Hirschfeld received his doctorate in 1966 from the University of Edinburgh with thesis advisor William Leonard Edge and thesis The geometry of cubic surfaces, and Grace's extension of the double-six, over finite fields.[1]
In 1979 Hirschfeld published the first of a trilogy on Galois geometry, pegged at a level depending only on "the group theory and linear algebra taught in a first degree course, as well as a little projective geometry, and a very little algebraic geometry." When q is a prime power then there is a finite field GF(q) with q elements called a Galois field. A vector space over GF(q) of n + 1 dimensions produces an n-dimensional Galois geometry PG(n,q) with its subspaces: one-dimensional subspaces are the points of the Galois geometry and two-dimensional subspaces are the lines. Non-singular linear transformations of the vector space provide motions of PG(n,q). The first book (1979) covered PG(1,q) and PG(2,q). The second book addressed PG(3,q) and the third PG(n,q). Chapters are numbered sequentially through the trilogy: 14 in the first book, 15 to 21 in the second, and 22 to 27 in the third. Finite geometry has contributed to coding theory, such as algebraic geometry codes, so the field is supported by computer science. In the preface of the 1991 text Hirschfeld summarizes the status of Galois geometry, mentioning maximum distance separable code, mathematics journals publishing finite geometry, and conferences on combinatorics featuring Galois geometry. Colleague Joseph A. Thas is coauthor of General Galois Geometries on PG(n,q) where n ≥ 4.
Hirschfeld was cited as the ultimate editor of Design Theory (1986).[3]
^"Official Web Pages of the ICA". The Institute of Combinatorics and Its Applications.
^Sherk, Frank Arthur (1981). "Review of Projective geometries over finite fields by J. W. P. Hirschfeld". Bulletin of the American Mathematical Society. New Series. 4 (2): 213–215. doi:10.1090/S0273-0979-1981-14887-4.
^Hagedorn, Thomas (2 July 2008). "Review of Algebraic Curves over a Finite Field by J. W. P. Hirschfeld, G. Korchmáros, and F. Torres". MAA Reviews, Mathematical Association of America.
james, william, peter, hirschfeld, born, 1940, australian, mathematician, resident, united, kingdom, specializing, combinatorial, geometry, geometry, finite, fields, emeritus, professor, tutorial, fellow, university, sussex, from, left, aart, blokhuis, dieter,. James William Peter Hirschfeld born 1940 is an Australian mathematician resident in the United Kingdom specializing in combinatorial geometry and the geometry of finite fields He is an emeritus professor and Tutorial Fellow at the University of Sussex From left Aart Blokhuis James William Peter Hirschfeld Dieter Jungnickel and Joseph A Thas at the MFO 2001Hirschfeld received his doctorate in 1966 from the University of Edinburgh with thesis advisor William Leonard Edge and thesis The geometry of cubic surfaces and Grace s extension of the double six over finite fields 1 To pursue further studies in finite geometry Hirschfeld went to University of Perugia and University of Rome with support from the Royal Society and Accademia nazionale dei Lincei He edited Beniamino Segre s 100 page monograph Introduction to Galois Geometries 1967 2 In 1979 Hirschfeld published the first of a trilogy on Galois geometry pegged at a level depending only on the group theory and linear algebra taught in a first degree course as well as a little projective geometry and a very little algebraic geometry When q is a prime power then there is a finite field GF q with q elements called a Galois field A vector space over GF q of n 1 dimensions produces an n dimensional Galois geometry PG n q with its subspaces one dimensional subspaces are the points of the Galois geometry and two dimensional subspaces are the lines Non singular linear transformations of the vector space provide motions of PG n q The first book 1979 covered PG 1 q and PG 2 q The second book addressed PG 3 q and the third PG n q Chapters are numbered sequentially through the trilogy 14 in the first book 15 to 21 in the second and 22 to 27 in the third Finite geometry has contributed to coding theory such as algebraic geometry codes so the field is supported by computer science In the preface of the 1991 text Hirschfeld summarizes the status of Galois geometry mentioning maximum distance separable code mathematics journals publishing finite geometry and conferences on combinatorics featuring Galois geometry Colleague Joseph A Thas is coauthor of General Galois Geometries on PG n q where n 4 Hirschfeld was cited as the ultimate editor of Design Theory 1986 3 In 2018 he received the 2016 Euler Medal 4 Selected publications edit1979 Projective Geometries over Finite Fields Oxford University Press 5 2nd ed Oxford Clarendon Press 1998 1985 Finite Projective Spaces of Three Dimensions Oxford University Press 1991 with Joseph A Thas General Galois Geometries Oxford University Press 2016 paperback reprint 2008 with Gabor Korchmaros amp Fernando Torres Algebraic Curves over a Finite Field Princeton University Press 6 References edit James William Peter Hirschfeld at the Mathematics Genealogy Project Preface page vii Projective Geometries over Finite Fields Beth Thomas Jungnickel Dieter Lenz Hanfried 1986 Design Theory Cambridge Cambridge University Press p 10 2nd ed 1999 ISBN 978 0 521 44432 3 Official Web Pages of the ICA The Institute of Combinatorics and Its Applications Sherk Frank Arthur 1981 Review of Projective geometries over finite fields by J W P Hirschfeld Bulletin of the American Mathematical Society New Series 4 2 213 215 doi 10 1090 S0273 0979 1981 14887 4 Hagedorn Thomas 2 July 2008 Review of Algebraic Curves over a Finite Field by J W P Hirschfeld G Korchmaros and F Torres MAA Reviews Mathematical Association of America External links editProf James Hirschfeld at University of Sussex Retrieved from https en wikipedia org w index php title James William Peter Hirschfeld amp oldid 1158495919, wikipedia, wiki, book, books, library,
