivière is a French mathematician, working on partial differential equations and the calculus of variations.
Tan Lei was a mathematician specialising in complex dynamics and functions of complex numbers. She is most well-known for her contributions to the study of the Mandelbrot set and Julia set.
Jean-Bernard Zuber is a French theoretical physicist.
In mathematics, especially in differential topology, Thom's first isotopy lemma states: given a smooth map between smooth manifolds and a closed Whitney stratified subset, if is proper and is a submersion for each stratum of , then is a locally trivial fibration. The lemma was originally introduced by René Thom who considered the case when . In that case, the lemma constructs an isotopy from the fiber to ; whence the name "isotopy lemma".
In mathematics, especially in differential topology, Thom's second isotopy lemma is a family version of Thom's first isotopy lemma; i.e., it states a family of maps between Whitney stratified spaces is locally trivial when it is a Thom mapping. Like the first isotopy lemma, the lemma was introduced by René Thom.
