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Ralph Kaufmann
Ralph Martin Kaufmann (born August 4, 1969) is a German mathematician working in the United States. Career Kaufmann studied mathematics, physics and philosophy at the University of Bonn. He obtained a master's degree in Physics in 1994 under the supervision of Werner Nahm and a master's degree in philosophy under the supervision of Rainer Stuhlmann-Laeisz in 1996. His doctoral studies were carried out at the Max Planck Institute for Mathematics under the supervision of Yuri Manin, and he graduated summa cum laude from University of Bonn in 1997 with a thesis entitled "The geometry of the moduli space of pointed curves, the tensor product in the theory of Frobenius manifolds and the explicit Künneth formula in quantum cohomology". He remained at the Max Planck Institute for one year after his graduation as a researcher before moving to the Institut des Hautes Études Scientifiques for a year with a Marie Curie Fellowship from the European Union. In 1999 Kaufmann moved to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oberwolfach
Oberwolfach ( gsw, label= Low Alemannic, Obberwolfä) is a town in the district of Ortenau in Baden-Württemberg, Germany. It is the site of the Oberwolfach Research Institute for Mathematics, or Mathematisches Forschungsinstitut Oberwolfach. Geography Geographical situation The town of Oberwolfach lies between 270 and 948 meters above sea level in the central Schwarzwald (Black Forest) on the river Wolf, a tributary of the Kinzig. Neighbouring localities The district is neighboured by Bad Peterstal-Griesbach to the north, Bad Rippoldsau-Schapbach in Landkreis Freudenstadt to the east, by the towns of Wolfach and Hausach to the south, and by Oberharmersbach Oberharmersbach ( gsw, label=Low Alemannic Low Alemannic German (german: Niederalemannisch) is a branch of Alemannic German, which is part of Upper German. Its varieties are only partly intelligible to non-Alemannic speakers. Subdivisions * ... to the west. References External links Gemeinde Oberwol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton Institute
The Isaac Newton Institute for Mathematical Sciences is an international research institute for mathematics and its many applications at the University of Cambridge. It is named after one of the university's most illustrious figures, the mathematician and natural philosopher Sir Isaac Newton and occupies one of the buildings in the Cambridge Centre for Mathematical Sciences. History After a national competition run by SERC, the Science and Engineering Research Council (now known as EPSRC Engineering and Physical Sciences Research Council), this institute was chosen to be the national research institute for mathematical sciences in the UK. It opened in 1992 with support from St John's College and Trinity College. St. John's provided the land and a purpose-built building, Trinity provided running costs for the first five years and the London Mathematical Society provided other support. Shortly afterwards at the institute, the British mathematician Andrew Wiles announced h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Deligne
Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal. Early life and education Deligne was born in Etterbeek, attended school at Athénée Adolphe Max and studied at the Université libre de Bruxelles (ULB), writing a dissertation titled ''Théorème de Lefschetz et critères de dégénérescence de suites spectrales'' (Theorem of Lefschetz and criteria of degeneration of spectral sequences). He completed his doctorate at the University of Paris-Sud in Orsay 1972 under the supervision of Alexander Grothendieck, with a thesis titled ''Théorie de Hodge''. Career Starting in 1972, Deligne worked with Grothendieck at the Institut des Hautes Études Scientifiques (IHÉS) near Paris, initially on the generalization within scheme theory of Zariski's main theorem. In 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Mathematics
''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed at publishing articles addressed to a broader "mathematical community", and not only to mathematicians in the author's field. Herbert Busemann writes, in the preface of the first issue, "The need for expository articles addressing either all mathematicians or only those in somewhat related fields has long been felt, but little has been done outside of the USSR. The serial publication ''Advances in Mathematics'' was created in response to this demand." Abstracting and indexing The journal is abstracted and indexed in: * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operad Theory
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 consi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dennis Sullivan
Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center and is a distinguished professor at Stony Brook University. Sullivan was awarded the Wolf Prize in Mathematics in 2010 and the Abel Prize in 2022. Early life and education Sullivan was born in Port Huron, Michigan, on February 12, 1941.. His family moved to Houston soon afterwards. He entered Rice University to study chemical engineering but switched his major to mathematics in his second year after encountering a particularly motivating mathematical theorem. The change was prompted by a special case of the uniformization theorem, according to which, in his own words: He received his Bachelor of Arts degree from Rice in 1963. He obtained his Doctor of Philosophy from Princeton University in 1966 with his thesis, ''Triangulating h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Topology
String topology, a branch of mathematics, is the study of algebraic structures on the homology of free loop spaces. The field was started by . Motivation While the singular cohomology of a space has always a product structure, this is not true for the singular homology of a space. Nevertheless, it is possible to construct such a structure for an oriented manifold M of dimension d. This is the so-called intersection product. Intuitively, one can describe it as follows: given classes x\in H_p(M) and y\in H_q(M), take their product x\times y \in H_(M\times M) and make it transversal to the diagonal M\hookrightarrow M\times M. The intersection is then a class in H_(M), the intersection product of x and y. One way to make this construction rigorous is to use stratifolds. Another case, where the homology of a space has a product, is the (based) loop space \Omega X of a space X. Here the space itself has a product :m\colon \Omega X\times \Omega X \to \Omega X by going first through the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbifold
In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space. Definitions of orbifold have been given several times: by Ichirô Satake in the context of automorphic forms in the 1950s under the name ''V-manifold''; by William Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name ''orbifold'', after a vote by his students; and by André Haefliger in the 1980s in the context of Mikhail Gromov (mathematician), Mikhail Gromov's programme on CAT(k) spaces under the name ''orbihedron''. Historically, orbifolds arose first as surfaces with Singularity (mathematics), singular points long before they were formally defined. One of the first classical examples arose in the theory of modular forms with the action of the modular group \mathrm(2,\Z) on the upper half-plane: a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maryam Mirzakhani
Maryam Mirzakhani ( fa, مریم میرزاخانی, ; 12 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller space, Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. In 2005, as a result of her research, she was honored in ''Popular Science's'' fourth annual "Brilliant 10" in which she was acknowledged as one of the top 10 young minds who have pushed their fields in innovative directions. On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics, becoming the first Iranian to be honored with the award and the first of only two women to date. The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces". On 14 July 2017, Mirzakhani died of breast cancer at the age of 40. Early life and education Mirzakhani was born on 12 May 1977 in Tehran, Ir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Don Zagier
Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the ''Collège de France'' in Paris from 2006 to 2014. Since October 2014, he is also a Distinguished Staff Associate at the International Centre for Theoretical Physics ( ICTP). Background Zagier was born in Heidelberg, West Germany. His mother was a psychiatrist, and his father was the dean of instruction at the American College of Switzerland. His father held five different citizenships, and he spent his youth living in many different countries. After finishing high school (at age 13) and attending Winchester College for a year, he studied for three years at MIT, completing his bachelor's and master's degrees and being named a Putnam Fellow in 1967 at the age of 16. He then wrote a doctoral dissertation on characteristic classes under Fri ... [...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 thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virasoro Algebra
In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory. Definition The Virasoro algebra is spanned by generators for and the central charge . These generators satisfy ,L_n0 and The factor of 1/12 is merely a matter of convention. For a derivation of the algebra as the unique central extension of the Witt algebra, see derivation of the Virasoro algebra. The Virasoro algebra has a presentation in terms of two generators (e.g. 3 and −2) and six relations. Representation theory Highest weight representations A highest weight representation of the Virasoro algebra is a representation generated by a primary state: a vector v such that : L_ v = 0, \quad L_0 v = hv, where the number is called the conformal dimension or conformal weight of v.P. Di Francesco, P. Mathieu, and D. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
