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William Francis Pohl
William Francis Pohl (16 September 1937 – 9 December 1988) was an American mathematician, specializing in differential geometry and known for the Clifton–Pohl torus. Pohl received from the University of Chicago his B.A in 1957 and his M.A.1958. He completed his Ph.D. at Berkeley in 1961 under the direction of Shiing-Shen Chern with dissertation ''Differential Geometry of Higher Order''. His dissertation was published in 1962 in the journal ''Topology'' and has received over 120 citations in the mathematical literature. He was a member of the mathematics faculty at the University of Minnesota from September 1964 until his untimely death. Pohl engaged in a famous controversy arguing against Francis Crick Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was an English molecular biologist, biophysicist, and neuroscientist. He, James Watson, Rosalind Franklin, and Maurice Wilkins played crucial roles in deciphering the helical struc ... but, in view of additiona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifton–Pohl Torus
In geometry, the Clifton–Pohl torus is an example of a compact Lorentzian manifold that is not geodesically complete. While every compact Riemannian manifold is also geodesically complete (by the Hopf–Rinow theorem), this space shows that the same implication does not generalize to pseudo-Riemannian manifolds.. It is named after Yeaton H. Clifton and William F. Pohl, who described it in 1962 but did not publish their result.. Definition Consider the manifold \mathrm = \mathbb^2 \setminus \ with the metric :g= \frac Any homothety is an isometry of M, in particular including the map: :\lambda(x,y)=2\cdot(x, y) Let \Gamma be the subgroup of the isometry group generated by \lambda. Then \Gamma has a proper, discontinuous action on M. Hence the quotient T = M/\Gamma, which is topologically the torus, is a Lorentz surface that is called the Clifton–Pohl torus. Sometimes, by extension, a surface is called a Clifton–Pohl torus if it is a finite covering of the quotient of M by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the best universities in the world and it is among the most selective in the United States. The university is composed of an undergraduate college and five graduate research divisions, which contain all of the university's graduate programs and interdisciplinary committees. Chicago has eight professional schools: the Law School, the Booth School of Business, the Pritzker School of Medicine, the Crown Family School of Social Work, Policy, and Practice, the Harris School of Public Policy, the Divinity School, the Graham School of Continuing Liberal and Professional Studies, and the Pritzker School of Molecular Engineering. The university has additional campuses and centers in London, Paris, Beijing, Delhi, and Hong Kong, as well as in downtown ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shiing-Shen Chern
Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize. In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics". Chern worked at the Institute for Advanced Study (1943–45), spent about a decade at the University of Chicago (1949-1960), and then moved to University of California, Berkeley, where he co-founded the Mathematical Sciences Research Institute in 1982 and was the institute's found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology (journal)
''Topology'' was a peer-reviewed mathematical journal covering topology and geometry. It was established in 1962 and was published by Elsevier. The last issue of ''Topology'' appeared in 2009. Pricing dispute On 10 August 2006, after months of unsuccessful negotiations with Elsevier about the price policy of library subscriptions, the entire editorial board of the journal handed in their resignation, effective 31 December 2006. Subsequently, two more issues appeared in 2007 with papers that had been accepted before the resignation of the editors. In early January the former editors instructed Elsevier to remove their names from the website of the journal, but Elsevier refused to comply, justifying their decision by saying that the editorial board should remain on the journal until all of the papers accepted during its tenure had been published. In 2007 the former editors of ''Topology'' announced the launch of the ''Journal of Topology'', published by Oxford University Press ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Minnesota
The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint Paul, Minnesota, United States. The Twin Cities campus comprises locations in Minneapolis and Falcon Heights, Minnesota, Falcon Heights, a suburb of St. Paul, approximately apart. The Twin Cities campus is the oldest and largest in the University of Minnesota system and has the List of United States university campuses by enrollment, ninth-largest main campus student body in the United States, with 52,376 students at the start of the 2021–22 academic year. It is the Flagship#Colleges and universities in the United States, flagship institution of the University of Minnesota System, and is organized into 19 colleges, schools, and other major academic units. The Minnesota Territorial Legislature drafted a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Crick
Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was an English molecular biologist, biophysicist, and neuroscientist. He, James Watson, Rosalind Franklin, and Maurice Wilkins played crucial roles in deciphering the helical structure of the DNA molecule. Crick and Watson's paper in ''Nature'' in 1953 laid the groundwork for understanding DNA structure and functions. Together with Maurice Wilkins, they were jointly awarded the 1962 Nobel Prize in Physiology or Medicine "for their discoveries concerning the molecular structure of nucleic acids and its significance for information transfer in living material". Crick was an important theoretical molecular biologist and played a crucial role in research related to revealing the helical structure of DNA. He is widely known for the use of the term " central dogma" to summarise the idea that once information is transferred from nucleic acids (DNA or RNA) to proteins, it cannot flow back to nucleic acids. In other words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Church Music Association Of America
The Church Music Association of America (CMAA) is a nonprofit 501(c)(3) association of Catholic church musicians and others who have a special interest in music and liturgy, active in advancing Gregorian chant, Renaissance polyphony, and other forms of sacred music for liturgical use. Founded in 1964, it is affiliated with the ''Consociatio Internationalis Musicae Sacrae'' (Roma), an advisory organization on sacred music founded by Pope Paul VI. The CMAA provides support for those interested in participating in a revival of Gregorian chant and sacred polyphony in Catholic liturgy. It sponsors scholarship and composition in the tradition of sacred music. It hosts the most-attended colloquium on sacred music in the English-speaking world, held annually since 1990. The CMAA embraces the statement made by Pope Benedict XVI on June 25, 2006: "An authentic updating of sacred music can take place only in the lineage of the great tradition of the past, of Gregorian chant and sacred pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Banchoff
Thomas Francis Banchoff (born April 7, 1938) is an American mathematician specializing in geometry. He is a professor at Brown University, where he has taught since 1967. He is known for his research in differential geometry in three and four dimensions, for his efforts to develop methods of computer graphics in the early 1990s, and most recently for his pioneering work in methods of undergraduate education utilizing online resources. Banchoff attended the University of Notre Dame and received his Ph.D. from UC Berkeley in 1964, where he was a student of Shiing-Shen Chern. Before going to Brown he taught at Harvard University and the University of Amsterdam. In 2012 he became a fellow of the American Mathematical Society. He was a president of the Mathematical Association of America. Selected works * with Stephen Lovett: Differential Geometry of Curves and Surfaces (2nd edition), A. K. Peters 2010 * with Terence Gaffney, Clint McCrory: Cusps of Gauss Mappings, Pitman 1982 * with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolaas Kuiper
Nicolaas Hendrik Kuiper (; 28 June 1920 – 12 December 1994) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem. Kuiper studied at University of Leiden in 1937-41, and worked as a secondary school teacher of mathematics in Dordrecht in 1942-47. He completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude. In 1947 he came to the United States at the invitation of Oscar Veblen, where he stayed at the Institute for Advanced Study for one year as Veblen's assistant, and the second year as member of the IAS, meeting Shiing-Shen Chern, and he also went to the University of Michigan at Ann Arbor. In February to June 1954, he went for a second time to Ann Arbor where he met Raoul Bott and his student Stephen Smale. In 1950 he was appointed professor of mathematics (and statistics) at the Agricultural University of Wageningen. In 1957, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometers
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
