mathematics

Phillip Griffiths

Phillip Griffiths is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Phillip Griffiths rather than just read about it. In short: 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 is a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory, which forms part of transcendental algebraic geometry and which also touches upon major and dist…

Key takeaways

Phillip Griffiths belongs to mathematics; place it in that map before memorising details.
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Connect Phillip Griffiths to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Phillip Griffiths from memory before moving on to harder problems.

Reference excerpt

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 is a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory, which forms part of transcendental algebraic geometry and which also touches upon major and distant areas of differential geometry. 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 BS from Wake Forest College in 1959 and his PhD from Princeton University in 1962 after completing a doctoral dissertation, titled "On certain homogeneous complex manifolds", under the supervision of Donald Spencer. Afterwards, he held positions at University of California, Berkeley (1962–1967) and Princeton University (1967–1972). Griffiths was a professor of mathematics at Harvard University from 1972 to 1983. He was then a Provost and James B. Duke Professor of Mathematics at Duke University from 1983 to 1991. From 1991 to 2003, he was the Director of the Institute for Advanced Study (IAS) in Princeton, New Jersey. He remained as part of the Faculty of Mathematics at the IAS until June 2009, after which he has been emeritus at the IAS. 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. He is co-author, with Joe Harris, of Principles of Algebraic Geometry, a well-regarded textbook on complex algebraic geometry.

Awards and honors Griffiths was elected to the National Academy of Sciences in 1979 and the American Philosophical Society in 1992. In 2008, he was awarded the Wolf Prize (jointly with Deligne and Mumford) and the Brouwer Medal. In 2012, he became a fellow of the American Mathematical Society. Moreover, in 2014 Griffiths was awarded the Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society. 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. Vol. Tome 1. pp. 113–119. Archived from the original (PDF) on December 28, 2013. Retrieved March 15, 2014. 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. Helv. 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.

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Illustrations

Worked examples

Example 1 — a first encounter with Phillip Griffiths

Start with the simplest possible case. Write down what Phillip Griffiths claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Phillip Griffiths before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Phillip Griffiths ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Phillip Griffiths

In research: Phillip Griffiths appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Phillip Griffiths in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Phillip Griffiths is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Phillip Griffiths outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Phillip Griffiths in 20 minutes

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Frequently asked questions

What is Phillip Griffiths in simple terms?

Why does Phillip Griffiths matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Phillip Griffiths?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Phillip Griffiths.