Phillip Griffiths

Phillip Augustus Griffiths ( born October 18, 1938 in Raleigh, North Carolina) is an American mathematician who works in the field of algebraic geometry.

Life and work

Griffiths was educated at Wake Forest College in Winston- Salem, North Carolina (Bachelor 1959) and at Princeton University, where he earned his doctorate at Donald Spencer 1962 On Certain homogeneous complex manifolds. The year before he visited Shiing - Shen Chern at the University of California, Berkeley, with whom he collaborated for decades. 1962-1964 he was a Miller Fellow at Berkeley, then to 1967, Professor. After a year visiting professorship, he became in 1968 Professor at Princeton (where he also at the Institute for Advanced Study, 1968-1970 ). 1972-1983 he was ( Dwight Parker Robinson ), a professor at Harvard University ( interrupted by the year 1975/6 as a Miller Fellow at Berkeley ). 1983 to 1991 he was at Duke University ( where he was also Rector ). 1991 to 2003 he was director of the Institute for Advanced Study in Princeton, where he is a professor of mathematics ever since.

Griffiths is best known for his work on complex - analytic algebraic geometry, where he also repeatedly forming bridges to the classical results of algebraic geometry ( as in his famous textbook with Harris Principles of algebraic geometry ). So he examined with the Chern connection of Abel's classical theorem for Abelian integrals addition to the geometry of the tissue, and with the geometric Harris disguise this theorem in classical Poncelet's closure theorem. In 1968 he introduced the concept of the variation of Hodge structure, which has since played an important role in algebraic geometry. Further activities of differential geometry and the geometry of partial differential equations (systems of external differential forms ).

In 1970 he gave a plenary lecture at the ICM in Nice (A Transcendental Method in Algebraic Geometry ), and in 1978 he was invited speaker on the ICM in Helsinki ( Some problems in complex analytic geometry with growth conditions ). He received the 1971 Leroy P. Steele Prize of the American Mathematical Society. In 2008 he received the Brouwer Medal, and in the same year, the Wolf Prize in Mathematics ( jointly with Pierre Deligne and David Mumford ). For 2014, the Leroy P. Steele Prize he was awarded.

Griffiths was elected in 1979 to the National Academy of Sciences of the USA, in 1995 the American Academy of Arts and Sciences and in 2001 in the Accademia dei Lincei. He is a Fellow of the American Mathematical Society.

His doctoral include Joe Harris, Mark Green, David R. Morrison, Andrew Sommese, Ron Donagi and Wilfried Schmid.

Griffiths has two children from his first marriage (from 1958) and two children from his second marriage (from 1968 ).

Works

  • Selected works, 4 vols, AMS 2003 ( Vol.1 Analytic geometry, Cornalba, M.Green, W.Schmid (Ed.), Algebraic geometry Vol.2, Arbarello, Harris ( ed.), Vol.3 Variations of Hodge structure, Clemens, Morrison ( ed.), Bd.4 differential systems, Bryant, Morrison ( ed.) )
  • Complex analysis and algebraic geometry, Bulletin AMS 1979, S.595
  • A method in transcendental algebraic geometry, ICM 1970, Nice, Vol.1, p.113
  • Joseph (Joe) Harris Topics in algebraic and analytic geometry in 1974
  • This. Entire holomorphic mappings in one and several complex variables 1976
  • This. Principles of algebraic geometry, Wiley 1978, 1994, 832 pages, ISBN 0-471-05059-8
  • This. An introduction to the theory of special divisors on algebraic curves 1980
  • This. A Poncelet theorem in space, Comm.Math.Helvetici Bd.52, 1977
  • Griffiths, John Morgan Rational homotopy theory and differential forms 1981
  • This. Exterior differential systems and the calculus of variations in 1983
  • With Robert Brown Gardner, SS Chern, HL Goldschmidt, Robert L. Bryant Exterior Differential Systems, MSRI Publ 18, Springer Verlag 1991
  • Gary Jensen: Differential systems and isometric embeddings in 1987
  • Introduction to algebraic curves 1989
  • With Enrico Arbarello, Maurizio Cornalba, Harris Geometry of algebraic curves I, Springer, basic teachings of the mathematical sciences, 1985, ISBN 978-0-387-90997-4.
  • With Mark Green On the tangent space to the space of algebraic cycles on a smooth algebraic variety, Princeton University Press 2005
  • With Mark Green, Matt Kerr: Hodge theory, complex geometry, and representation theory, American Mathematical Society 2013
  • Griffiths Variations on a theorem of Abel, Inventiones Math.1976
  • With Chern Abel's theorem and webs, Annual Report 1978 DMV
  • Griffiths, Harris Algebraic geometry and local differential geometry, Annales Scientifiques de l' École Normale Supérieure Sér. 4, vol 12, 1979, pp. 355-452
  • Carlson, Green, Griffiths, Harris infinitesimal variation on Hodge Structure 1, Compositio Math.1983, Part 2: Part 3:
Raleigh (North Carolina) Winston-Salem, North Carolina Joe Harris (mathematician) John Morgan (mathematician) Carl Ludwig Siegel Jean Leray Henri Cartan Oscar Zariski Hassler Whitney Mark Krein Kunihiko Kodaira Hans Lewy Samuel Eilenberg Atle Selberg Ennio de Giorgi Ilya Piatetski-Shapiro Lennart Carleson Mikhail Leonidovich Gromov Jacques Tits Joseph Keller Yakov Sinai Raoul Bott Jean-Pierre Serre John Tate Sergei Novikov (mathematician) Stephen Smale Luis Caffarelli Michael Artin Integrated Authority File
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