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Grigory Perelman Biography

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Grigory Perelman Biography Grigory Perelman Life & Education Soul conjecture Poincare conjecture Topology Mathematics Genealogy Park Hong-gil Early life and education Born in June 13, 1966 (Leningrad, Soviet Union) lived in Saint Petersburg, Russia Blood Russian-Jewish parents Education Leningrad Secondary School #239 Leningrad State University Doctoral advisor Aleksandr Aleksandrov Yuri Burago Prize International Mathematical Olympiad Gold Medal After his PhD in 1990 : work at the Leningrad Department of Steklov Institute of Mathematics of USSR Academy of Sciences The late 1980s and early 1990s : research positions at several universities in the United States 1991 : the Young Mathematician Prize of the St. Petersburg Mathematical Society 1992 : invited to spend a semester each at the Courant Institute in New York University and Stony Brook University 1993 : accepted a two-year Miller Research Fellowship at the University of California, Berkeley . 1994 : proved the soul conjecture The summer of 1995 : returned to the Steklov Institute in Saint Petersburg for a research-only position. 2003 : proved Thurston's geometrization conjecture. 2006 : confirmed the above August, 2006 : offered the Fields Medal but he declined the award December 22, 2006 : the scientific journal Science recognized Perelman's proof of the Poincaré conjecture March 18, 2010 : the first Clay Millennium Prize July 1, 2010 : rejected the prize of one million dollars Soul conjecture Cheeger and Gromoll's soul conjecture states: Suppose (M, g) is complete, connected and non-compact with sectional curvature K ≥ 0, and there exists a point in M where the sectional curvature (in all sectional directions) is strictly positive. Then the soul of M is a point; equivalently M is diffeomorphic to Rn. Perelman proved the conjecture by establishing that in the general case K ≥ 0, Sharafutdinov's retraction P : M → S is a submersion. Poincaré conjecture In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states: Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. Neither of the two colored loops on this torus can be continuously tightened to a point. A torus is not homeomorphic to a sphere. Topology(位相數學) study of shapes and spaces. Leonhard Euler impossible to find a route through the town of Königsberg (now Kaliningrad) that would cross each of its seven bridges exactly once. connectivity properties This problem led to the branch of mathematics known as graph theory. To a topologist, a bun and a sphere are the same, as are an oval and a circle. However, a sphere and a doughnut are not homeomorphic to one another: Baseball and doughnut are not homeomorphic . William P. Thurston’s 8 1 Dimension Manifolds 2 Dimension Thurston’s Geometrization 3 Dimension conjecture 4 Dimension 5 Dimension Geometrization and Poincare conjecture November, 2002 : eprints to the arXiv, in which he claimed to have outlined a proof of the geometrization conjecture, of which the Poincaré conjecture is a particular case. Perelman modified Richard S. Hamilton's program for a proof of the conjecture. The central idea is the notion of the Ricci flow. Ricci flow is an intrinsic geometric flow in differential geometry. It is a process that deforms the metric of a Riemannian Several stages of manifold in a way formally analogous to the diffusion of heat, Ricci flow on a 2D smoothing out irregularities in the metric. manifold. Mathematics Genealogy Leonhard Euler(1707~1783) Joseph Louis Lagrange(1736~1813) Marquis de Laplace(1749~1827) Joseph Fourier(1768~1830) Siméon Denis Poisson(1781~1840) Johann Peter Gustav Lejeune Dirichlet (1805~1859) Leopold Kronecker(1823~1891) Rudolf Otto Sigismund Lipschitz (1832–1903) Felix Christian Klein(1849~1925) Von Lindemann(1852~ 1939) David Hilbert(1862~1943) .
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