William Vallance Douglas Hodge

William Vallance Douglas Hodge (born June 17, 1903 in Edinburgh , † July 7, 1975 in Cambridge ) was a British mathematician .

Life

He was the son of Janet Vallence, daughter of a candy merchant, and Archibald James Hodge, a real estate agent. He had an older brother and a younger sister.

After finishing school at George Watson's College, he studied from 1920 with Edmund Taylor Whittaker (1873-1956) in Edinburgh, then - on the advice of Whittacker - from 1923 at St John's College in Cambridge . In 1926 he took on a teaching position at the University of Bristol , which he filled out until 1931, and which was followed by a study visit with Solomon Lefschetz (1884–1972) in Princeton until 1932 . From 1933 he worked in Cambridge as a lecturer and from 1935 as a Fellow of Pembroke College , from 1936 to 1970 he finally held the Lowdean Professorship for Astronomy and Geometry. In 1928 he became a member ( Fellow ) of the Royal Society of Edinburgh and in 1938 of the Royal Society of London and 1958 Master of the Pembroke College, a task that he held until his retirement .

While in Bristol , he married Kathleen Anne Cameron, the daughter of a manager of the Edinburgh branch of Oxford University Press. The couple had a son and a daughter.

His main field of work was algebraic geometry and differential geometry . He developed the connections between geometry , analysis and topology , and did some of his greatest achievements in the theory of harmonic integrals on algebraic and Riemannian manifolds - the latter describing the space of harmonic forms . For this he proved decomposition theorems ( decomposition theorem of Hogde-Kodaira , Hodge manifold ) and derived summation representations for Betti numbers from them.

In 1947 he and Daniel Pedoe wrote a four-volume, broad-based presentation of the Algebraic Geometry Methods of Algebraic Geometry , in which the classical theory was still presented and which in England was supposed to replace the outdated Principles of Geometry by HFBaker.

Hodge was one of the initiators of the British Mathematical Colloquium and in 1952 one of the key founders of the International Mathematical Union and its Vice President from 1954 to 1958. In 1957 he was awarded the Royal Medal and in 1974 the Copley Medal of the Royal Society . In 1950 he gave a plenary lecture at the International Congress of Mathematicians in Cambridge (Massachusetts) (The topological invariants of algebraic varieties). In 1958 he was elected to the American Academy of Arts and Sciences , 1959 to the National Academy of Sciences , 1964 to the American Philosophical Society and 1963 to the corresponding member of the Göttingen Academy of Sciences .

The following terms are associated with his work:

• Hodge derivative
• Hodge algebra
• Hodge identities
• Hodge manifold
• Hodge metric
• Hodge structure
• Mixed Hodge structure
• Hodge theorem
• Hodge theory
• Hodge decomposition
• Hodge star operator
• Decomposition theorem from Hodge-Kodaira

and last but not least, Hodge's conjecture , one of the great unsolved problems of algebraic geometry .

Works

• William HD Hodge, Daniel Pedoe: Methods of algebraic geometry , 4 vols., (Vol. 1 Algebraic preliminaries, Vol. 2 Projective space, Vol. 3 General theory of algebraic varieties in projective space, Vol. 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

literature

• Michael Atiyah : Biography in Bulletin of the London Mathematical Society, Vol. 9, 1977, pp. 99-118 and Biographical Memoirs of the Royal Society, Vol. 22, 1976, pp. 169-192 (reprinted in Atiyah's Gesammelte Abhandlungen Vol. 1) online

Web links

• John J. O'Connor, Edmund F. Robertson :  William Vallance Douglas Hodge. In: MacTutor History of Mathematics archive .
• Literature by and about William Vallance Douglas Hodge in the WorldCat bibliographic database

Individual evidence

1. ^ Member History: William Hodge. American Philosophical Society, accessed October 2, 2018 . 
2. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 116.