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Geoffrey Horrocks (mathematician)
Geoffrey Horrocks (1932/33 Leicester – 12 September 2012) was a British mathematician working on vector bundles, who introduced the Horrocks construction used in the ADHM construction, and the Horrocks–Mumford bundle and monads. He was a professor at Newcastle University Newcastle University (legally the University of Newcastle upon Tyne) is a UK public university, public research university based in Newcastle upon Tyne, North East England. It has overseas campuses in Singapore and Malaysia. The university is ... until his retirement in 1998. Publications * * ReferencesLMS newsletter obituary 2012 deaths 1930s births Academics of Newcastle University Alumni of Queens' College, Cambridge 20th-century British mathematicians 21st-century British mathematicians Algebraic geometers {{UK-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leicester
Leicester ( ) is a city status in the United Kingdom, city, Unitary authorities of England, unitary authority and the county town of Leicestershire in the East Midlands of England. It is the largest settlement in the East Midlands. The city lies on the River Soar and close to the eastern end of the National Forest, England, National Forest. It is situated to the north-east of Birmingham and Coventry, south of Nottingham and west of Peterborough. The population size has increased by 38,800 ( 11.8%) from around 329,800 in 2011 to 368,600 in 2021 making it the most populous municipality in the East Midlands region. The associated Urban area#United Kingdom, urban area is also the 11th most populous in England and the List of urban areas in the United Kingdom, 13th most populous in the United Kingdom. Leicester is at the intersection of two railway lines: the Midland Main Line and the Birmingham to London Stansted Airport line. It is also at the confluence of the M1 motorway, M1/M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X. The simplest example is the case that the family of vector spaces is constant, i.e., there is a fixed vector space V such that V(x)=V for all x in X: in this case there is a copy of V for each x in X and these copies fit together to form the vector bundle X\times V over X. Such vector bundles are said to be ''trivial''. A more complicated (and prototypical) class of examples are the tangent bundles of smooth (or differentiable) manifolds: to every point of such a manifold w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horrocks Construction
In mathematics, the Horrocks construction is a method for constructing vector bundles, especially over projective spaces, introduced by . His original construction gave an example of an indecomposable rank 2 vector bundle over 3-dimensional projective space, and generalizes to give examples of vector bundles of higher ranks over other projective spaces. The Horrocks construction is used in the ADHM construction to construct instantons over the 4-sphere In mathematics, an -sphere or a hypersphere is a topological space that is homeomorphic to a ''standard'' -''sphere'', which is the set of points in -dimensional Euclidean space that are situated at a constant distance from a fixed point, call .... References * * Vector bundles {{topology-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ADHM Construction
In mathematical physics and gauge theory, the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld, Nigel Hitchin, Yuri I. Manin in their paper "Construction of Instantons." ADHM data The ADHM construction uses the following data: * complex vector spaces ''V'' and ''W'' of dimension ''k'' and ''N'', * ''k'' × ''k'' complex matrices ''B''1, ''B''2, a ''k'' × ''N'' complex matrix ''I'' and a ''N'' × ''k'' complex matrix ''J'', * a real moment map \mu_r = _1,B_1^\dagger _2,B_2^\daggerII^\dagger-J^\dagger J, * a complex moment map \displaystyle\mu_c = _1,B_2IJ. Then the ADHM construction claims that, given certain regularity conditions, * Given ''B''1, ''B''2, ''I'', ''J'' such that \mu_r=\mu_c=0, an anti-self-dual instanton in a SU(''N'') gauge theory with instanton number ''k'' can be constructed, * All anti-self-dual instantons c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horrocks–Mumford Bundle
In algebraic geometry, the Horrocks–Mumford bundle is an indecomposable rank 2 vector bundle on 4-dimensional projective space ''P''4 introduced by . It is the only such bundle known, although a generalized construction involving Paley graphs produces other rank 2 sheaves (Sasukara et al. 1993). The zero sets of sections of the Horrocks–Mumford bundle are abelian surfaces of degree 10, called Horrocks–Mumford surfaces. By computing Chern classes one sees that the second exterior power \wedge^2 F of the Horrocks–Mumford bundle ''F'' is the line bundle ''O(5)'' on ''P4''. Therefore, the zero set ''V'' of a general section of this bundle is a quintic threefold called a Horrocks–Mumford quintic. Such a ''V'' has exactly 100 nodes; there exists a small resolution ''V′'' which is a Calabi–Yau threefold fibered by Horrocks–Mumford surfaces. See also *List of algebraic surfaces This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monad (homological Algebra)
In homological algebra, a monad is a 3-term complex : ''A'' → ''B'' → ''C'' of objects in some abelian category whose middle term ''B'' is projective, whose first map ''A'' → ''B'' is injective, and whose second map ''B'' → ''C'' is surjective. Equivalently, a monad is a projective object together with a 3-step filtration ''B'' ⊃ ker(''B'' → ''C'') ⊃ im(''A'' → ''B''). In practice ''A'', ''B'', and ''C'' are often vector bundles over some space, and there are several minor extra conditions that some authors add to the definition. Monads were introduced by . See also *ADHM construction In mathematical physics and gauge theory, the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld, Nigel Hitchin, Yuri I. Manin in their paper "Constru ... References * * Vector bundles Homological algebra {{algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newcastle University
Newcastle University (legally the University of Newcastle upon Tyne) is a UK public university, public research university based in Newcastle upon Tyne, North East England. It has overseas campuses in Singapore and Malaysia. The university is a red brick university and a member of the Russell Group, an association of research-intensive UK universities. The university finds its roots in the School of Medicine and Surgery (later the College of Medicine), established in 1834, and the Edward Fenwick Boyd#College of Physical Science, College of Physical Science (later renamed Armstrong College), founded in 1871. These two colleges came to form the larger division of the federal University of Durham, with the Durham Colleges forming the other. The Newcastle colleges merged to form King's College in 1937. In 1963, following an Act of Parliament, King's College became the University of Newcastle upon Tyne. The university subdivides into three faculties: the Faculty of Humanities and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The 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†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology (journal)
''Topology'' was a peer-reviewed mathematical journal covering topology and geometry. It was established in 1962 and was published by Elsevier. The last issue of ''Topology'' appeared in 2009. Pricing dispute On 10 August 2006, after months of unsuccessful negotiations with Elsevier about the price policy of library subscriptions, the entire editorial board of the journal handed in their resignation, effective 31 December 2006. Subsequently, two more issues appeared in 2007 with papers that had been accepted before the resignation of the editors. In early January the former editors instructed Elsevier to remove their names from the website of the journal, but Elsevier refused to comply, justifying their decision by saying that the editorial board should remain on the journal until all of the papers accepted during its tenure had been published. In 2007 the former editors of ''Topology'' announced the launch of the ''Journal of Topology'', published by Oxford University Press ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2012 Deaths
This is a list of deaths of notable people, organised by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked here. 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 See also * Lists of deaths by day The following pages, corresponding to the Gregorian calendar, list the historical events, births, deaths, and holidays and observances of the specified day of the year: Footnotes See also * Leap year * List of calendars * List of non-standard ... * Deaths by year {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1930s Births
Year 193 ( CXCIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sosius and Ericius (or, less frequently, year 946 ''Ab urbe condita''). The denomination 193 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * January 1 – Year of the Five Emperors: The Roman Senate chooses Publius Helvius Pertinax, against his will, to succeed the late Commodus as Emperor. Pertinax is forced to reorganize the handling of finances, which were wrecked under Commodus, to reestablish discipline in the Roman army, and to suspend the food programs established by Trajan, provoking the ire of the Praetorian Guard. * March 28 – Pertinax is assassinated by members of the Praetorian Guard, who storm the imperial palace. The Empire is auctioned off ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academics Of Newcastle University
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 accumulation, dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
