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Gabriele Vezzosi
Gabriele Vezzosi is an Italian mathematician, born in Florence (Italy). His main interest is algebraic geometry. Vezzosi earned an MS degree in Physics at the University of Florence, under the supervision of Alexandre M. Vinogradov, and a PhD in Mathematics at the Scuola Normale Superiore in Pisa, under the supervision of Angelo Vistoli. His first papers dealt with differential calculus over commutative rings, intersection theory, (equivariant) algebraic K-theory, motivic homotopy theory, and existence of vector bundles on singular algebraic surfaces. Around 2001–2002 he started his collaboration with Bertrand Toën. Together, they created homotopical algebraic geometry (HAG), whose more relevant part is Derived algebraic geometry (DAG) which is by now a powerful and widespread theory. Slightly later, this theory have been reconsidered, and highly expanded by Jacob Lurie. More recently, Vezzosi together with Tony Pantev, Bertrand Toën and Michel Vaquié defined a deri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Lurie
Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the Institute for Advanced Study. Lurie is a 2014 MacArthur Fellow. Life When he was a student in the Science, Mathematics, and Computer Science Magnet Program at Montgomery Blair High School, Lurie took part in the International Mathematical Olympiad, where he won a gold medal with a perfect score in 1994. In 1996 he took first place in the Westinghouse Science Talent Search and was featured in a front-page story in the ''Washington Times''. Lurie earned his bachelor's degree in mathematics from Harvard College in 2000 and was awarded in the same year the Morgan Prize for his undergraduate thesis on Lie algebras. He earned his Ph.D. from the Massachusetts Institute of Technology under supervision of Michael J. Hopkins, in 2004 with a thesis on derived algebraic geometry. In 2007, he became associate professor at MIT, and in 2009 he became professor at Harvard University. In 20 ... [...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] |
Characteristic (algebra)
In mathematics, the characteristic of a ring (mathematics), ring , often denoted , is defined to be the smallest number of times one must use the ring's identity element, multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive identity the ring is said to have characteristic zero. That is, is the smallest positive number such that: :\underbrace_ = 0 if such a number exists, and otherwise. Motivation The special definition of the characteristic zero is motivated by the equivalent definitions characterized in the next section, where the characteristic zero is not required to be considered separately. The characteristic may also be taken to be the exponent (group theory), exponent of the ring's additive group, that is, the smallest positive integer such that: :\underbrace_ = 0 for every element of the ring (again, if exists; otherwise zero). Some authors do not include the multiplicative identity element in their r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Langlands Program
In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theory, number theoretic version by function field of an algebraic variety, function fields and applying techniques from algebraic geometry. The geometric Langlands correspondence relates algebraic geometry and representation theory. History In mathematics, the classical Langlands correspondence is a collection of results and conjectures relating number theory and representation theory. Formulated by Robert Langlands in the late 1960s, the Langlands correspondence is related to important conjectures in number theory such as the Taniyama–Shimura conjecture, which includes Fermat's Last Theorem as a special case.Frenkel 2007, p. 3 Establishing the Langlands correspondence in the number theoretic context has proven extremely difficult. As a result, some mathematicians have posed the geometric Langlands corres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conductor Conjecture
Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble, such as an orchestra. * ''Conductor'' (album), an album by indie rock band The Comas * Conduction, a type of structured free improvisation in music notably practiced by Butch Morris Mathematics * Conductor (ring theory), an ideal of a ring that measures how far it is from being integrally closed * Conductor of an abelian variety, a description of its bad reduction * Conductor of a Dirichlet character, the natural (smallest) modulus for a character * Conductor (class field theory), a modulus describing the ramification in an abelian extension of local or global fields * Artin conductor, an ideal or number associated to a representation of a Galois group of a local or global field * Conductor of a numerical semigroup, the smallest integer in the semigroup such that all subsequent integers are likewise in the semigroup Physics * Electrical conductor, an object, substanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spencer Bloch
Spencer Janney Bloch (born May 22, 1944; New York City) is an American mathematician known for his contributions to algebraic geometry and algebraic ''K''-theory. Bloch is a R. M. Hutchins Distinguished Service Professor Emeritus in the Department of Mathematics of the University of Chicago. He is a member of the U.S. National Academy of Sciences and a Fellow of the American Academy of Arts and SciencesScholars, visiting faculty, leaders represent Chicago as AAAS fellows The University of Chicago Chronicle, April 30, 2009, Vol. 28 No. 15. Accessed January 12, 2010 and of the . At the |
Deformation Quantization
Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies. * Deformation (meteorology), a measure of the rate at which the shapes of clouds and other fluid bodies change. * Deformation (mathematics), the study of conditions leading to slightly different solutions of mathematical equations, models and problems. * Deformation (volcanology), a measure of the rate at which the shapes of volcanoes change. * Deformation (biology), a harmful mutation or other deformation in an organism. See also * Deformity (medicine), a major difference in the shape of a body part or organ compared to its common or average shape. * Plasticity (physics), the study of the non-reversible deformation of materials subjected to forces. * Super-deformed Chibi, also known as super deformation, or S.D. is a style of caricatur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Topology
The ''Journal of Topology'' is a peer-reviewed scientific journal which publishes papers of high quality and significance in topology, geometry, and adjacent areas of mathematics. It was established in 2008, when the Editorial Board of ''Topology'' resigned due to the increasing costs of Elsevier's subscriptions. The journal is owned and managed by the London Mathematical Society and produced, distributed, sold and marketed by John Wiley & Sons. It appears quarterly with articles published individually online prior to appearing in a printed issue. Editorial Board * Arthur Bartels (University of Münster) * Andrew Blumberg (University of Texas at Austin) * Jeffrey Brock (Yale University) * Simon Donaldson (Imperial College London) * Cornelia Druţu Badea (University of Oxford) * Mark Gross (University of Cambridge) * Lars Hesselholt (University of Copenhagen) * Misha Kapovich (UC Davis) *Frances Kirwan (University of Oxford) * Marc Lackenby (University of Oxford) * Osca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Manifold
In differential geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M , subject to the Leibniz rule : \ = \h + g \ . Equivalently, \ defines a Lie algebra structure on the vector space (M) of smooth functions on M such that X_:= \: (M) \to (M) is a vector field for each smooth function f (making (M) into a Poisson algebra). Poisson structures on manifolds were introduced by André Lichnerowicz in 1977. They were further studied in the classical paper of Alan Weinstein, where many basic structure theorems were first proved, and which exerted a huge influence on the development of Poisson geometry — which today is deeply entangled with non-commutative geometry, integrable systems, topological field theories and representation theory, to name a few. Poisson structures are named after the French mathematician Siméon Denis Poisson, due to their ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Damien Calaque
Damien is a given name and less frequently a surname. The name is a variation of Damian which comes from the Greek ''Damianos''. This form originates from the Greek derived from the Greek word δαμάζω (damazō), "(I) conquer, master, overcome, tame", in the form of δαμάω/-ῶ (damaō), a form assumed as the first person of δαμᾷ (damāi) Given name A * Damien Abad (born 1980), French politician *Damien Adam (born 1989), French politician * Damien Adkins (born 1981), Australian rules footballer *Damien Alamos (born 1990), French Muay Thai kickboxer * Damien Allen (born 1986), English footballer *Damien Anderson (born 1979), American football player *Damien Angove (born 1970), Australian rules footballer * Damien Arsenault, Canadian politician *Damien Atkins (born 1975), Canadian actor and playwright B * Damien Balisson (born 1996), Mauritian footballer *Damien Berry (born 1989), American football player * Damien Birkinhead (born 1993), Australian shot putter *Dam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Obstruction Theory
In algebraic geometry, given a Deligne–Mumford stack ''X'', a perfect obstruction theory for ''X'' consists of: # a perfect two-term complex E = ^ \to E^0/math> in the derived category D(\text(X)_) of quasi-coherent étale sheaves on ''X'', and # a morphism \varphi\colon E \to \textbf_X, where \textbf_X is the cotangent complex of ''X'', that induces an isomorphism on h^0 and an epimorphism on h^. The notion was introduced by for an application to the intersection theory on moduli stacks; in particular, to define a virtual fundamental class. Examples Schemes Consider a regular embedding I \colon Y \to W fitting into a cartesian square : \begin X & \xrightarrow & V \\ g \downarrow & & \downarrow f \\ Y & \xrightarrow & W \end where V,W are smooth. Then, the complex :E^\bullet = ^*N_^ \to j^*\Omega_V/math> (in degrees -1, 0) forms a perfect obstruction theory for ''X''. The map comes from the composition :g^*N_^\vee \to g^*i^*\Omega_W =j^*f^*\Omega_W \to j^*\Omega_V This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
