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Shlomo Sternberg
Shlomo Zvi Sternberg (born 1936), is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. Education and career Sternberg earned his PhD in 1955 from Johns Hopkins University, with a thesis entitled "''Some Problems in Discrete Nonlinear Transformations in One and Two Dimensions''", supervised by Aurel Wintner. After postdoctoral work at New York University (1956–1957) and an instructorship at University of Chicago (1957–1959), Sternberg joined the Mathematics Department at Harvard University in 1959, where he was George Putnam Professor of Pure and Applied Mathematics until 2017. Since 2017, he is Emeritus Professor at the Harvard Mathematics Department. Among other honors, Sternberg was awarded a List of Guggenheim Fellowships awarded in 1974, Guggenheim fellowship in 1974 and a honorary doctorate by the University of Mannheim in 1991. He delivered the American Mathematical Society, AMS in 1990 and the Hebrew University ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebrew University
The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weizmann in July 1918, the public university officially opened in April 1925. It is the second-oldest Israeli university, having been founded 30 years before the establishment of the State of Israel but six years after the older Technion university. The HUJI has three campuses in Jerusalem and one in Rehovot. The world's largest library for Jewish studies—the National Library of Israel—is located on its Edmond J. Safra campus in the Givat Ram neighbourhood of Jerusalem. The university has five affiliated teaching hospitals (including the Hadassah Medical Center), seven faculties, more than 100 research centers, and 315 academic departments. , one-third of all the doctoral candidates in Israel were studying at the HUJI. Among its first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Quillen
Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic ''K''-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. Education and career Quillen was born in Orange, New Jersey, and attended Newark Academy. He entered Harvard University, where he earned both his AB, in 1961, and his PhD in 1964; the latter completed under the supervision of Raoul Bott, with a thesis in partial differential equations. He was a Putnam Fellow in 1959. Quillen obtained a position at the Massachusetts Institute of Technology after completing his doctorate. He also spent a number of years at several other universities. He visited France twice: first as a Sloan Fellow in Paris, during the academic year 1968–69, where he was greatly influenced by Grothendieck, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal D'Analyse Mathématique
The ''Journal d'Analyse Mathématique'' is a triannual peer-reviewed scientific journal published by Magnes Press (Hebrew University of Jerusalem). It was established in 1951 by Binyamin Amirà. It covers research in mathematics, especially classical analysis and related areas such as complex function theory, ergodic theory, functional analysis, harmonic analysis, partial differential equations, and quasiconformal mapping. Abstracting and indexing The journal is abstracted and indexed in: *MathSciNet *Science Citation Index Expanded *Scopus *ZbMATH Open According to the ''Journal Citation Reports'', the journal has a 2021 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 i ... of 1.132. References External links *{{Official website, 1=https://www.springer.com/mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G-structure
In differential geometry, a ''G''-structure on an ''n''- manifold ''M'', for a given structure group ''G'', is a principal ''G''- subbundle of the tangent frame bundle F''M'' (or GL(''M'')) of ''M''. The notion of ''G''-structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields. For example, for the orthogonal group, an O(''n'')-structure defines a Riemannian metric, and for the special linear group an SL(''n'',R)-structure is the same as a volume form. For the trivial group, an -structure consists of an absolute parallelism of the manifold. Generalising this idea to arbitrary principal bundles on topological spaces, one can ask if a principal G-bundle over a group G "comes from" a subgroup H of G. This is called reduction of the structure group (to H). Several structures on manifolds, such as a complex structure, a symplectic structure, or a Kähler structure, are ''G''-structures with an additional integrabilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudogroup
In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example). The modern theory of pseudogroups was developed by Élie Cartan in the early 1900s. Definition A pseudogroup imposes several conditions on a sets of homeomorphisms (respectively, diffeomorphisms) defined on open sets ''U'' of a given Euclidean space or more generally of a fixed topological space (respectively, smooth manifold). Since two homeomorphisms and compose to a homeomorphism from ''U'' to ''W'', one asks that the pseudogroup is closed under composition and inversion. However, unlike those for a group, the axioms defining a pseudogroup are not purely algebraic; the further requirements are related to the po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Élie Cartan
Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He also made significant contributions to general relativity and indirectly to quantum mechanics. He is widely regarded as one of the greatest mathematicians of the twentieth century. His son Henri Cartan was an influential mathematician working in algebraic topology. Life Élie Cartan was born 9 April 1869 in the village of Dolomieu, Isère to Joseph Cartan (1837–1917) and Anne Cottaz (1841–1927). Joseph Cartan was the village blacksmith; Élie Cartan recalled that his childhood had passed under "blows of the anvil, which started every morning from dawn", and that "his mother, during those rare minutes when she was free from taking care of the children and the house, was working with a spinning-wheel". Élie had an elder sister Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isadore Singer
Isadore Manuel Singer (May 3, 1924 – February 11, 2021) was an American mathematician. He was an Emeritus Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley. Singer is noted for his work with Michael Atiyah, proving the Atiyah–Singer index theorem in 1962, which paved the way for new interactions between pure mathematics and theoretical physics. In early 1980s, while a professor at Berkeley, Singer co-founded the Mathematical Sciences Research Institute (MSRI) with Shiing-Shen Chern and Calvin Moore. Biography Early life and education Singer was born on May 3, 1924, in Detroit, Michigan, to Polish Jewish immigrants. His father Simon was employed as a printer and only spoke Yiddish, and his mother, Freda (Rosemaity), worked as a seamstress. Singer learned English swiftly and subsequently taught it to the rest of his family. Isadore was born with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Fixed Point
In the study of dynamical systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds. Near a hyperbolic point the orbits of a two-dimensional, non-dissipative system resemble hyperbolas. This fails to hold in general. Strogatz notes that "hyperbolic is an unfortunate name—it sounds like it should mean ' saddle point'—but it has become standard." Several properties hold about a neighborhood of a hyperbolic point, notably * A stable manifold and an unstable manifold exist, * Shadowing occurs, * The dynamics on the invariant set can be represented via symbolic dynamics, * A natural measure can be defined, * The system is structurally stable. Maps If T \colon \mathbb^ \to \mathbb^ is a ''C''1 map and ''p'' is a fixed point then ''p'' is said to be a hyperbolic fixed point when the Jacobian matrix \operatorname T (p) has no eigenvalues on the unit circle. One example of a map whose only fixed point is hyper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smooth Map
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of differentiability class ''C^k'' if the derivatives f',f'',\dots,f^ exist and are continuous on U. If f is k-differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and community outreach. Considered the first learned society in the United States, it has about 1,000 elected members, and by April 2020 had had only 5,710 members since its creation. Through research grants, published journals, the American Philosophical Society Museum, an extensive library, and regular meetings, the society supports a variety of disciplines in the humanities and the sciences. Philosophical Hall, now a museum, is just east of Independence Hall in Independence National Historical Park; it was designated a National Historic Landmark in 1965. History The Philosophical Society, as it was originally called, was founded in 1743 by Benjamin Franklin, James Alexander (lawyer), James Alexander, Francis Hopkinson, John Bartram, Philip Syn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Academia De Ciencias Exactas, Físicas Y Naturales
The Spanish Royal Academy of Sciences (Spanish: ''Real Academia de Ciencias Exactas, Físicas y Naturales'') is an academic institution and learned society that was founded in Madrid in 1847. It is dedicated to the study and research of mathematics, physics, chemistry, biology, engineering, and related sciences. History The forerunner of the modern Academy of Sciences, the Academy of Mathematics, was created in Madrid in 1582, during the reign of Philip II. It evolved from the environment of cooperation among the cosmographers, architects and civil engineers that served the monarch, and also involved prominent artillery experts and military engineers. The initiative was motivated by an interest that existed in the Spain of the late sixteenth century in promoting the teaching of mathematics with an eye to its practical applications in areas as diverse as mercantile calculation, cosmography, astrology on one hand, and the art of navigation and specific problems relating to militar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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