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Victor Ginzburg
Victor Ginzburg (born 1957) is a Russian American mathematician who works in representation theory and in noncommutative geometry. He is known for his contributions to geometric representation theory, especially, for his works on representations of quantum groups and Hecke algebras, and on the geometric Langlands program (Satake equivalence of categories). He is currently a Professor of Mathematics at the University of Chicago. Career Ginzburg received his Ph.D. at Moscow State University in 1985, under the direction of Alexandre Kirillov and Israel Gelfand. Ginzburg wrote a textbook ''Representation theory and complex geometry'' with Neil Chriss on geometric representation theory. A paper by Alexander Beilinson, Ginzburg, and Wolfgang Soergel introduced the concept of Koszul duality (cf. Koszul algebra) and the technique of "mixed categories" to representation theory. Furthermore, Ginzburg and Mikhail Kapranov developed Koszul duality theory for operads. In noncommutative g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Of Categories
In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities between the mathematical structures concerned. In some cases, these structures may appear to be unrelated at a superficial or intuitive level, making the notion fairly powerful: it creates the opportunity to "translate" theorems between different kinds of mathematical structures, knowing that the essential meaning of those theorems is preserved under the translation. If a category is equivalent to the opposite (or dual) of another category then one speaks of a duality of categories, and says that the two categories are dually equivalent. An equivalence of categories consists of a functor between the involved categories, which is required t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1957 Births
1957 ( MCMLVII) was a common year starting on Tuesday of the Gregorian calendar, the 1957th year of the Common Era (CE) and ''Anno Domini'' (AD) designations, the 957th year of the 2nd millennium, the 57th year of the 20th century, and the 8th year of the 1950s decade. Events January * January 1 – The Saarland joins West Germany. * January 3 – Hamilton Watch Company introduces the first electric watch. * January 5 – South African player Russell Endean becomes the first batsman to be dismissed for having ''handled the ball'', in Test cricket. * January 9 – British Prime Minister Anthony Eden resigns. * January 10 – Harold Macmillan becomes Prime Minister of the United Kingdom. * January 11 – The African Convention is founded in Dakar. * January 14 – Kripalu Maharaj is named fifth Jagadguru (world teacher), after giving seven days of speeches before 500 Hindu scholars. * January 15 – The film ''Throne of Blood'', Akira Kurosawa's reworking of '' Ma ... [...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 Joseph Miller Thomas (16 January 1898 – 1979) was an American mathematician, known for the Thomas decomposition of algebraic and differential systems. Thomas received his Ph.D., supervised by Frederick Wahn Beal, from the University of Pennsylva .... 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 of 2.194, ranking it in the top ten mathematics journals in the world. References External links * Mathematics journals Duke University, Mathematical Journal Publications established in 1935 Multilingual journals English-language jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inventiones Mathematicae
''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editors are Camillo De Lellis (Institute for Advanced Study, Princeton) and Jean-Benoît Bost (University of Paris-Sud Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, in ...). Abstracting and indexing The journal is abstracted and indexed in: References External links *{{Official website, https://www.springer.com/journal/222 Mathematics journals Publications established in 1966 English-language journals Springer Science+Business Media academic journals Monthly journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The American Mathematical Society
The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988. Abstracting and indexing This journal is abstracted and indexed in: 2011. American Mathematical Society. * * * * ISI Ale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quiver (mathematics)
In graph theory, a quiver is a directed graph where Loop (graph theory), loops and multiple arrows between two vertex (graph theory), vertices are allowed, i.e. a multidigraph. They are commonly used in representation theory: a representation of a quiver assigns a vector space to each vertex of the quiver and a linear map to each arrow . In category theory, a quiver can be understood to be the underlying structure of a category (mathematics), category, but without composition or a designation of identity morphisms. That is, there is a forgetful functor from to . Its left adjoint is a free functor which, from a quiver, makes the corresponding free category. Definition A quiver Γ consists of: * The set ''V'' of vertices of Γ * The set ''E'' of edges of Γ * Two functions: ''s'': ''E'' → ''V'' giving the ''start'' or ''source'' of the edge, and another function, ''t'': ''E'' → ''V'' giving the ''target'' of the edge. This definition is identica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Algebra
In graph theory, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph. They are commonly used in representation theory: a representation of a quiver assigns a vector space to each vertex of the quiver and a linear map to each arrow . In category theory, a quiver can be understood to be the underlying structure of a category, but without composition or a designation of identity morphisms. That is, there is a forgetful functor from to . Its left adjoint is a free functor which, from a quiver, makes the corresponding free category. Definition A quiver Γ consists of: * The set ''V'' of vertices of Γ * The set ''E'' of edges of Γ * Two functions: ''s'': ''E'' → ''V'' giving the ''start'' or ''source'' of the edge, and another function, ''t'': ''E'' → ''V'' giving the ''target'' of the edge. This definition is identical to that of a multidigraph. A morphism of quivers is defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donaldson–Thomas Theory
In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants. Given a compact moduli space of sheaves on a Calabi–Yau threefold, its Donaldson–Thomas invariant is the virtual number of its points, i.e., the integral of the cohomology class 1 against the virtual fundamental class. The Donaldson–Thomas invariant is a holomorphic analogue of the Casson invariant. The invariants were introduced by . Donaldson–Thomas invariants have close connections to Gromov–Witten invariants of algebraic three-folds and the theory of stable pairs due to Rahul Pandharipande and Thomas. Donaldson–Thomas theory is physically motivated by certain BPS states that occur in string and gauge theorypg 5. This is due to the fact the invariants depend on a stability condition on the derived category D^b(\mathcal) of the moduli spaces being studied. Essentially, these stability conditions correspond to points in the Kahler moduli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calabi–Yau Manifold
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their name was coined by , after who first conjectured that such surfaces might exist, and who proved the Calabi conjecture. Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex dimensions (i.e. any even number of real dimensions). They were originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions are sometimes used. Definitions The motivational definition given by Shing-Tung Yau is of a compact Kähl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxim Kontsevich
Maxim Lvovich Kontsevich (russian: Макси́м Льво́вич Конце́вич, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, and the Breakthrough Prize in Mathematics in 2014. Academic career and research He was born into the family of Lev Kontsevich, Soviet orientalist and author of the Kontsevich system. After ranking second in the All-Union Mathematics Olympiads, he attended Moscow State University but left without a degree in 1985 to become a researcher at the Institute for Information Transmission Problems in Moscow. While at the institute he published papers that caught the interest of the Max Planck Institute in Bonn and was invited for three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operads
In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad O, one defines an ''algebra over O'' to be a set together with concrete operations on this set which behave just like the abstract operations of O. For instance, there is a Lie operad L such that the algebras over L are precisely the Lie algebras; in a sense L abstractly encodes the operations that are common to all Lie algebras. An operad is to its algebras as a group is to its group representations. History Operads originate in algebraic topology; they were introduced to characterize iterated loop spaces by J. Michael Boardman and Rainer M. Vogt in 1969 and by J. Peter May in 1970. The word "operad" was created by May as a portmanteau of "operations" and "monad" (and also because his mother was an opera singer). Interest in operads was cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
