mathematics

John M. Lee

John M. Lee 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 John M. Lee rather than just read about it. In short: John "Jack" Marshall Lee (born September 2, 1950) is an American mathematician and professor at the University of Washington specializing in differential geometry. Education Lee graduated from Princeton University with a bachelor's degree in 1972, then became a systems programmer (at Texas Instruments from 1972 to 1974 and at the Geophysical Fluid Dynamics Laboratory in 1974–1975) and a teacher at Wooster School in…

Key takeaways

John M. Lee belongs to mathematics; place it in that map before memorising details.
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Reproduce the core statement of John M. Lee from memory before moving on to harder problems.

Reference excerpt

John "Jack" Marshall Lee (born September 2, 1950) is an American mathematician and professor at the University of Washington specializing in differential geometry.

Education Lee graduated from Princeton University with a bachelor's degree in 1972, then became a systems programmer (at Texas Instruments from 1972 to 1974 and at the Geophysical Fluid Dynamics Laboratory in 1974–1975) and a teacher at Wooster School in Danbury, Connecticut in 1975–1977. He continued his studies at Tufts University in 1977–1978. He received his doctorate from Massachusetts Institute of Technology in 1982 under the direction of Richard Melrose with the dissertation Higher asymptotics of the complex Monge-Ampère equation and geometry of CR manifolds.

Career From 1982 to 1987, Lee was an assistant professor at Harvard University. At the University of Washington he became in 1987 an assistant professor, in 1989 an associate professor, and in 1996 a full professor.

Research Lee's research has focused on the Yamabe problem, geometry of and analysis on CR manifolds, and differential geometry questions of general relativity (such as the constraint equations in the initial value problem of Einstein equations and existence of Einstein metrics on manifolds). Lee created a mathematical software package named Ricci for performing tensor calculations in differential geometry. Ricci, named in honor of Gregorio Ricci-Curbastro and completed in 1992, consists of 7000 lines of Mathematica code. It was chosen for inclusion in the MathSource library of Mathematica packages supported by Wolfram Research.

Awards In 2012, Lee received, jointly with David Jerison, the Stefan Bergman Prize from the American Mathematical Society.

Selected publications Lee, John M. (1986), "The Fefferman metric and pseudo-Hermitian invariants", Transactions of the American Mathematical Society, 296 (1): 411–429, doi:10.1090/S0002-9947-1986-0837820-2 Jerison, David; Lee, John M. (1987), "The Yamabe problem on CR manifolds", Journal of Differential Geometry, 25 (2): 167–197, doi:10.4310/jdg/1214440849 Lee, John M.; Parker, Thomas H. (1987), "The Yamabe problem", Bulletin of the American Mathematical Society, New Series, 17 (1): 37–91, doi:10.1090/S0273-0979-1987-15514-5 Jerison, David; Lee, John M. (1988), "Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem", Journal of the American Mathematical Society, 1 (1): 1–13, doi:10.1090/S0894-0347-1988-0924699-9 Lee, John M. (1988), "Pseudo-Einstein structures on CR manifolds", American Journal of Mathematics, 110 (1): 157–178, doi:10.2307/2374543, JSTOR 2374543 Jerison, David; Lee, John M. (1989), "Intrinsic CR normal coordinates and the CR Yamabe problem", Journal of Differential Geometry, 29 (2): 303–343, doi:10.4310/jdg/1214442877 Lee, John M.; Uhlmann, Gunther (1989), "Determining anisotropic real-analytic conductivities by boundary measurements", Communications on Pure and Applied Mathematics, 42 (8): 1097–1112, doi:10.1002/cpa.3160420804 Graham, C. Robin; Lee, John M. (1991), "Einstein metrics with prescribed conformal infinity on the ball", Advances in Mathematics, 87 (2): 186–225, doi:10.1016/0001-8708(91)90071-E

Textbooks Lee, John M. (1997). Riemannian Manifolds: An Introduction to Curvature. Graduate Texts in Mathematics. Vol. 176. New York: Springer-Verlag. ISBN 978-0-387-98322-6. OCLC 54850593. Riemannian Manifolds: An Introduction to Curvature, Springer-Verlag, Graduate Texts in Mathematics 1997 Lee, John M. (2018). Introduction to Riemannian Manifolds. Graduate Texts in Mathematics. Vol. 176 (2nd ed.). doi:10.1007/978-3-319-91755-9. ISBN 978-3-319-91755-9. (formally, the second edition of the above text) Introduction to Topological Manifolds, Springer-Verlag, Graduate Texts in Mathematics 2000, 2nd edition 2011 Lee, John M. (2012). Introduction to Smooth Manifolds. Graduate Texts in Mathematics. Vol. 218 (Second ed.). New York London: Springer-Verlag. ISBN 978-1-4419-9981-8. OCLC 808682771. Introduction to Smooth Manifolds, Springer-Verlag, Graduate Texts in Mathematics, 2002, 2nd edition 2012 Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds. American Mathematical Soc. 2006 doi:10.1090/memo/0864 Lee, John M. (2024). Introduction to Complex Manifolds. Graduate Studies in Mathematics. Vol. 244. ISBN 9781470476953. Axiomatic Geometry, AMS 2013

References

External links Homepage

Worked examples

Example 1 — a first encounter with John M. Lee

Start with the simplest possible case. Write down what John M. Lee 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 John M. Lee 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 John M. Lee 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 John M. Lee

In research: John M. Lee 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 John M. Lee 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: John M. Lee is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1950 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John M. Lee 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 John M. Lee in 20 minutes

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Frequently asked questions

What is John M. Lee in simple terms?

John "Jack" Marshall Lee (born September 2, 1950) is an American mathematician and professor at the University of Washington specializing in differential geometry. Education Lee graduated from Princeton University with a bachelor's degree in 1972, then became a systems programmer (at Texas Instrume…

Why does John M. Lee 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 John M. Lee?

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 John M. Lee.