W. V. D. Hodge

Sir William Vallance Douglas Hodge (hɒdʒ; 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. 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. They lived at 1 Church Hill Place in the Morningside district. He attended George Watson's College, and studied at Edinburgh University, graduating MA in 1923. With help from E. T. Whittaker, whose son J. M. Whittaker was a college friend, he then took the Cambridge Mathematical Tripos. At Cambridge he fell under the influence of the geometer H. F. Baker. He gained a Cambridge BA degree in 1925, receiving the MA in 1930 and the Doctor of Science (ScD) degree in 1950. 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. This made his reputation, but led to some initial scepticism on the part of 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. In the end Lefschetz was convinced. In 1928 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir Edmund Taylor Whittaker, Ralph Allan Sampson, Charles Glover Barkla, and Sir Charles Galton Darwin. He was awarded the Society's Gunning Victoria Jubilee Prize for the period 1964 to 1968. In 1930 Hodge was awarded a Research Fellowship at St. John's College, Cambridge.

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W. V. D. Hodge

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.

H. F. Baker

Henry Frederick Baker FRS FRSE (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups. He was born in Cambridge the son of Henry Baker, a butler, and Sarah Ann Britham. He was educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.

Étale Motives and the Hodge Conjecture

Explores étale motivic cohomology and the Hodge conjecture with a focus on counter-examples.

Algebraic Cycles and Etale Cohomology

Explores algebraic cycles, etale cohomology, and counterexamples to the Hodge conjecture.

L-values and Extensions

Explores de Rham theory, L-values, and extensions, including special value formulas and examples related to Hecke characters and modular forms.