mathematics

Paolo Piccione

Paolo Piccione 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 Paolo Piccione rather than just read about it. In short: Paolo Piccione (born 24 April 1964) is an Italian mathematician working in differential geometry, Riemannian geometry and analysis. He is professor at the University of São Paulo since 1996 and president of the Brazilian Mathematical Society since 2017.

Key takeaways

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

Reference excerpt

Paolo Piccione (born 24 April 1964) is an Italian mathematician working in differential geometry, Riemannian geometry and analysis. He is professor at the University of São Paulo since 1996 and president of the Brazilian Mathematical Society since 2017.

Biography Piccione was born in Rome on 24 April 1964, in a genuinely Italian family – his paternal grandfather was from Sicily; and the maternal one of central Italy – of a social class "without any particular prominence", although he enjoyed the important advances of Italian society in the postwar period, Piccione achieved an education in high-level public schools. Like his parents, three decades before him, he graduated from the same Sapienza University of Rome, in Rome, where he obtained Laurea in Matematica and Master degree in 1987 supervisor by Alessandro Figà Talamanca. He received his a PhD in Mathematics degree from the Pennsylvania State University in 1994 advisor by Adrian Ocneanu. He is currently a full professor at the Institute of Mathematics and Statistics, University of São Paulo, where he teaches since 1996 and completed his livre docência (Doctor of Law's USP).

Work His research has emphasis on differential geometry, he works mainly on the following topics: calculus of variations and variational geometric problems, Riemannian and global Lorentzian geometry, Morse theory, symplectic geometry and Hamiltonian systems. Piccione develops research that deals with topics with possible applications to physics. The main results achieved in the area of Lorentzian geometry have an interpretation within general relativity.

Awards and honors Brazilian Academy of Sciences, Member (2012) Brazilian Mathematical Society, President (2017-) National Order of Scientific Merit, Commander (2018)

Selected publications jointly with GIAMBO, R.; MAGLI, G., "Naked Singularities Formation in the Gravitational Collapse of Barotropic Spherical Fluids.". General Relativity and Gravitation. vol. 36 (2004), no. 6, pp. 1279–1298. jointly with Giambo, R.; Giannoni, F.; MAGLI, G., "New solutions of Einstein equations in spherical symmetry: the Cosmic Censor to the court". Communications in Mathematical Physics. vol. 235 (2003), no. 3, pp. 545–563. jointly with Exel, R.; Dokuchaev, M., "Partial Representations and Partial Group Algebras". Journal of Algebra. vol. 226 (2000), no. 1, pp. 505–532.

References

External links Home page of Paolo Piccione

Illustrations

Worked examples

Example 1 — a first encounter with Paolo Piccione

Start with the simplest possible case. Write down what Paolo Piccione 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 Paolo Piccione 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 Paolo Piccione 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 Paolo Piccione

In research: Paolo Piccione 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 Paolo Piccione 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: Paolo Piccione is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1964 births, 20th-century Italian mathematicians, 21st-century Italian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paolo Piccione 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 Paolo Piccione in 20 minutes

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

Frequently asked questions

What is Paolo Piccione in simple terms?

Why does Paolo Piccione 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 Paolo Piccione?

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 Paolo Piccione.