astronomy

John D'Angelo

John D'Angelo is a astronomy 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 D'Angelo rather than just read about it. In short: John D'Angelo is an American mathematician. He is currently Professor Emeritus in the Department of Mathematics at the University of Illinois at Champaign-Urbana.

Key takeaways

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

Reference excerpt

John D'Angelo is an American mathematician. He is currently Professor Emeritus in the Department of Mathematics at the University of Illinois at Champaign-Urbana.

Education D'Angelo received his PhD from Princeton University in 1976, under the direction of J.J. Kohn. He was then a C.L.E. Moore Instructor at MIT from 1976 to 1978, becoming an Assistant Professor at University of Illinois in 1978, and was promoted to Full Professor in 1987. He became an emeritus professor in 2018.

Awards and honors D'Angelo was the recipient of the Stefan Bergman Prize in 1999 for "remarkable geometric insight that has led him to make several spectacular contributions to complex analysis". In 2014 he became a fellow of the American Mathematical Society: "For contributions to several complex variables and Cauchy-Riemann geometry, and for his inspiration of students".

Research D'Angelo's early work involved the study of order of contact between analytic subvarieties and boundaries of weakly pseudoconvex domains, which resulted in the definition and analysis of what are now known as points of D'Angelo finite type. The D'Angelo type provides a quantitative measure of the order contact between the boundary of the domain and analytic subvarieties. D'Angelo's work uses analysis and commutative algebra. A domain all of whose boundary points have finite D'Angelo type has analytic properties, with respect to holomorphic functions, that are quite similar to strictly pseudoconvex domains. David Catlin was able to prove regularity estimates for the ∂ ¯ {\displaystyle {\bar {\partial }}} -Neumann problem, the Bergman projection, and related operators for domains all of whose boundary points satisfy a condition closely related to finite D'Angelo type. Since 1990 D'Angelo's work has been focused on problems connected to the existence of proper holomorphic mappings between balls of different dimensions. That work led him to a study of complex variables analogues of Hilbert’s 17th problem and to various combinatorial and algebraic properties of Rational Sphere Maps.

Books Several Complex Variables and the Geometry of Real Hypersurfaces. CRC Press, 1992. Mathematical Thinking: Problem Solving and Proofs. Prentice-Hall, 2000. (joint with Douglas B. West) Inequalities from Complex Analysis. Mathematics Assoc. of America, 2002. An Introduction to Complex Analysis and Geometry. American Math. Society, 2010. Hermitian Analysis: From Fourier series to Cauchy-Riemann Geometry. Springer, 2013. Linear and Complex Analysis for Applications. CRC Press, 2017. Rational Sphere Maps. Springer-Birkhauser, 2021.

References

Worked examples

Example 1 — a first encounter with John D'Angelo

Start with the simplest possible case. Write down what John D'Angelo claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 D'Angelo 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 D'Angelo 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 D'Angelo

In research: John D'Angelo appears in astronomy 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 D'Angelo 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 D'Angelo is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fellows of the American Mathematical Society, Living people, Princeton University alumni, so understanding it makes those chapters shorter.
In everyday life: Look for John D'Angelo 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 D'Angelo in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John D'Angelo 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.
Explain John D'Angelo out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John D'Angelo in simple terms?

John D'Angelo is an American mathematician. He is currently Professor Emeritus in the Department of Mathematics at the University of Illinois at Champaign-Urbana.

Why does John D'Angelo matter?

Because it connects several astronomy 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 D'Angelo?

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 D'Angelo.