Phillip Griffiths

Phillip Griffiths (2008)

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 in Beijing 2010

Griffiths studied at Wake Forest College in Winston-Salem , North Carolina (Bachelor 1959) and at Princeton University , where he received his doctorate in 1962 under Donald Spencer with On certain homogeneous complex manifolds . The previous year he attended Shiing-Shen Chern at the University of California, Berkeley , with whom he collaborated for decades. 1962–1964 he was Miller Fellow at Berkeley, then until 1967 professor. After a year visiting professor, he became a professor at Princeton in 1968 (where he was also at the Institute for Advanced Study from 1968 to 1970 ). 1972 to 1983 he was (Dwight Parker Robinson) professor at Harvard University (interrupted from 1975/6 as Miller Fellow at Berkeley). 1983 to 1991 he was at Duke University (where he was also principal). From 1991 to 2003 he was director of the Institute for Advanced Study at Princeton, where he has been Professor of Mathematics ever since.

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

In 1972 he gave a three-dimensional counterexample to the Lüroth problem with Herbert Clemens . Yuri Manin and Vasily Alexejewitsch Iskowskich did this independently .

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 at the ICM in Helsinki ( Some problems in complex analytic geometry with growth conditions ). In 1971 he received the Leroy P. Steele Prize from the American Mathematical Society . In 2008 he received the Brouwer Medal and in the same year the Wolf Prize for Mathematics (together with Pierre Deligne and David Mumford ). For 2014 he was awarded the Leroy P. Steele Prize and the Chern Medal .

Griffiths was elected to the US National Academy of Sciences in 1979, the American Philosophical Society in 1992 , the American Academy of Arts and Sciences in 1993, and the Accademia dei Lincei in 2001 . He is a fellow of the American Mathematical Society .

His PhD students include Joe Harris , Mark Green , David R. Morrison , Andrew Sommese , Ron Donagi , Robert Friedman, 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 vol., AMS 2003 (vol. 1 Analytic geometry, Cornalba, M.Green, W.Schmid (ed.), Vol. 2 Algebraic geometry, Arbarello, Harris (ed.), Vol. 3 Variations of Hodge structure, Clemens, Morrison (Ed.), Vol. 4 Differential systems, Bryant, Morrison (Ed.))
Complex analysis and Algebraic geometry , Bulletin AMS 1979, p. 595
A transcendental method in algebraic geometry , ICM 1970, Nizza, Vol. 1, p. 113
with Joseph (Joe) Harris Topics in algebraic and analytic geometry 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 Vol. 52, 1977
Griffiths, John Morgan Rational homotopy theory and differential forms 1981
this. Exterior differential systems and the calculus of variations 1983
with Robert Brown Gardner , SS Chern , HL Goldschmidt, Robert L. Bryant Exterior Differential Systems , MSRI Publ. 18, Springer Verlag 1991
with Gary Jensen: Differential systems and isometric embeddings 1987
Introduction to algebraic curves 1989
with Enrico Arbarello , Maurizio Cornalba , Harris Geometry of algebraic curves I , Springer, Grundlehren der Mathematischen Wissenschaften 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
with Mark Green, Matt Kerr: Mumford-Tate groups and domains: their geometry and arithmetic , Princeton University Press 2012
Griffiths Variations on a theorem of Abel , Inventiones Math. 1976
with Chern Abel's theorem and Webs , Annual Report DMV 1978
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: [1] , Part 3: [2]

Web links

Individual evidence

^ Griffiths Periods of integrals on algebraic manifolds , Part 1, Amer. J. Math., Vol. 90, 1968, pp. 568-626, Part 2, pp. 808-865, Part 3 Pub. Math. IHES, Vol. 38, 1970, pp. 228-286, on this Pierre Deligne Travaux de Griffiths , Seminar Bourbaki, No. 376, 1970

personal data
SURNAME	Griffiths, Phillip
ALTERNATIVE NAMES	Griffiths, Phillip Augustus; Griffiths, Phillip A.
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	October 18, 1938
PLACE OF BIRTH	Raleigh , North Carolina

[1] Griffiths Periods of integrals on algebraic manifolds , Part 1, Amer. J. Math., Vol. 90, 1968, pp. 568-626, Part 2, pp. 808-865, Part 3 Pub. Math. IHES, Vol. 38, 1970, pp. 228-286, on this Pierre Deligne Travaux de Griffiths , Seminar Bourbaki, No. 376, 1970