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John Norman Mather
John Norman Mather (June 9, 1942 – January 28, 2017) was a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He was descended from Atherton Mather (1663–1734), a cousin of Cotton Mather. His early work dealt with the stability of smooth function, smooth mappings between smooth manifolds of dimensions ''n'' (for the source manifold ''N'') and ''p'' (for the target manifold ''P''). He determined the precise dimensions ''(n,p)'' for which smooth mappings are stable with respect to smooth equivalence by diffeomorphisms of the source and target (i.e., infinitely differentiable coordinate changes). Mather also proved the conjecture of the French Topology, topologist René Thom that under topological equivalence smooth mappings are generically stable: the subset of the space of smooth mappings between two smooth manifolds consisting of the topologically stable mappings is a dense subset in the smooth Whitney topology. His not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that ... [...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] |
Painlevé Conjecture
In physics, the Painlevé conjecture is a theorem about singularities among the solutions to the ''n''-body problem: there are noncollision singularities for ''n'' ≥ 4. The theorem was proven for ''n'' ≥ 5 in 1988 by Jeff Xia and for n=4 in 2014 by Jinxin Xue. Background and statement Solutions (\mathbf,\mathbf) of the ''n''-body problem \dot = M^\mathbf,\; \dot = \nabla U(\mathbf) (where M are the masses and U denotes the gravitational potential) are said to have a singularity if there is a sequence of times t_n converging to a finite t^* where \nabla U\left(\mathbf\left(t_n\right)\right) \rightarrow \infty. That is, the forces and accelerations become infinite at some finite point in time. A ''collision singularity'' occurs if \mathbf(t) tends to a definite limit when t \rightarrow t^*, t [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard McGehee
Richard Paul McGehee (born 20 September 1943, in San Diego) is an American mathematician, who works on dynamical systems with special emphasis on celestial mechanics. McGehee received from Caltech in 1964 his bachelor's degree and from University of Wisconsin–Madison in 1965 his master's degree and in 1969 his Ph.D. under Charles C. Conley with thesis ''Homoclinic orbits in the restricted three body problem''. As a postdoc he was at the Courant Institute of Mathematical Sciences of New York University. In 1970 he became an assistant professor and in 1979 a full professor at the University of Minnesota in Minneapolis, where he was from 1994 to 1998 the director of the Center for the Computation and Visualization of Geometric Structures. In the 1970s he introduced a coordinate transformation (now known as the McGehee transformation) which he used to regularize singularities arising in the Newtonian three-body problem. In 1975 he, with John N. Mather, proved that for the Newtoni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
