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Eckhard Meinrenken
Eckhard Meinrenken is a German-Canadian mathematician working in differential geometry and mathematical physics. He is a professor at University of Toronto. Education and career Meinrenken studied Physics at Albert-Ludwigs-Universität Freiburg, where he obtained a Diplom in 1990 and a PhD in 1994, with a thesis entitled ''Vielfachheitsformeln für die Quantisierung von Phasenräumen'' (Multiplicity formulas for the quantization of phase spaces), under the supervision of . He was a postdoc at Massachusetts Institute of Technology from 1995 to 1997, and then he joined University of Toronto Department of Mathematics in 1998 as assistant professor. In 2000 he become Associated Professor and since 2004 he is Full Professor at the same university. Meinrenken was awarded in 2001 an André Aisenstadt Prize, in 2003 a McLean Award and in 2007 a NSERC Steacie Memorial Fellowship. In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing and in 2008 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Theory
In mathematics, the mathematician Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan. The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence. The subject is part of differential geometry since Lie groups are differentiable manifolds. Lie groups evolve out of the identity (1) and the tangent vectors to one-parameter subgroups generate the Lie algebra. The structure of a Lie group is implicit in its algebra, and the structure of the Lie algebra is expressed by root systems and root data. Lie theory has been particularly useful in mathematical physics s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars. For the Gregorian calendar, the average length of the calendar year (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of The University Of Toronto
An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, '' Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, established what is known today as the Old Academy. By extension, ''academia'' has come to mean the accumulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canadian Mathematicians
Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of their being ''Canadian''. Canada is a multilingual and multicultural society home to people of groups of many different ethnic, religious, and national origins, with the majority of the population made up of Old World immigrants and their descendants. Following the initial period of French and then the much larger British colonization, different waves (or peaks) of immigration and settlement of non-indigenous peoples took place over the course of nearly two centuries and continue today. Elements of Indigenous, French, British, and more recent immigrant customs, languages, and religions have combined to form the culture of Canada, and thus a Canadian identity. Canada has also been strongly influenced by its linguistic, geographic, and e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Mathematicians
German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Germanic peoples (Roman times) * German language **any of the Germanic languages * German cuisine, traditional foods of Germany People * German (given name) * German (surname) * Germán, a Spanish name Places * German (parish), Isle of Man * German, Albania, or Gërmej * German, Bulgaria * German, Iran * German, North Macedonia * German, New York, U.S. * Agios Germanos, Greece Other uses * German (mythology), a South Slavic mythological being * Germans (band), a Canadian rock band * "German" (song), a 2019 song by No Money Enterprise * ''The German'', a 2008 short film * "The Germans", an episode of ''Fawlty Towers'' * ''The German'', a nickname for Congolese rebel André Kisase Ngandu See also * Germanic (other) * German ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Algebra
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford. The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (''pseudo-'')''Riemannian Clifford algebras'', as distinct from ''symplectic Clifford algebras''.see for ex. Introduction and basic properties A Clifford algebra is a unital associative algebra that contains and is generated by a vector space over a field , where is equipped with a qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Map
In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The momentum map generalizes the classical notions of linear and angular momentum. It is an essential ingredient in various constructions of symplectic manifolds, including symplectic (Marsden–Weinstein) quotients, discussed below, and symplectic cuts and sums. Formal definition Let ''M'' be a manifold with symplectic form ω. Suppose that a Lie group ''G'' acts on ''M'' via symplectomorphisms (that is, the action of each ''g'' in ''G'' preserves ω). Let \mathfrak be the Lie algebra of ''G'', \mathfrak^* its dual, and :\langle, \rangle : \mathfrak^* \times \mathfrak \to \mathbf the pairing between the two. Any ξ in \mathfrak induces a vector field ρ(ξ) on ''M'' describing the infinitesimal action of ξ. To be precise, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anton Alekseev (mathematician)
Anton Yurevich Alekseev (Антон Юрьевич Алексеев, born 9 August 1967) is a Russian mathematician. Alekseev was a student of Ludvig Faddeev. Alekseev worked at the Steklov Institute in Saint Petersburg and at the beginning of the 1990s at Uppsala University. He is now a professor ordinarius at the University of Geneva. Alekseev does research on representation theory of Lie groups and algebras, moment theory, symplectic geometry and mathematical physics. In 2006 he, with Eckhard Meinrenken, published in ''Inventiones Mathematicae'' a proof of the Kashiwara-Vergne conjecture. In 2008 he gave a new proof with Charles Torossian. In 2014 Alekseev was an invited speaker with talk ''Three lives of the Gelfand-Zeitlin integrable system'' at the International Congress of Mathematicians in Seoul. Selected publications *as editor with A. Hietamäki, K. Huitu, A. Morozov, Antti Juhani Niemi: Integrable Models and Strings, Proceedings of the 3rd Baltic Rim Student Seminar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Victor Guillemin
Victor William Guillemin (born 1937 in Boston) is an American mathematician working in the field of symplectic geometry, who has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics. He is a tenured Professor in the Department of Mathematics at the Massachusetts Institute of Technology. His uncle Ernst Guillemin was a Professor of Electrical Engineering and Computer Science (EECS) at MIT, and his daughter Karen Guillemin is a Professor of Biology at the University of Oregon. Professional career Guillemin received a Ph.D. in mathematics from Harvard University in 1962, after earlier completing his B. A. at Harvard in 1959, as well as an M. A. at the University of Chicago in 1960. His thesis, entitled ''Theory of Finite G-Structures,'' was written under the direction of Shlomo Sternberg. He is the author or co-author of numerous books and monographs, including a widely used textbook on differential topology, written jointly wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
