mathematics

Xavier Buff

Xavier Buff 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 Xavier Buff rather than just read about it. In short: Xavier Buff (born 16 December 1971) is a French mathematician, specializing in dynamical systems. Buff received in 1996 his Ph.D.

Key takeaways

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

Reference excerpt

Xavier Buff (born 16 December 1971) is a French mathematician, specializing in dynamical systems. Buff received in 1996 his Ph.D. (promotion) from the University of Paris-Sud under Adrien Douady with thesis Points fixe de renormalisation. As a postdoc he was in the academic year 1997–1998 the H. C. Wang Assistant Professor at Cornell University. At the Paul Sabatier University (Université Toulouse III) he became in 1998 a maître de conférences, achieved in 2006 his habilitation with habilitation thesis Disques de Siegel et ensembles de Julia d'aire strictement positive, and became in 2008 a full professor. In 2010 he was an invited speaker at the International Congress of Mathematicians in Hyderabad and gave a talk Quadratic Julia Sets with Positive Area based on joint work with Arnaud Chéritat. In 2006 Buff and Chéritat received the Prix Leconte of the French Academy of Sciences for their collaborative work on Julia sets with positive mass; they proved the existence of quadratic polynomials that have positive Lebesgue measure. In 2008 Buff, Chéritat, and Pascale Roesch received a Young Researchers grant from Agence Nationale de la Recherche. In 2009 Buff became a member of the Institut Universitaire de France.

Selected publications with A. Chéritat: Quadratic Julia sets with positive area, Annals of Mathematics, vol. 176, 2012, pp. 673–746 with A. Chéritat: A new proof of a conjecture of Yoccoz, Annales de l’institut Fourier, vol. 61, 2011, pp. 319–350 with A. Chéritat: The Brjuno function continuously estimates the size of quadratic Siegel disks, Annals of Mathematics, vol. 164, 2006, pp. 265–312 with A. Chéritat: Upper Bound for the Size of Quadratic Siegel Disks, Inventiones Mathematicae, vol. 156, 2004, pp. 1–24 doi:10.1007/s00222-003-0331-6 with C. Henriksen: Julia sets in parameter spaces, Communications in Mathematical Physics, vol. 220, 2001, pp. 333–375 doi:10.1007/PL00005568 with A. Chéritat: Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive, C. R. Acad. Sci. Paris, vol. 341, 2005, pp. 669–674 doi:10.1016/j.crma.2005.10.001 with Leila Schneps, Jérôme Fehrenbach, Pierre Lochak, Pierre Vogel: Moduli Spaces of Curves, Mapping Class Groups and Field Theory, AMS and SMF 2003

References

Illustrations

Worked examples

Example 1 — a first encounter with Xavier Buff

Start with the simplest possible case. Write down what Xavier Buff 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 Xavier Buff 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 Xavier Buff 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 Xavier Buff

In research: Xavier Buff 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 Xavier Buff 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: Xavier Buff is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1971 births, 20th-century French mathematicians, 21st-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Xavier Buff 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 Xavier Buff in 20 minutes

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

Frequently asked questions

What is Xavier Buff in simple terms?

Xavier Buff (born 16 December 1971) is a French mathematician, specializing in dynamical systems. Buff received in 1996 his Ph.D.

Why does Xavier Buff 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 Xavier Buff?

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 Xavier Buff.