W. V. D. Hodge
William Vallance Douglas Hodge ( born June 17, 1903 in Edinburgh, † 7 July 1975 in Cambridge ) was a British mathematician.
Life and work
He was the son of Janet Vallence, daughter of a confectionery dealer, and Archibald James Hodge, a real estate agent. He had an older brother and a younger sister.
After education at the George Watson 's College, he studied from 1920 with Edmund Taylor Whittaker ( 1873-1956 ) in Edinburgh, then - on the advice Whittackers - from 1923 at St John's College, Cambridge. In 1926 he took a teaching position at the University of Bristol, which he held until 1931, and until 1932 a study visit at Solomon Lefschetz ( 1884-1972 ) followed in Princeton. From 1933 on, he worked in Cambridge as a lecturer and from 1935 as a Fellow of Pembroke College, from 1936 to 1970, he finally had the Lowdean Professor of Astronomy and Geometry held. In 1938 he became a member of the Royal Society of London in 1958 and Master of Pembroke College, a job which he held until his retirement.
During his time in Bristol, he married Kathleen Anne Cameron, the daughter of a manager of the Edinburgh branch of the Oxford University Press. The couple had a son and a daughter.
His main area of work were the algebraic geometry and differential geometry. He developed the connections between geometry, analysis and topology, and brought some of his greatest achievements in the theory of harmonic integrals on algebraic manifolds and Riemannian - to the latter, he described the space of harmonic forms. He proved this decomposition rates ( decomposition theorem of Kodaira - Hogde, Hodge manifold), and deduced from sum representations for Betti numbers from.
In 1947 he wrote with Daniel Pedoe a four-volume broad-based representation of algebraic geometry, Methods of Algebraic Geometry, in the still, the classical theory has been shown and which should replace the outdated Principles of Geometry of HFBaker in England.
Hodge was one of the initiators of the British Mathematical Colloquium 1952 and one of the principal founders of the International Mathematical Union and the vice president of 1954 until 1958. 1957 him the Royal Medal of the Royal Society was awarded. In 1950 he gave a plenary lecture at the International Congress of Mathematicians in Cambridge (Massachusetts ) (The topological invariants of algebraic varieties ).
Through its work, the following terms are connected:
- Hodge derivation
- Hodge algebra
- Hodge identities
- Hodge manifold
- Hodge metric
- Hodge structure
- Mixed Hodge structure
- Hodge theorem
- Hodge theory
- Hodge decomposition
- Hodge star operator
- Decomposition theorem of Hodge - Kodaira
And not least the conjecture of Hodge, one of the great unsolved problems in algebraic geometry.
Works
- HD William Hodge, Daniel Pedoe: Methods of algebraic geometry, 4 vols, ( Vol.1 Algebraic preliminaries, Vol.2 Projective space, Bd.3 General theory of algebraic varieties in projective space, Bd.4 Quadrics and Grassmannian varieties ), Reprint 1994 ( first 1947), Cambridge University Press
- Hodge theory and application of harmonic integrals, Teubner 1958, engl. Theory and Applications of harmonic integrals, Cambridge University Press 1989