mathematics

Guido De Philippis

Guido De Philippis 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 Guido De Philippis rather than just read about it. In short: Guido De Philippis (born August 16, 1985 at Fiesole) is an Italian mathematician. He works on the calculus of variations, partial differential equations and geometric measure theory.

Key takeaways

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

Reference excerpt

Guido De Philippis (born August 16, 1985 at Fiesole) is an Italian mathematician. He works on the calculus of variations, partial differential equations and geometric measure theory. In 2016, he was awarded the EMS Prize, "for his outstanding contributions to the regularity of solutions of Monge–Ampère equation and optimal maps and for his deep work on quantitative stability inequalities for the first eigenvalue of the Laplacian and rigidity in some isoperimetric type inequalities.". In 2018 he was awarded the Stampacchia Medal. In 2021, he received the ISAAC award. De Philippis was a PhD student of Luigi Ambrosio and Luis Caffarelli.

Selected publications De Philippis, Guido; Figalli, Alessio (May 16, 2014). "The Monge–Ampère equation and its link to optimal transportation". Bulletin of the American Mathematical Society. 51 (4). American Mathematical Society (AMS): 527–580. arXiv:1310.6167. doi:10.1090/s0273-0979-2014-01459-4. ISSN 0273-0979. S2CID 4655511. De Philippis, G.; Figalli, A. (2014). "Partial Regularity Results in Optimal Transportation". Trends in Contemporary Mathematics. Cham: Springer International Publishing. doi:10.1007/978-3-319-05254-0_21. ISBN 978-3-319-05253-3. ISSN 2281-518X. De Philippis, Guido; Rindler, Filip (November 1, 2016). "On the structure of \mathscr A-free measures and applications". Annals of Mathematics. 184 (3): 1017–1039. arXiv:1601.06543. doi:10.4007/annals.2016.184.3.10. ISSN 0003-486X. S2CID 67844397. Regularity of optimal transport maps and applications, Ed. della Normale, Springer 2013 (Dissertation)

References

Illustrations

Worked examples

Example 1 — a first encounter with Guido De Philippis

Start with the simplest possible case. Write down what Guido De Philippis 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 Guido De Philippis 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 Guido De Philippis 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 Guido De Philippis

In research: Guido De Philippis 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 Guido De Philippis 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: Guido De Philippis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1985 births, 21st-century Italian mathematicians, Italian mathematical analysts, so understanding it makes those chapters shorter.
In everyday life: Look for Guido De Philippis 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 Guido De Philippis in 20 minutes

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

Frequently asked questions

What is Guido De Philippis in simple terms?

Guido De Philippis (born August 16, 1985 at Fiesole) is an Italian mathematician. He works on the calculus of variations, partial differential equations and geometric measure theory.

Why does Guido De Philippis 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 Guido De Philippis?

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 Guido De Philippis.