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| Zhu Xiping | |||||||||
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| Chinese | 朱熹平 | ||||||||
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Zhu Xiping (born 1962 in Shixing,Guangdong) is a Chinese mathematician. He is a professor of Mathematics at Sun Yat-sen University,China.
In 2002 and 2003,Grigori Perelman posted three preprints to the arXiv claiming a resolution of the renowned Poincaréconjecture,along with the more general geometrization conjecture. His work contained a number of notable new results on the Ricci flow,although many proofs were only sketched and a number of details were unaddressed. Zhu collaborated with Huai-Dong Cao of Lehigh University in filling in the details of Perelman's work,along with reworking various elements. Their work,containing expositions of Perelman's work along with the foundational work of Richard Hamilton,was published in the June 2006 issue of the Asian Journal of Mathematics . [1] Other notable expositions were released around the same time,one by John Morgan of Columbia University and Gang Tian of Princeton University,and the other by Bruce Kleiner of Yale University and John Lott of University of Michigan.
Cao and Zhu later posted a version with revised wording to the arxiv,following criticism alleging that their original version claimed too much credit for themselves. [2] They also published an erratum,as it had been found that one of the pages of their work was essentially identical to a page from a publicly available draft of Kleiner and Lott from 2003. [3] They explained that they had taken down some notes from Kleiner and Lott's paper. When writing their exposition,they had failed to realize these particular notes' original source.
In December 2004,Zhu won the Morningside Medal of Mathematics at the Third International Congress of Chinese Mathematicians (ICCM),a triennial congress hosted by institutions in Mainland China,Taiwan,and Hong Kong on a rotating basis. According to ICCM, [4] "Awardees (of the Morningside Medal) are selected by a panel of international renowned mathematicians with the aim to encourage outstanding mathematicians of Chinese descent in their pursuit of mathematical truth."
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's Last Theorem, have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.
In the mathematical field of geometric topology, 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.
William Paul Thurston was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.
In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected Riemann surface can be given one of three geometries . In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by William Thurston (1982), and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture.
Grigori Yakovlevich Perelman is a Russian mathematician who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman abruptly quit his research job at the Steklov Institute of Mathematics, and in 2006 stated that he had quit professional mathematics, due to feeling disappointed over the ethical standards in the field. He lives in seclusion in Saint Petersburg, and has not accepted offers for interviews since 2006.
In the mathematical field of Riemannian geometry, the scalar curvature is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls. In the context of the differential geometry of surfaces, the scalar curvature is twice the Gaussian curvature, and completely characterizes the curvature of a surface. In higher dimensions, however, the scalar curvature only represents one particular part of the Riemann curvature tensor.
In the mathematical fields of differential geometry and geometric analysis, the Ricci flow, sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be analogous to the diffusion of heat and the heat equation, due to formal similarities in the mathematical structure of the equation. However, it is nonlinear and exhibits many phenomena not present in the study of the heat equation.
Shing-Tung Yau is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau retired from Harvard to become a professor of mathematics at Tsinghua University.
Richard Streit Hamilton is an American mathematician who serves as the Davies Professor of Mathematics at Columbia University. He is known for contributions to geometric analysis and partial differential equations. Hamilton is best known for foundational contributions to the theory of the Ricci flow and the development of a corresponding program of techniques and ideas for resolving the Poincaré conjecture and geometrization conjecture in the field of geometric topology. Grigori Perelman built upon Hamilton's results to prove the conjectures, and was awarded a Millennium Prize for his work. However, Perelman declined the award, regarding Hamilton's contribution as being equal to his own.
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.
In topology, an area of mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is virtually Haken. That is, it has a finite cover that is a Haken manifold.
Tian Gang is a Chinese mathematician. He is a professor of mathematics at Peking University and Higgins Professor Emeritus at Princeton University. He is known for contributions to the mathematical fields of Kähler geometry, Gromov-Witten theory, and geometric analysis.
"Manifold Destiny" is an article in The New Yorker written by Sylvia Nasar and David Gruber and published in the 28 August 2006 issue of the magazine. It claims to give a detailed account of some of the circumstances surrounding the proof of the Poincaré conjecture, one of the most important accomplishments of 20th and 21st century mathematics, and traces the attempts by three teams of mathematicians to verify the proof given by Grigori Perelman.
John Willard Morgan is an American mathematician known for his contributions to topology and geometry. He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University.
Bruce Alan Kleiner is an American mathematician, working in differential geometry and topology and geometric group theory.
Huai-Dong Cao is a Chinese–American mathematician. He is the A. Everett Pitcher Professor of Mathematics at Lehigh University. He is known for his research contributions to the Ricci flow, a topic in the field of geometric analysis.
In the mathematical area of topology, the generalized Poincaré conjecture is a statement that a manifold which is a homotopy sphere is a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise linear (PL), or differentiable (Diff). Then the statement is
In geometry, Thurston's geometrization theorem or hyperbolization theorem implies that closed atoroidal Haken manifolds are hyperbolic, and in particular satisfy the Thurston conjecture.
John William Lott is a professor of Mathematics at the University of California, Berkeley. He is known for contributions to differential geometry.
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$1 million prize for the first correct solution to each problem.
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