mathematics

Terence Gaffney

Terence Gaffney 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 Terence Gaffney rather than just read about it. In short: Terence Gaffney (born 9 March 1948) is an American mathematician who has made fundamental contributions to singularity theory – in particular, to the fields of singularities of maps and equisingularity theory. Professional career He is a Professor of Mathematics at Northeastern University.

Key takeaways

Terence Gaffney belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Terence Gaffney to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Terence Gaffney from memory before moving on to harder problems.

Reference excerpt

Terence Gaffney (born 9 March 1948) is an American mathematician who has made fundamental contributions to singularity theory – in particular, to the fields of singularities of maps and equisingularity theory.

Professional career He is a Professor of Mathematics at Northeastern University. He did his undergraduate studies at Boston College. He received his Ph.D. from Brandeis University in 1975 under the direction of Edgar Henry Brown Jr. and Harold Levine. In 1975 he became an AMS Centennial Fellow at MIT and a year later he joined the Brown University faculty as Tamarkind instructor. In 1979 Gaffney became professor at Northeastern University where he has remained ever since. He has served as department chair, graduate director, chair of the undergraduate curriculum committee, and faculty senator.

Selected publications Gaffney, T. (1976), "On the order of determination of a finitely determined germ", Inventiones Mathematicae, 37 (2): 83–92, Bibcode:1976InMat..37...83G, doi:10.1007/BF01418963, S2CID 120952434. Gaffney, T. (1979), "A note on the order of determination of a finitely determined germ", Inventiones Mathematicae, 52 (2): 127–130, Bibcode:1979InMat..52..127G, doi:10.1007/BF01403059, S2CID 119519319. Gaffney, T.; Lazarsfeld, Robert L. (1980), "On the ramification of branched coverings of P^n", Inventiones Mathematicae, 59: 53–58, Bibcode:1980InMat..59...53G, doi:10.1007/BF01390313, S2CID 121387129. Gaffney, T.; du Plessis, A.A. (1982), "More on the determinacy of smooth map-germs", Inventiones Mathematicae, 66: 137–163, Bibcode:1982InMat..66..137G, doi:10.1007/BF01404761, S2CID 120417306. Gaffney, T.; Damon, J.N. (1983), "Topological triviality of deformations of functions and Newton filtrations", Inventiones Mathematicae, 72 (3): 335–358, Bibcode:1983InMat..72..335D, doi:10.1007/BF01398391, S2CID 121284485. Gaffney, T.; Hauser, H. (1985), "Characterizing singularities of varieties of mappings", Inventiones Mathematicae, 81 (3): 427–447, Bibcode:1985InMat..81..427G, doi:10.1007/BF01388580, S2CID 122597073. Gaffney, T. (1988), "Multiple points, chaining and Hilbert schemes", Amer. J. Math., 110 (4): 595–628, doi:10.2307/2374643, JSTOR 2374643. Gaffney, T. (1992), "Integral closure of modules and Whitney equisingularity", Inventiones Mathematicae, 107: 301–322, Bibcode:1992InMat.107..301G, doi:10.1007/BF01231892, S2CID 121234668. Gaffney, T. (1993), "Polar multiplicities and equisingularity of map germs", Topology, 32: 185–223, Bibcode:1992InMat.107..301G, doi:10.1007/BF01231892, S2CID 121234668. Gaffney, T. (1993), "Punctual Hilbert schemes and resolutions of multiple point singularities", Math. Ann., 295: 269–289, doi:10.1007/BF01444888, S2CID 122728280. Gaffney, T. (1996), "Multiplicities and equsingularity of ICIS germs", Inventiones Mathematicae, 123 (2): 209–220, doi:10.1007/s002220050022, S2CID 189819930. Gaffney, T.; Kleiman, Steven L. (1999), "Specialization of integral dependence for modules", Inventiones Mathematicae, 137 (3): 541–574, arXiv:alg-geom/9610003, Bibcode:1999InMat.137..541G, doi:10.1007/s002220050335, S2CID 7215999. Gaffney, T. (2009), "The Multiplicity Polar Theorem and isolated singularities", J. Algebraic Geom., 18 (3): 547–574, arXiv:math/0509285, doi:10.1090/S1056-3911-08-00516-X, S2CID 18078670.

Worked examples

Example 1 — a first encounter with Terence Gaffney

Start with the simplest possible case. Write down what Terence Gaffney 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 Terence Gaffney 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 Terence Gaffney 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 Terence Gaffney

In research: Terence Gaffney 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 Terence Gaffney 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: Terence Gaffney is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1948 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Terence Gaffney 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 Terence Gaffney in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Terence Gaffney means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Terence Gaffney in simple terms?

Why does Terence Gaffney 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 Terence Gaffney?

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 Terence Gaffney.