mathematics

Henri Berestycki

Henri Berestycki 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 Henri Berestycki rather than just read about it. In short: Henri Berestycki (born 25 March 1951) is a French mathematician who obtained his PhD from Université Paris VI – Pierre and Marie Curie University in 1975. His Dissertation was titled Contributions à l'étude des problèmes elliptiques non linéaires, and his doctoral advisor was Haïm Brezis.

Key takeaways

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

Reference excerpt

Henri Berestycki (born 25 March 1951) is a French mathematician who obtained his PhD from Université Paris VI – Pierre and Marie Curie University in 1975. His Dissertation was titled Contributions à l'étude des problèmes elliptiques non linéaires, and his doctoral advisor was Haïm Brezis. He was an L.E. Dickson Instructor in Mathematics at the University of Chicago from 1975–77, after which he returned to France to continue his research. He has made many contributions in nonlinear analysis, ranging from nonlinear elliptic equations, hamiltonian systems, spectral theory of elliptic operators, and with applications to the description of mathematical modelling of fluid mechanics and combustion. His current research interests include the mathematical modelling of financial markets, mathematical models in biology and especially in ecology, and modelling in social sciences (in particular, urban planning and criminology). For these latter topics, he obtained an ERC Advanced grant in 2012. He worked at the French National Center of Scientific Research (CNRS), then moved to an appointment as Professor at University Paris XIII (1983–1985). He became a Professor of Mathematics in 1988 at Université Pierre et Marie Curie, Paris VI (1988–2001 of “exceptional class” since 1993), and became professor at École normale supérieure, Paris (1994–1999), and part-time professor at the École Polytechnique (1987–1999). He is also a visiting Professor in the Department of Mathematics at the University of Chicago, and was also co-director of the Stevanovich Center of Financial Mathematics in Chicago. He is currently the Directeur d'études (Research Professor) at École des hautes études en sciences sociales (EHESS), since 2001.

Services National Committee of French universities (1992 – 1995). Since 2002 director of Centre d'analyse et mathématique sociales (CAMS), CNRS – EHESS. Vice-president, EHESS (2004 – 2006). Member of the thesis prize committee of the Universities of Paris (since 2006).

Awards Carrière Prize(1988) Prix Sophie Germain of the French Academy of Sciences (2004), Humboldt Prize in Germany (2004) French Legion of Honor in 2010. American Mathematical Society Fellowship (2012). Foreign honorary member of the American Academy of Arts and Sciences, 2013.

Articles Berestycki, Henri; Coville, Jérôme; Vo, Hoang-Hung Persistence criteria for populations with non-local dispersion. J. Math. Biol. 72 (2016), no. 7, 1693–1745. Berestycki, Henri; Coville, Jérôme; Vo, Hoang-Hung On the definition and the properties of the principal eigenvalue of some nonlocal operators. J. Funct. Anal. 271 (2016), no. 10, 2701–2751. Berestycki, Henri; Roquejoffre, Jean-Michel; Rossi, Luca; The influence of a line with fast diffusion on Fisher-KPP propagation. J. Math. Biol. 66 (2013), no. 4-5, 743–766. Barthélemy, Marc; Nadal, Jean-Pierre; Berestycki, Henri Disentangling collective trends from local dynamics. Proc. Natl. Acad. Sci. USA 107 (2010), no. 17, 7629–7634. Berestycki, Henri; Hamel, François; Nadirashvili, Nikolai Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena. Comm. Math. Phys. 253 (2005), no. 2, 451–480. Berestycki, Henri; Hamel, François Front propagation in periodic excitable media. Comm. Pure Appl. Math. 55 (2002), no. 8, 949–1032. Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. Inequalities for second-order elliptic equations with applications to unbounded domains. I. A celebration of John F. Nash, Jr. Duke Math. J. 81 (1996), no. 2, 467–494. Berestycki, H.; Nirenberg, L.; Varadhan, S. R. S. The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Comm. Pure Appl. Math. 47 (1994), no. 1, 47–92. Berestycki, H.; Lions, P.-L. Nonlinear scalar field equations. I. Existence of a ground state. Arch. Rational Mech. Anal. 82 (1983), no. 4, 313–345; II. Existence of infinitely many solutions, Arch. Rational Mech. Anal. 82 (1983), no. 4, 347–375. Bahri, Abbas; Berestycki, Henri A perturbation method in critical point theory and applications. Trans. Amer. Math. Soc. 267 (1981), no. 1, 1–32.

References

Worked examples

Example 1 — a first encounter with Henri Berestycki

Start with the simplest possible case. Write down what Henri Berestycki 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 Henri Berestycki 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 Henri Berestycki 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 Henri Berestycki

In research: Henri Berestycki 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 Henri Berestycki 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: Henri Berestycki is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1951 births, 20th-century French mathematicians, 21st-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henri Berestycki 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 Henri Berestycki in 20 minutes

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

Frequently asked questions

What is Henri Berestycki in simple terms?

Why does Henri Berestycki 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 Henri Berestycki?

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 Henri Berestycki.