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F. Kirwan
Dame Frances Clare Kirwan, (born 21 August 1959) is a British mathematician, currently Savilian Professor of Geometry at the University of Oxford. Her fields of specialisation are algebraic and symplectic geometry. Education Kirwan was educated at Oxford High School, and studied maths as an undergraduate at Clare College in the University of Cambridge. She took a D.Phil at Oxford in 1984, with the dissertation title ''The Cohomology of Quotients in Symplectic and Algebraic Geometry'', which was supervised by Michael Atiyah. Research Kirwan's research interests include moduli spaces in algebraic geometry, geometric invariant theory (GIT), and in the link between GIT and moment maps in symplectic geometry. Her work endeavours to understand the structure of geometric objects by investigation of their algebraic and topological properties. She introduced the Kirwan map. From 1983 to 1985 she held a junior fellowship at Harvard. From 1983 to 1986 she held a Fellowship at Magda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dame
''Dame'' is an honorific title and the feminine form of address for the honour of damehood in many Christian chivalric orders, as well as the Orders, decorations, and medals of the United Kingdom, British honours system and those of several other Commonwealth realms, such as Australia and New Zealand, with the masculine form of address being ''Sir''. It is the female equivalent for knighthood, which is traditionally granted to males. Dame is also style used by baronetesses Suo jure, in their own right. A woman appointed to the grades of the Dame Commander or Dame Grand Cross of the Order of Saint John (Bailiwick of Brandenburg), Order of Saint John, Equestrian Order of the Holy Sepulchre, Most Honourable Order of the Bath, the Most Distinguished Order of Saint Michael and Saint George, the Royal Victorian Order, or the Most Excellent Order of the British Empire becomes a dame. A Central European order in which female members receive the rank of Dame is the Order of St. George (H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symplectic Geometry
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed differential form, closed, nondegenerate form, nondegenerate differential form, 2-form. Symplectic geometry has its origins in the Hamiltonian mechanics, Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. The term "symplectic", introduced by Weyl, is a calque of "complex"; previously, the "symplectic group" had been called the "line complex group". "Complex" comes from the Latin ''com-plexus'', meaning "braided together" (co- + plexus), while symplectic comes from the corresponding Greek ''sym-plektikos'' (συμπλεκτικός); in both cases the stem comes from the Indo-European root wiktionary:Reconstruction:Proto-Indo-European/pleḱ-, *pleḱ- The name reflects the deep connections between complex and sym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering And Physical Sciences Research Council
The Engineering and Physical Sciences Research Council (EPSRC) is a British Research Council that provides government funding for grants to undertake research and postgraduate degrees in engineering and the physical sciences, mainly to universities in the United Kingdom. EPSRC research areas include mathematics, physics, chemistry, artificial intelligence and computer science, but exclude particle physics, nuclear physics, space science and astronomy (which fall under the remit of the Science and Technology Facilities Council). Since 2018 it has been part of UK Research and Innovation, which is funded through the Department for Business, Energy and Industrial Strategy. History EPSRC was created in 1994. At first part of the Science and Engineering Research Council (SERC), in 2018 it was one of nine organisations brought together to form UK Research and Innovation (UKRI). Its head office is in Swindon, Wiltshire in the same building (Polaris House) that houses the AHRC, BBSRC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Mathematics
This is a list of Institutes of Mathematics or Mathematical Institutes. Americas * American Institute of Mathematics * Clay Mathematics Institute, Cambridge, Massachusetts * Centre de Recherches Mathématiques, at the Université de Montréal * Center for Mathematical Modeling, at the University of Chile * Centro de Investigación en Matemáticas, Guanajuato, Guanajuato in Mexico * Courant Institute of Mathematical Sciences, at New York University * Fields Institute, at the University of Toronto * Institute for Advanced Study, in Princeton, New Jersey * Institute for Mathematics and its Applications, at the University of Minnesota * Institute for Pure and Applied Mathematics, at the University of California, Los Angeles * Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil * Mathematical Sciences Research Institute, at the University of California, Berkeley * PPGMAp, at the Universidade Federal do Rio Grande do Sul in Brazil Europe * Brunel Institute of C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after the society's first president), at 57–5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Title Of Distinction
The University of Oxford introduced Titles of Distinction for senior academics in the 1990s. These are not established chairs, which are posts funded by endowment for academics with a distinguished career in British and European universities. However, since there was a limited number of established chairs in these universities and an abundance of distinguished academics it was decided to introduce these Titles of Distinction. 'Reader' and the more senior 'Professor' were conferred annually. In the 1994–95 academic year, Oxford's congregation decided to confer the titles of Professor and Reader on distinguished academics without changes to their salaries or duties; the title of professor would be conferred on those whose research was "of outstanding quality", leading "to a significant international reputation". Reader would be conferred on those with "a research record of a high order, the quality of which has gained external recognition". This article provides a list of people upon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balliol College, Oxford
Balliol College () is one of the constituent colleges of the University of Oxford in England. One of Oxford's oldest colleges, it was founded around 1263 by John I de Balliol, a landowner from Barnard Castle in County Durham, who provided the foundation and endowment for the college. When de Balliol died in 1268, his widow, Dervorguilla, a woman whose wealth far exceeded that of her husband, continued his work in setting up the college, providing a further endowment and writing the statutes. She is considered a co-founder of the college. The college's alumni include four former Prime Ministers of the United Kingdom (H. H. Asquith, Harold Macmillan, Edward Heath, and Boris Johnson), Harald V of Norway, Empress Masako of Japan, five Nobel laureates, several Lords of Appeal in Ordinary, and numerous literary and philosophical figures, including Shoghi Effendi, Adam Smith, Gerard Manley Hopkins, and Aldous Huxley. John Wycliffe, who translated the Bible into English, was master o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magdalen College, Oxford
Magdalen College (, ) is a constituent college of the University of Oxford. It was founded in 1458 by William of Waynflete. Today, it is the fourth wealthiest college, with a financial endowment of £332.1 million as of 2019 and one of the strongest academically, setting the record for the highest Norrington Score in 2010 and topping the table twice since then. It is home to several of the university's distinguished chairs, including the Agnelli-Serena Professorship, the Sherardian Professorship, and the four Waynflete Professorships. The large, square Magdalen Tower is an Oxford landmark, and it is a tradition, dating to the days of Henry VII, that the college choir sings from the top of it at 6 a.m. on May Morning. The college stands next to the River Cherwell and the University of Oxford Botanic Garden. Within its grounds are a deer park and Addison's Walk. History Foundation Magdalen College was founded in 1458 by William of Waynflete, Bishop of Winchester a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard
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] |
Kirwan Map
In differential geometry, the Kirwan map, introduced by British mathematician Frances Kirwan, is the homomorphism :H^*_G(M) \to H^*(M /\!/_p G) where *M is a Hamiltonian G-space; i.e., a symplectic manifold acted by a Lie group ''G'' with a moment map \mu: M \to ^*. *H^*_G(M) is the equivariant cohomology ring of M; i.e.. the cohomology ring of the homotopy quotient EG \times_G M of M by G. *M /\!/_p G = \mu^(p)/G is the symplectic quotient of M by G at a regular central value p \in Z(^*) of \mu. It is defined as the map of equivariant cohomology induced by the inclusion \mu^(p) \hookrightarrow M followed by the canonical isomorphism H_G^*(\mu^(p)) = H^*(M /\!/_p G). A theorem of Kirwan says that if M is compact, then the map is surjective in rational coefficients. The analogous result holds between the K-theory In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...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] |
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