J. A. Todd

For other people with the same name, seeJohn Todd (disambiguation).

J. A. Todd
Born	(1908-08-23)23 August 1908 Liverpool,England
Died	22 December 1994(1994-12-22)(aged 86) Croydon,England
Alma mater	University of Cambridge
Known for	Todd class Todd–Coxeter algorithm Chevalley–Shephard–Todd theorem Coset enumeration Todd genus Todd polynomials
Awards	Smith's Prize(1930) Rockefeller Fellowship(1933),Fellow of the Royal Society
Scientific career
Fields	Mathematician
Institutions	University of Manchester University of Cambridge
Thesis	Grassmannian Varieties / The Conic as a Space Element(1932)
Doctoral advisor	H.F. Baker
Doctoral students	Roger Penrose Geoffrey Shephard Christine Hamill

John Arthur ToddFRS(23 August 1908 – 22 December 1994) was an English mathematician who specialised in geometry.

Biography

He was born inLiverpool,and went up toTrinity College, Cambridgein 1925. He did research underH.F. Baker,and in 1931 took a position at theUniversity of Manchester.He became a lecturer at Cambridge in 1937. He remained at Cambridge for the rest of his working life.

Work

TheTodd classin the theory of the higher-dimensionalRiemann–Roch theoremis an example of acharacteristic class(or, more accurately, a reciprocal of one) that was discovered by Todd in work published in 1937. It used the methods of theItalian school of algebraic geometry.TheTodd–Coxeter processforcoset enumerationis a major method of computational algebra, and dates from a collaboration withH.S.M. Coxeterin 1936. In 1953 he and Coxeter discovered theCoxeter–Todd lattice.In 1954 he and G. C. Shephard classified the finitecomplex reflection groups.

Honours

In March 1948 he was elected aFellow of the Royal Society.

Selected publications

• 1936: "A practical method for enumerating cosets of a finite abstract group", Proc. Edin. Math. Soc. 5(1), 26-34 (withHarold Scott MacDonald Coxeter)
• 1937: "Rational quartic primals and associated Cremona transformations of four-dimensional space", Proc. London Math. Soc. s2-42, 324-339 (withDennis Babbage), "The geometrical invariants of algebraic varieties", Proc. London Math. Soc. 43(2), 127-138, "The arithmetical invariants of algebraic loci", Proc. London Math. Soc. 43(2), 190-225
• 1939: "The geometrical invariants of algebraic loci", Proc. London Math. Soc. 45, 410-424
• 1953: "An extreme duodenary form", Can. J. Math. 5, 384-392 (withHarold Scott MacDonald Coxeter)
• 1954: "Finite unitary reflection groups", Canadian Journal of Mathematics 6, 274-304 (withGeoffrey Colin Shephard)
• 1960: "On complex Stiefel manifolds", Mathematical Proc. Camb. Phil. Soc. 56, 342-353 (withMichael Atiyah)
• 1966: "A representation of the Mathieu group M₂₄as a collineation group ", Ann. Mat. Pura Appl. 71(4), 199-238

External links

• Todd's Mactutor biography