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J. A. Todd
John Arthur Todd (23 August 1908 – 22 December 1994) was an English mathematician who specialised in geometry. Biography He was born in Liverpool, and went up to Trinity College, Cambridge in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester. He became a lecturer at Cambridge in 1937. He remained at Cambridge for the rest of his working life. Work The Todd class in the theory of the higher-dimensional Riemann–Roch theorem is an example of a characteristic class (or, more accurately, a reciprocal of one) that was discovered by Todd in work published in 1937. It used the methods of the Italian school of algebraic geometry. The Todd–Coxeter process for coset enumeration is a major method of computational algebra, and dates from a collaboration with H.S.M. Coxeter in 1936. In 1953 he and Coxeter discovered the Coxeter–Todd lattice. In 1954 he and G. C. Shephard classified the finite complex reflection groups. Honours In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liverpool
Liverpool is a city and metropolitan borough in Merseyside, England. With a population of in 2019, it is the 10th largest English district by population and its metropolitan area is the fifth largest in the United Kingdom, with a population of 2.24 million. On the eastern side of the Mersey Estuary, Liverpool historically lay within the ancient hundred of West Derby in the county of Lancashire. It became a borough in 1207, a city in 1880, and a county borough independent of the newly-created Lancashire County Council in 1889. Its growth as a major port was paralleled by the expansion of the city throughout the Industrial Revolution. Along with general cargo, freight, and raw materials such as coal and cotton, merchants were involved in the slave trade. In the 19th century, Liverpool was a major port of departure for English and Irish emigrants to North America. It was also home to both the Cunard and White Star Lines, and was the port of registry of the ocean lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematics, engineering science, and medical science". Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to many eminent scientists throughout history, including Isaac Newton (1672), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Albert Einstein (1921), Paul Dirac (1930), Winston Churchill (1941), Subrahmanyan Chandrasekhar (1944), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955) and Francis Crick (1959). More recently, fellowship has been awarded to Stephen Hawking (1974), David Attenborough (1983), Tim Hunt (1991), Elizabeth Blackburn (1992), Tim Berners-Lee (2001), Venki Ramakrishn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004. Life Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at the University of Oxford and the University of Cambridge and in the United States at the Institute for Advanced Study. He was the President of the Royal Society (1990–1995), founding director of the Isaac Newton Institute (1990–1996), master of Trinity College, Cambridge (1990–1997), chancellor of the University of Leicester (1995–2005), and the President of the Royal Society of Edinburgh (2005–2008). From 1997 until his death, he was an honorary professor in the University of Edinburgh. Atiyah's mathematical collaborators included Raoul Bott, Friedrich Hirzebruch and Isadore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geoffrey Colin Shephard
Geoffrey Colin Shephard is a mathematician who works on convex geometry and reflection groups. He asked Shephard's problem on the volumes of projected convex bodies, posed another problem on polyhedral nets, proved the Shephard–Todd theorem in invariant theory of finite groups, began the study of complex polytopes, and classified the complex reflection groups. Shephard earned his Ph.D. in 1954 from Queens' College, Cambridge, under the supervision of J. A. Todd. He was a professor of mathematics at the University of East Anglia The University of East Anglia (UEA) is a public research university in Norwich, England. Established in 1963 on a campus west of the city centre, the university has four faculties and 26 schools of study. The annual income of the institution f ... until his retirement. University of East Anglia School of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dennis Babbage
Dennis William Babbage (26 April 1909 – 9 June 1991) was an English mathematician associated with Magdalene College, Cambridge, and with codebreaking at Bletchley Park during World War II. In 1980 Babbage was President of Magdalene College, Cambridge. Early life and career He attended St Paul's School, and then Magdalene College from 1927. He wrote 12 papers between 1931 and 1938 on algebraic geometry, and was associated with Professor H. F. Baker. He had a research fellowship in 1933, then a fellowship in 1936. Postwar he was made a tutor in 1946, and a senior tutor in 1964. He was a distant relative of the 19th century mathematician Charles Babbage, but was not a descendant. Bletchley Park During World War II Babbage was the chief cryptanalyst in Hut 6 at Bletchley Park, which decrypted German Army and Air Force Enigma messages. Babbage and Hugh Alexander were leaders in the Machine Room and in all matters related to the techniques of breaking Enigma keys. Babbage was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century. Biography Coxeter was born in Kensington to Harold Samuel Coxeter and Lucy (). His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases (including a mechanism for anaesthetising surgical patients with nitrous oxide), but was able to retire early and focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter who had attended the Royal Academy of Arts. A maternal cousin was the architect Sir Giles Gilbert Scott. In his youth, Coxeter composed music and was an accomplished pianist at the age of 10. Roberts, Siobhan, ''King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry'', Walker & Company, 2006, He felt that mathematics and music were intimately related, outlining his idea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Reflection Group
In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise. Complex reflection groups arise in the study of the invariant theory of polynomial rings. In the mid-20th century, they were completely classified in work of Shephard and Todd. Special cases include the symmetric group of permutations, the dihedral groups, and more generally all finite real reflection groups (the Coxeter groups or Weyl groups, including the symmetry groups of regular polyhedra). Definition A (complex) reflection ''r'' (sometimes also called ''pseudo reflection'' or ''unitary reflection'') of a finite-dimensional complex vector space ''V'' is an element r \in GL(V) of finite order that fixes a complex hyperplane pointwise, that is, the ''fixed-space'' \operatorname(r) := \operatorname(r-\operatorname_V) has codimension 1. A (finite) complex reflectio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coxeter–Todd Lattice
In mathematics, the Coxeter–Todd lattice K12, discovered by , is a 12-dimensional even integral lattice of discriminant 36 with no norm-2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 3, and is analogous to the Barnes–Wall lattice. The automorphism group of the Coxeter–Todd lattice has order 210·37·5·7=78382080, and there are 756 vectors in this lattice of norm 4 (the shortest nonzero vectors in this lattice). Properties The Coxeter–Todd lattice can be made into a 6-dimensional lattice self dual over the Eisenstein integers. The automorphism group of this complex lattice has index 2 in the full automorphism group of the Coxeter–Todd lattice and is a complex reflection group (number 34 on the list) with structure 6.PSU4(F3).2, called the Mitchell group. The genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coset Enumeration
In mathematics, coset enumeration is the problem of counting the cosets of a subgroup ''H'' of a group ''G'' given in terms of a presentation. As a by-product, one obtains a permutation representation for ''G'' on the cosets of ''H''. If ''H'' has a known finite order, coset enumeration gives the order of ''G'' as well. For small groups it is sometimes possible to perform a coset enumeration by hand. However, for large groups it is time-consuming and error-prone, so it is usually carried out by computer. Coset enumeration is usually considered to be one of the fundamental problems in computational group theory. The original algorithm for coset enumeration was invented by John Arthur Todd and H. S. M. Coxeter. Various improvements to the original Todd–Coxeter algorithm have been suggested, notably the classical strategies of V. Felsch and HLT (Haselgrove, Leech and Trotter). A practical implementation of these strategies with refinements is available at the ACE website. The K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italian School Of Algebraic Geometry
In relation to the history of mathematics, the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces, centered around Rome roughly from 1885 to 1935. There were 30 to 40 leading mathematicians who made major contributions, about half of those being Italian. The leadership fell to the group in Rome of Guido Castelnuovo, Federigo Enriques and Francesco Severi, who were involved in some of the deepest discoveries, as well as setting the style. Algebraic surfaces The emphasis on algebraic surfaces—algebraic varieties of dimension two—followed on from an essentially complete geometric theory of algebraic curves (dimension 1). The position in around 1870 was that the curve theory had incorporated with Brill–Noether theory the Riemann–Roch theorem in all its refinements (via the detailed geometry of the theta-divisor). The classification of algebraic surfaces was a bold and successful atte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic Class
In mathematics, a characteristic class is a way of associating to each principal bundle of ''X'' a cohomology class of ''X''. The cohomology class measures the extent the bundle is "twisted" and whether it possesses sections. Characteristic classes are global invariants that measure the deviation of a local product structure from a global product structure. They are one of the unifying geometric concepts in algebraic topology, differential geometry, and algebraic geometry. The notion of characteristic class arose in 1935 in the work of Eduard Stiefel and Hassler Whitney about vector fields on manifolds. Definition Let ''G'' be a topological group, and for a topological space X, write b_G(X) for the set of isomorphism classes of principal ''G''-bundles over X. This b_G is a contravariant functor from Top (the category of topological spaces and continuous functions) to Set (the category of sets and functions), sending a map f\colon X\to Y to the pullback operation f^*\colon b_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
