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John Lott (mathematician)
John William Lott (born January 12, 1959) is a professor of Mathematics at the University of California, Berkeley. He is known for contributions to differential geometry. Academic history Lott received his B.S. from the Massachusetts Institute of Technology in 1978 and M.A. degrees in mathematics and physics from University of California, Berkeley. In 1983, he received a Ph.D. in mathematics under the supervision of Isadore Singer. After postdoctoral positions at Harvard University and the Institut des Hautes Études Scientifiques, he joined the faculty at the University of Michigan. In 2009, he moved to University of California, Berkeley. Among his awards and honors: * Sloan Research Fellowship (1989-1991) * Alexander von Humboldt Fellowship (1991-1992) * U.S. National Academy of Sciences Award for Scientific Reviewing (with Bruce Kleiner) Mathematical contributions A 1985 article of Dominique Bakry and Michel Émery introduced a generalized Ricci curvature, in which one adds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rolla, Missouri
Rolla () is a city in, and the county seat of, Phelps County, Missouri, United States. The population in the 2020 United States Census was 19,943. Rolla is located approximately midway between St. Louis and Springfield along I-44. The Rolla, Mo Micropolitan Statistical area consists of Phelps County, Missouri. It is the home of the Missouri University of Science and Technology, well known, both nationally and internationally, for its many engineering departments and computer science department. The headquarters of the Mark Twain National Forest is located in Rolla. The city is also within the Ozark Highlands American Viticultural Area, with vineyards established first by Italian immigrants to the area. History The first European-American settlers in Phelps County arrived in the early 19th century, working as farmers and iron workers along the local rivers, such as the Meramec, the Gasconade, and the Little Piney. In 1842, John Webber built the first house in what beca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isometry Group
In mathematics, the isometry group of a metric space is the set of all bijective isometries (i.e. bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation. Its identity element is the identity function. The elements of the isometry group are sometimes called motions of the space. Every isometry group of a metric space is a subgroup of isometries. It represents in most cases a possible set of symmetries of objects/figures in the space, or functions defined on the space. See symmetry group. A discrete isometry group is an isometry group such that for every point of the space the set of images of the point under the isometries is a discrete set. In pseudo-Euclidean space the metric is replaced with an isotropic quadratic form; transformations preserving this form are sometimes called "isometries", and the collection of them is then said to form an isometry group of the pseudo-Euclidean space. Examples * The isometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl-Theodor Sturm
Karl-Theodor "Theo" Sturm (born 7.November 1960) is a German mathematician working in stochastic analysis. Life and work After obtaining his Abitur from the Platen-Gymnasium Ansbach in 1980, Sturm began to study Mathematics and Physics at the University of Erlangen-Nuremberg where he graduated in 1986 with the Diploma in Mathematics and the State Examination in Mathematics and Physics. In 1989, he obtained his PhD (with a thesis on „Perturbation of Hunt processes by signed additive functionals“) under the supervision of Heinz Bauer and in 1993 he received his habilitation. Visiting and research positions led him to the universities of Stanford, Zurich, and Bonn as well as to the MPI Leipzig. In 1994, he was awarded a Heisenberg fellowship of the DFG. Since 1997, he is professor of mathematics at the University of Bonn. From 2002 to 2012, he was vice spokesman and member of the executive board of the Collaborative Research Center 611 "Singular Phenomena in Mathematical Model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gang Tian
Tian Gang (; born November 24, 1958) 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. As of 2020, he is the Vice Chairman of the China Democratic League and the President of the Chinese Mathematical Society. From 2017 to 2019 he served as the Vice President of Peking University. Biography Tian was born in Nanjing, Jiangsu, China. He qualified in the second college entrance exam after Cultural Revolution in 1978. He graduated from Nanjing University in 1982, and received a master's degree from Peking University in 1984. In 1988, he received a Ph.D. in mathematics from Harvard University, under the supervision of Shing-Tung Yau. In 1998, he was appointed as a Cheung Kong Scholar professor at Peking University. Later his appointment was changed to Cheung Kong Schol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Morgan (mathematician)
John Willard Morgan (born March 21, 1946) 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. Life Morgan received his B.A. in 1968 and Ph.D. in 1969, both from Rice University. His Ph.D. thesis, entitled ''Stable tangential homotopy equivalences'', was written under the supervision of Morton L. Curtis. He was an instructor at Princeton University from 1969 to 1972, and an assistant professor at MIT from 1972 to 1974. He has been on the faculty at Columbia University since 1974, serving as the Chair of the Department of Mathematics from 1989 to 1991 and becoming Professor Emeritus in 2010. Morgan is a member of the Simons Center for Geometry and Physics at Stony Brook University and served as its founding director from 2009 to 2016. From 1974 to 1976, Morgan was a Sloan Research Fellow. In 2008, he was awarde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Xi-Ping Zhu
Zhu Xiping (born 1962 in Shixing, Guangdong) is a Chinese mathematician. He is a professor of Mathematics at Sun Yat-sen University, China. Poincaré conjecture In 2002 and 2003, Grigori Perelman posted three preprints to the arXiv claiming a resolution of the renowned Poincaré conjecture, 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 S. Hamilton, Richard Hamilton, was published in the June 2006 issue of the ''Asian Journal of Mathematics''. Other notable expositions were released around the same time, one by John Morgan (mathematician), John Morgan of Columbia University and Gang Tian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huai-Dong Cao
Huai-Dong Cao (born 8 November 1959, in Jiangsu) 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. Academic history Cao received his B.A. from Tsinghua University in 1981 and his Ph.D. from Princeton University in 1986 under the supervision of Shing-Tung Yau. Cao is a former Associate Director, Institute for Pure and Applied Mathematics (IPAM) at UCLA. He has held visiting Professorships at MIT, Harvard University, Isaac Newton Institute, Max-Planck Institute, IHES, ETH Zurich, and University of Pisa. He has been the managing editor of the ''Journal of Differential Geometry'' since 2003. His awards and honors include: * Sloan Research Fellowship (1991-1993) * Guggenheim Fellowship (2004) * Outstanding Overseas Young Researcher Award awarded by the National Natural Science Foundation of China (2005) Mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Academy Of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the National Academy of Medicine (NAM). As a national academy, new members of the organization are elected annually by current members, based on their distinguished and continuing achievements in original research. Election to the National Academy is one of the highest honors in the scientific field. Members of the National Academy of Sciences serve '' pro bono'' as "advisers to the nation" on science, engineering, and medicine. The group holds a congressional charter under Title 36 of the United States Code. Founded in 1863 as a result of an Act of Congress that was approved by Abraham Lincoln, the NAS is charged with "providing independent, objective advice to the nation on matters related to science and technology. ... to provide scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ricci Flow
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. The Ricci flow, so named for the presence of the Ricci tensor in its definition, was introduced by Richard Hamilton, who used it through the 1980s to prove striking new results in Riemannian geometry. Later extensions of Hamilton's methods by various authors resulted in new applications to geometry, including the resolution of the differentiable sphere conjecture by Simon Brendle and Richard Schoen. Following Shing-Tung Yau's suggestion that the singularities of solutions of the Ricci flow could identify the topo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard S
Richard is a male given name. It originates, via Old French, from Old Frankish and is a compound of the words descending from Proto-Germanic ''*rīk-'' 'ruler, leader, king' and ''*hardu-'' 'strong, brave, hardy', and it therefore means 'strong in rule'. Nicknames include "Richie", "Dick", "Dickon", " Dickie", "Rich", "Rick", "Rico", "Ricky", and more. Richard is a common English, German and French male name. It's also used in many more languages, particularly Germanic, such as Norwegian, Danish, Swedish, Icelandic, and Dutch, as well as other languages including Irish, Scottish, Welsh and Finnish. Richard is cognate with variants of the name in other European languages, such as the Swedish "Rickard", the Catalan "Ricard" and the Italian "Riccardo", among others (see comprehensive variant list below). People named Richard Multiple people with the same name * Richard Andersen (other) * Richard Anderson (other) * Richard Cartwright (other) * Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometrization Conjecture
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 ( Euclidean, spherical, or hyperbolic). 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 , and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture. Thurston announced a proof in the 1980s and since then sever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Thurston
William Paul Thurston (October 30, 1946August 21, 2012) 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. Thurston was a professor of mathematics at Princeton University, University of California, Davis, and Cornell University. He was also a director of the Mathematical Sciences Research Institute. Early life and education William Thurston was born in Washington, D.C. to Margaret Thurston (), a seamstress, and Paul Thurston, an aeronautical engineer. William Thurston suffered from congenital strabismus as a child, causing issues with depth perception. His mother worked with him as a toddler to reconstruct three-dimensional images from two-dimensional ones. He received his bachelor's degree from New College in 1967 as part of its inaugural class. For his undergraduate thesis, he developed an intuitionist foundation for topology. Following this, he r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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