J. A. Todd
Encyclopedia
John Arthur Todd FRS (23 August 1908 – 22 December 1994) was a British
geometer. He was born in Liverpool
, and went to Trinity College
of the University of Cambridge
in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester
. He became a lecturer at Cambridge in 1937. He remained at Cambridge for the rest of his working life.
The Todd class
in the theory of the higher-dimensional Riemann–Roch theorem
is an example of a characteristic class
(or, more accurately, a reciprocal of one) that was discovered by Todd in work published in 1937. It used the methods of the Italian school of algebraic geometry
. The Todd–Coxeter process for coset enumeration
is a major method of computational algebra, and dates from a collaboration with H.S.M. Coxeter in 1936. In 1953 he and Coxeter discovered the Coxeter–Todd lattice
. In 1954 he and G. C. Shephard classified the finite complex reflection group
s.
In March 1948 he was elected a Fellow of the Royal Society.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
geometer. He was born in Liverpool
Liverpool
Liverpool is a city and metropolitan borough of Merseyside, England, along the eastern side of the Mersey Estuary. It was founded as a borough in 1207 and was granted city status in 1880...
, and went to Trinity College
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
of the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester
University of Manchester
The University of Manchester is a public research university located in Manchester, United Kingdom. It is a "red brick" university and a member of the Russell Group of research-intensive British universities and the N8 Group...
. He became a lecturer at Cambridge in 1937. He remained at Cambridge for the rest of his working life.
The Todd class
Todd class
In mathematics, the Todd class is a certain construction now considered a part of the theory in algebraic topology of characteristic classes. The Todd class of a vector bundle can be defined by means of the theory of Chern classes, and is encountered where Chern classes exist — most notably...
in the theory of the higher-dimensional Riemann–Roch theorem
Riemann–Roch theorem
The Riemann–Roch theorem is an important tool in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles...
is an example of a characteristic class
Characteristic class
In mathematics, a characteristic class is a way of associating to each principal bundle on a topological space X a cohomology class of X. The cohomology class measures the extent to which the bundle is "twisted" — particularly, whether it possesses sections or not...
(or, more accurately, a reciprocal of one) that was discovered by Todd in work published in 1937. It used the methods of the Italian school of algebraic geometry
Italian school of algebraic geometry
In relation with the history of mathematics, the Italian school of algebraic geometry refers to the work over half a century or more done internationally in birational geometry, particularly on algebraic surfaces. There were in the region of 30 to 40 leading mathematicians who made major...
. The Todd–Coxeter process for coset enumeration
Coset enumeration
In mathematics, coset enumeration is the problem of counting the cosets of a subgroup H of a group G given in terms of a presentation. As a by-product, one obtains a permutation representation for G on the cosets of H...
is a major method of computational algebra, and dates from a collaboration with H.S.M. Coxeter in 1936. In 1953 he and Coxeter discovered the Coxeter–Todd lattice
Coxeter–Todd lattice
In mathematics, the Coxeter–Todd lattice K12, discovered by , is a the 12-dimensional even integral lattice of discriminant 36 with no norm-2 vectors...
. In 1954 he and G. C. Shephard classified the finite complex reflection group
Complex reflection group
In mathematics, a complex reflection group is a group acting on a finite-dimensional complex vector space, that is generated by complex reflections: non-trivial elements that fix a complex hyperplane in space pointwise...
s.
In March 1948 he was elected a Fellow of the Royal Society.