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G2 Manifold
In differential geometry, a ''G''2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in ''G''2. The group G_2 is one of the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper subgroup of special orthogonal group SO(7) that preserves a spinor in the eight-dimensional spinor representation or lastly as the subgroup of the general linear group GL(7) which preserves the non-degenerate 3-form \phi, the associative form. The Hodge dual, \psi=*\phi is then a parallel 4-form, the coassociative form. These forms are calibrations in the sense of Reese Harvey and H. Blaine Lawson, and thus define special classes of 3- and 4-dimensional submanifolds. Properties All G_2-manifold are 7-dimensional, Ricci-flat, orientable spin manifolds. In addition, any compact manifold with holonomy equal to G_2 has finite fundamental group, non-zero first Pontryagin class, and non-zero third ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
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 st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Manifold
In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory. They form the foundation for spin geometry. Overview In geometry and in field theory, mathematicians ask whether or not a given oriented Riemannian manifold (''M'',''g'') admits spinors. One method for dealing with this problem is to require that ''M'' has a spin structure. This is not always possible since there is potentially a topological obstruction to the existence of spin structures. Spin structures will exist if and only if the second Stiefel–Whitney class ''w''2(''M'') ∈ H2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sema Salur
Sema Salur is a Turkish-American mathematician, currently serving as a Professor of Mathematics at the University of Rochester. She was awarded the Ruth I. Michler Memorial Prize for 2014–2015, a prize intended to give a recently promoted associate professor a year-long fellowship at Cornell University; and has been the recipient of a National Science Foundation Research Award beginning in 2017. She specialises in the "geometry and topology of the moduli spaces of calibrated submanifolds inside Calabi–Yau, G2 and Spin(7) manifolds", which are important to certain aspects of string theory and M-theory in physics, theories that attempt to unite gravity, electromagnetism, and the strong and weak nuclear forces into one coherent Theory of Everything. Education * 1993: B.S. in Mathematics, Boğaziçi University Boğaziçi University ( tr, Boğaziçi Üniversitesi), also known as Bosphorus University, is a major research university in Istanbul, Turkey. Its main campus is loc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dominic Joyce
Dominic David Joyce Fellow of the Royal Society, FRS (born 8 April 1968) is a British mathematician, currently a professor at the University of Oxford and a fellow of Lincoln College, Oxford, Lincoln College since 1995. His undergraduate and doctoral studies were at Merton College, Oxford. He undertook a DPhil in geometry under the supervision of Simon Donaldson, completed in 1992. After this he held short-term research posts at Christ Church, Oxford, as well as Princeton University and the University of California, Berkeley in the United States. Joyce is known for his construction of the first known explicit examples of compact Joyce manifolds (i.e., manifolds with G2 (mathematics), G2 holonomy). He has received the London Mathematical Society Junior Whitehead Prize and the European Mathematical Society Young Mathematicians Prize. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. Selected publications * * * with Yinan Song:arxiv.or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duke Mathematical Journal
''Duke Mathematical Journal'' is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz. Leonard Carlitz served on the editorial board for 35 years, from 1938 to 1973. The current managing editor is Richard Hain (Duke University). Impact According to the journal homepage, the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 2.194, ranking it in the top ten mathematics journals in the world. References External links * Mathematics journals Mathematical Journal Publications established in 1935 Multilingual journals English-language journals French- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Bryant (mathematician)
Robert Leamon Bryant (born August 30, 1953, Kipling) is an American mathematician. He works at Duke University and specializes in differential geometry. Education and career Bryant grew up in a farming family in Harnett County and was a first-generation college student. He obtained a bachelor's degree at North Caroline State University at Raleigh in 1974 and a PhD at University of North Carolina at Chapel Hill in 1979. His thesis was entitled "''Some Aspects of the Local and Global Theory of Pfaffian Systems''" and was written under the supervision of Robert Gardner. He worked at Rice University for seven years, as assistant professor (1979–1981), associate professor (1981–1982) and full professor (1982–1986). He then moved to Duke University, where he worked for twenty years as J. M. Kreps Professor. Between 2007 and 2013 he worked as full professor at University of California, Berkeley, where he served as the director of the Mathematical Sciences Research Institut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edmond Bonan
Edmond Bonan (born 27 January 1937 in Haifa, Mandatory Palestine) is a French mathematician, known particularly for his work on special holonomy. Biography After completing his undergraduate studies at the École polytechnique, Bonan went on to write his 1967 University of Paris doctoral dissertation in Differential geometry under the supervision of André Lichnerowicz. From 1968 to 1997, he held the post of lecturer and then professor at the University of Picardie Jules Verne in Amiens, where he currently holds the title of professor emeritus. Early in his career, from 1969 to 1981, he also lectured at the École Polytechnique. See also * G2 manifold * G2 structure * Spin(7) manifold *Holonomy * Quaternion-Kähler manifold * Calibrated geometry * Hypercomplex manifold *Hyperkähler manifold *Uniform polyhedron In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Harris Simons
James Harris Simons (; born 25 April 1938) is an American mathematician, billionaire hedge fund manager, and philanthropist. He is the founder of Renaissance Technologies, a quantitative hedge fund based in East Setauket, New York. He and his fund are known to be quantitative investors, using mathematical models and algorithms to make investment gains from market inefficiencies. Due to the long-term aggregate investment returns of Renaissance and its Medallion Fund, Simons is described as the "greatest investor on Wall Street," and more specifically "the most successful hedge fund manager of all time." As reported by ''Bloomberg Billionaires Index'', Simons' net worth is estimated to be $25.2 billion, making him the 66th-richest person in the world. Simons is known for his studies on pattern recognition. He developed the Chern–Simons form (with Shiing-Shen Chern), and contributed to the development of string theory by providing a theoretical framework to combine geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marcel Berger
Marcel Berger (14 April 1927 – 15 October 2016) was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France. Formerly residing in Le Castera in Lasseube, Berger was instrumental in Mikhail Gromov's accepting positions both at the University of Paris and at the IHÉS. Awards and honors *1956 Prix Peccot, Collège de France *1962 Prix Maurice Audin *1969 Prix Carrière, Académie des Sciences *1978 Prix Leconte, Académie des Sciences *1979 Prix Gaston Julia *1979–1980 President of the French Mathematical Society. *1991 Lester R. Ford Award Selected publications * Berger, M.Geometry revealed Springer, 2010. * Berger, M.: What is... a Systole? Notices of the AMS 55 (2008), no. 3, 374–376online text* * * *Berger, Marcel; Gauduchon, Paul; Mazet, Edmond: Le spectre d'une variété riemannienne. (French) Lecture Notes in Mathematics, Vol. 194 Springer-Verlag, Berlin-New York 1971. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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