Phillip Griffiths | |
---|---|

Phillip Griffiths in 2008 (photo from MFO) | |

Born | |

Nationality | American |

Alma mater | Wake Forest College (B.S.) (1959) Princeton University (Ph.D) (1962) |

Known for | complex algebraic geometry complex differential geometry variations of Hodge moduli algebraic cycles Hodge theory |

Awards | Chern Medal (2014) Leroy P. Steele Prize for Lifetime Achievement (2014) Wolf Prize (2008) Brouwer Medal (2008) Leroy P. Steele Prize (1971) |

Scientific career | |

Fields | Mathematics |

Institutions | University of California, Berkeley Princeton University Harvard University Duke University Institute for Advanced Study |

Doctoral advisor | Donald C. Spencer |

Doctoral students | Herbert Clemens Howard Garland Mark Lee Green Joe Harris David R. Morrison Wilfried Schmid Andrew J. Sommese |

Influences | Shiing-Shen Chern |

**Phillip Augustus Griffiths IV** (born October 18, 1938) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory. He also worked on partial differential equations, coauthored with Shiing-Shen Chern, Robert Bryant and Robert Gardner on Exterior Differential Systems.

## Professional career

He received his B.S. from Wake Forest College in 1959 and his Ph.D. from Princeton University in 1962 after completing a doctoral dissertation, titled "On certain homogeneous complex manifolds", under the supervision of Donald Spencer.^{[1]} Afterwards, he held positions at University of California, Berkeley (1962–1967) and Princeton University (1967–1972).^{[citation needed]} Griffiths was a professor of mathematics at Harvard University from 1972 to 1983.^{[2]} He was then a Provost and James B. Duke Professor of Mathematics at Duke University from 1983 to 1991.^{[2]} From 1991 to 2003, he was the Director of the Institute for Advanced Study (IAS) in Princeton, New Jersey.^{[2]} He remained as part of the Faculty of Mathematics at the IAS until June 2009, after which he has been emeritus at the IAS.^{[2]} He has published on algebraic geometry, differential geometry, geometric function theory, and the geometry of partial differential equations.

Griffiths serves as the Chair of the Science Initiative Group.^{[2]} He is co-author, with Joe Harris, of *Principles of Algebraic Geometry*, a well-regarded textbook on complex algebraic geometry.^{[3]}

## Awards and honors

In 2008 he was awarded the Wolf Prize (jointly with Deligne and Mumford)^{[4]} and the Brouwer Medal.^{[5]} In 2012 he became a fellow of the American Mathematical Society.^{[6]} Moreover, in 2014 Griffiths was awarded the Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society.^{[7]} Also in 2014, Griffiths was awarded the Chern Medal for lifetime devotion to mathematics and outstanding achievements.

## Selected publications

### Articles

- Griffiths, P. A. (1962). "On certain homogeneous complex manifolds".
*Proc Natl Acad Sci U S A*.**48**(5): 780–783. Bibcode:1962PNAS...48..780G. doi:10.1073/pnas.48.5.780. PMC 220851. PMID 16590943. - Griffiths, P. A. (1963). "Some remarks on automorphisms, analytic bundles, and embeddings of complex algebraic varieties".
*Proc Natl Acad Sci U S A*.**49**(6): 817–820. Bibcode:1963PNAS...49..817G. doi:10.1073/pnas.49.6.817. PMC 300013. PMID 16591103. - Griffiths, Phillip A. (1963). "On the differential geometry of homogeneous vector bundles".
*Trans. Amer. Math. Soc*.**109**: 1–34. doi:10.1090/s0002-9947-1963-0162248-5. MR 0162248. - Griffiths, P. A. (1966). "The residue calculus and some transcendental results in algebraic geometry, I".
*Proc Natl Acad Sci U S A*.**55**(5): 1303–1309. Bibcode:1966PNAS...55.1303G. doi:10.1073/pnas.55.5.1303. PMC 224316. PMID 16591357. - Griffiths, P. A. (1966). "The residue calculus and some transcendental results in algebraic geometry, II".
*Proc Natl Acad Sci U S A*.**55**(6): 1392–1395. Bibcode:1966PNAS...55.1392G. doi:10.1073/pnas.55.6.1392. PMC 224330. PMID 16578635. - Griffiths, P. A. (1966). "Some results on locally homogeneous complex manifolds".
*Proc Natl Acad Sci U S A*.**56**(2): 413–416. Bibcode:1966PNAS...56..413G. doi:10.1073/pnas.56.2.413. PMC 224387. PMID 16591369. - "A transcendental method in algebraic geometry" (PDF).
*Actes, Congrès intern. math. 1970*. Tome 1. pp. 113–119. - Griffiths, Phillip A. (1970). "Periods of integrals on algebraic manifolds".
*Bull. Amer. Math. Soc*.**76**(2): 228–296. doi:10.1090/s0002-9904-1970-12444-2. MR 0258824. - Deligne, Pierre; Griffiths, Phillip; Morgan, John; Sullivan, Dennis (1975). "Real homotopy theory of Kähler manifolds".
*Inventiones Mathematicae*.**29**(3): 245–274. Bibcode:1975InMat..29..245D. doi:10.1007/BF01389853. MR 0382702. S2CID 1357812. - with Joe Harris: Griffiths, Phillip; Harris, Joe (1977). "A Poncelet theorem in space".
*Comment. Math. Helvetici*.**52**: 145–160. doi:10.1007/bf02567361. S2CID 119686396. - with S. S. Chern: "Abel's Theorem and Webs" (PDF).
*Jber. D. Dt. Math.-Verein*.**80**: 13–110. 1978. - Griffiths, Phillip A. (1979). "Complex analysis and algebraic geometry".
*Bull. Amer. Math. Soc*.**1**(4): 595–626. doi:10.1090/s0273-0979-1979-14640-8. MR 0532551. - Griffiths, Phillip A. (1982). "Poincaré and algebraic geometry".
*Bull. Amer. Math. Soc. (N.S.)*.**6**(2): 147–159. doi:10.1090/s0273-0979-1982-14967-9. MR 0640942.

### Books

*Mumford–Tate groups and domains: their geometry and arithmetic*, with Mark Green and Matt Kerr, Princeton University Press, 2012, ISBN 978-0-691-154251^{[8]}*Selected Works of Phillip A. Griffiths with Commentary*. 4 vols. American Mathematical Soc. 2003. in pbk: Griffiths, Phillip; Cornalba, Maurizio (2003).*vol. 1*. ISBN 0-8218-2086-9. Griffiths, Phillip; Cornalba, Maurizio (2003).*vol. 2*. ISBN 0-8218-2087-7. Griffiths, Phillip; Cornalba, Maurizio (2003).*vol. 3*. ISBN 0-8218-2088-5. Griffiths, Phillip; Cornalba, Maurizio (2003).*vol. 4*. ISBN 0-8218-2089-3.*Exterior differential systems and Euler-Lagrange partial differential equations*, with Robert Bryant and Daniel Grossman, University of Chicago Press, 2003, ISBN 0-226-07793-4 cloth; ISBN 0-226-07794-2^{[9]}*Introduction to Algebraic Curves*, American Mathematical Society, Providence, RI, 1989, ISBN 0821845306*Differential Systems and Isometric Embeddings*, with Gary R. Jensen, Princeton University Press, Princeton, NJ, 1987, ISBN 0-691-08429-7^{[10]}*Topics in Transcendental Algebraic Geometry*, Princeton University Press, Princeton, NJ, 1984, ISBN 0691083355*Exterior Differential Systems and the Calculus of Variations*, Birkhäuser, Boston, 1983, ISBN 3764331038*Rational Homotopy Theory and Differential Forms*, with John W. Morgan, Birkhäuser, Boston, 1981, ISBN 3764330414^{[11]}*Principles of Algebraic Geometry*, with Joe Harris, Wiley, New York, 1978, ISBN 0471327921^{[12]}*Entire Holomorphic Mappings in One and Several Complex Variables*, Princeton University Press, Princeton, NJ, 1976, ISBN 0691081719^{[13]}

## References

**^**Griffith, Phillip (1962). "On certain homogeneous complex manifolds".*Proceedings of the National Academy of Sciences*.**48**(5): 780. Bibcode:1962PNAS...48..780G. doi:10.1073/pnas.48.5.780.- ^
^{a}^{b}^{c}^{d}^{e}"Phillip A. Griffiths". Institute for Advanced Study. Retrieved September 11, 2020. **^**Review: Phillip Griffiths and Joseph Harris, Principles of algebraic geometry by Joseph Lipman**^**"The Wolf Foundation Prize in Mathematics".**^**Institute for Advanced Study: Royal Dutch Mathematical Society Awards Tri-annual Brouwer Prize to Phillip A. Griffiths**^**List of Fellows of the American Mathematical Society, retrieved 2013-01-19.**^**AMS Steel Prizes,**^**Pearlstein, Gregory (2015). "Review of*Mumford–Tate groups and domains: their geometry and arithmetic*by Mark Green, Phillip A. Griffiths, and Matt Kerr".*Bull. Amer. Math. Soc. (N.S.)*.**52**(4): 711–724. doi:10.1090/bull/1505.**^**Olver, Peter J. (2005). "Review of*Exterior differential systems and Euler-Lagrange partial differential equations*by Robert Bryant, Phillip Griffiths, and Daniel Grossman".*Bulletin of the American Mathematical Society*. (N.S.).**42**(3): 407–412. doi:10.1090/S0273-0979-05-01062-1.**^**Jacobowitz, Howard (1988). "Review:*Differential systems and isometric embeddings*, by P. A. Griffiths and Gary R. Jensen" (PDF).*Bulletin of the American Mathematical Society*. (N.S.).**19**(2): 498–504. doi:10.1090/s0273-0979-1988-15717-5.**^**Chen, K. T. (1983). "Review:*Rational homotopy theory and differential forms*, by P. A. Griffiths and J. W. Morgan" (PDF).*Bulletin of the American Mathematical Society*. (N.S.).**8**(3): 496–498. doi:10.1090/s0273-0979-1983-15135-2.**^**Lipman, Joseph (1980). "Review of*Principles of algebraic geometry*by Phillip Griffiths and Joseph Harris".*Bulletin of the American Mathematical Society*. (N.S.).**2**: 197–200. doi:10.1090/S0273-0979-1980-14717-5.**^**Drasin, David (1977). "Review:*Entire holomorphic mappings in one and several complex variables*, by P. A. Griffiths" (PDF).*Bulletin of the American Mathematical Society*. (N.S.).**83**(5): 942–946. doi:10.1090/s0002-9904-1977-14330-9.