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W. V. D. Hodge
Sir William Vallance Douglas Hodge (; 17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer. His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on subsequent work in geometry. Life and career Hodge was born in Edinburgh in 1903, the younger son and second of three children of Jane (born 1875) and Archibald James Hodge (1869–1938) His father was a searcher of records in the property market and a partner in the firm of Douglas and Company and his mother was the daughter of a confectionery business owner William Vallance. They lived at 1 Church Hill Place in the Morningside district. He attended George Watson's College, and studied at the University of Edinburgh graduating with an MA in 1923. With help from E. T. Whittaker, whose son J. M. Whittaker was a college friend, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edinburgh
Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh had a population of in , making it the List of towns and cities in Scotland by population, second-most populous city in Scotland and the List of cities in the United Kingdom, seventh-most populous in the United Kingdom. The Functional urban area, wider metropolitan area had a population of 912,490 in the same year. Recognised as the capital of Scotland since at least the 15th century, Edinburgh is the seat of the Scottish Government, the Scottish Parliament, the Courts of Scotland, highest courts in Scotland, and the Palace of Holyroodhouse, the official residence of the Monarchy of the United Kingdom, British monarch in Scotland. It is also the annual venue of the General Assembly of the Church of Scotland. The city has long been a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Watson's College
George Watson's College is a co-educational Private schools in the United Kingdom, private day school in Scotland, situated on Colinton Road, in the Merchiston area of Edinburgh. It was first established as a Scottish education in the eighteenth century#School building, hospital school in 1723, became a day school in 1871, and was merged with its sister school George Watson's Ladies College in 1974. It is a Merchant Company of Edinburgh school and a member of the Headmasters' and Headmistresses' Conference. History Foundation The school was established according to the instructions of George Watson (accountant), George Watson (1654–1723) who bequeathed the bulk of his fortune of £12,000 – a vast sum in 1723 – to found a school for the provision of post-primary boarding education. George Watson, since 1696, had been clerk to Sir John Dick. Unlike his father, John Watson, George was not a member of the Merchant Company of Edinburgh, but he was impressed by their co-foun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solomon Lefschetz
Solomon Lefschetz (; 3 September 1884 – 5 October 1972) was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations. Life He was born in Moscow, the son of Alexander Lefschetz and his wife Sarah or Vera Lifschitz, Jewish traders who used to travel around Europe and the Middle East (they held Ottoman passports). Shortly thereafter, the family moved to Paris. He was educated there in engineering at the École Centrale Paris, but emigrated to the US in 1905. He was badly injured in an industrial accident in 1907, losing both hands. He moved towards mathematics, receiving a Ph.D. in algebraic geometry from Clark University in Worcester, Massachusetts in 1911. He then took positions in University of Nebraska and University of Kansas, moving to Princeton University in 1924, where he was soon given a permanent position. He remained there until 1953. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francesco Severi
Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematician. He was the chair of the committee on Fields Medal in 1936, at the first delivery. Severi was born in Arezzo, Italy. He is famous for his contributions to algebraic geometry and the theory of functions of several complex variables. He became the effective leader of the Italian school of algebraic geometry. Together with Federigo Enriques, he won the '' Bordin prize'' from the French Academy of Sciences. He contributed in a major way to birational geometry, the theory of algebraic surfaces, in particular of the curves lying on them, the theory of moduli spaces and the theory of functions of several complex variables. He wrote prolifically, and some of his work (following the intuition-led approach of Federigo Enriques) has subsequently been shown to be not rigorous according to the then new standards set in particular by Oscar Zariski and André Weil. Although many of his arguments have si ... [...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 att ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bristol
The University of Bristol is a public university, public research university in Bristol, England. It received its royal charter in 1909, although it can trace its roots to a Merchant Venturers' school founded in 1595 and University College, Bristol, which had been in existence since 1876. Bristol Medical School, founded in 1833, was merged with the University College in 1893, and later became the university's school of medicine. The university is organised into #Academic structure, six academic faculties composed of multiple schools and departments running over 200 undergraduate courses, largely in the Tyndalls Park area of the city. It had a total income of £1.06 billion in 2023–24, of which £294.1 million was from research grants and contracts, with an expenditure of £768.7 million. It is the largest independent employer in Bristol. Current academics include 23 fellows of the Academy of Medical Sciences, 13 fellows of the British Academy, 43 fellows of the Academy of Soc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Tripos
The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics, University of Cambridge, Faculty of Mathematics at the University of Cambridge. Origin In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate students of the University of Cambridge. Prior to 1824, the Mathematical Tripos was formally known as the "Senate House Examination". From about 1780 to 1909, the "Old Tripos" was distinguished by a number of features, including the publication of an order of merit of successful candidates, and the difficulty of the mathematical problems set for solution. By way of example, in 1854, the Tripos consisted of 16 papers spread over eight days, totaling 44.5 hours. The total number of questions was 211. It was divided into two parts, with Part I (the first three days) covering more elementary topics. The actual marks for the exams were never published, but there is reference to an exam in the 1860s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morningside, Edinburgh
Morningside is a district and former village in the south of Edinburgh, Scotland. It lies alongside the main arterial Morningside Road, part of an ancient route from Edinburgh to the south west of Scotland. The original village served several farms and estates in the area. In the 19th century, it developed as a residential suburb, its growth being stimulated by the arrival of a railway service and other transport improvements. Location Morningside is located approximately south of Edinburgh's city centre. It is bordered by Bruntsfield to the north, the Grange to the north east, Blackford to the east, Comiston to the south, Greenbank to the south west, and Merchiston to the north west. It includes Braidburn Valley Park, the Royal Edinburgh Hospital and parts of the Braid Hills and Blackford Hill. The district is bisected by the A702 road, which forms part of an ancient route from Edinburgh to Biggar and the south west of Scotland. The south eastern part of Mornings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kähler Manifold
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähler in 1933. The terminology has been fixed by André Weil. Kähler geometry refers to the study of Kähler manifolds, their geometry and topology, as well as the study of structures and constructions that can be performed on Kähler manifolds, such as the existence of special connections like Hermitian Yang–Mills connections, or special metrics such as Kähler–Einstein metrics. Every smooth complex projective variety is a Kähler manifold. Hodge theory is a central part of algebraic geometry, proved using Kähler metrics. Definitions Since Kähler manifolds are equipped with several compatible structures, they can be described from different points of vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological
Topology (from the Greek words , and ) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
