W. V. D. Hodge

Sir William Vallance Douglas Hodge FRS FRSE[2] (/hɒdʒ/; 17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer.

Hodge was born in Edinburgh in 1903, the younger son and second of three children of Archibald James Hodge (1869–1938), a searcher of records in the property market and a partner in the firm of Douglas and Company, and his wife, Jane (born 1875), daughter of confectionery business owner William Vallance.

[9] In 1926 he took up a teaching position at the University of Bristol, and began work on the interface between the Italian school of algebraic geometry, particularly problems posed by Francesco Severi, and the topological methods of Solomon Lefschetz.

According to Atiyah's memoir, Lefschetz and Hodge in 1931 had a meeting in Max Newman's rooms in Cambridge, to try to resolve issues.

The Hodge index theorem was a result on the intersection number theory for curves on an algebraic surface: it determines the signature of the corresponding quadratic form.

This result was sought by the Italian school of algebraic geometry, but was proved by the topological methods of Lefschetz.

In broad terms, Hodge theory contributes both to the discrete and the continuous classification of algebraic varieties.

Further developments by others led in particular to an idea of mixed Hodge structure on singular varieties, and to deep analogies with étale cohomology.