Xavier Buff (born 16 December 1971) is a French mathematician, specializing in

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

s. Buff received in 1996 his Ph.D. (

promotion Promotion may refer to: Marketing * Promotion (marketing), one of the four marketing mix elements, comprising any type of marketing communication used to inform or persuade target audiences of the relative merits of a product, service, brand or i ...

) from the

University of Paris-Sud Paris-Sud University (), also known as the University of Paris — XI (or as the Orsay Faculty of Sciences, University of Paris before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, ...

under

Adrien Douady Adrien Douady (; 25 September 1935 – 2 November 2006) was a French mathematician born in La Tronche, Isère. He was the son of Daniel Douady and Guilhen Douady. Douady was a student of Henri Cartan at the École normale supérieure, and initi ...

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 Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

. At the

Paul Sabatier University Paul Sabatier University (''Université Paul Sabatier'' , UPS, also known as Toulouse III) was a French university, in the Academy of Toulouse. It was one of the several successor universities of the University of Toulouse, established in 1229, m ...

(Université Toulouse III) he became in 1998 a ''

maître de conférences The following summarizes basic academic ranks in the France, French higher education system. Most academic institutions are state-run and most academics with permanent positions are French Civil Service, civil servants, and thus are Academic tenur ...

'', achieved in 2006 his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

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 An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

in Hyderabad and gave a talk ''Quadratic Julia Sets with Positive Area'' based on joint work with

Arnaud Chéritat Arnaud Chéritat (born June 7, 1975) is a French mathematician who works as a director of research at the Institut de Mathématiques de Toulouse.Julia set In complex dynamics, the Julia set and the Classification of Fatou components, Fatou set are two complement set, complementary sets (Julia "laces" and Fatou "dusts") defined from a function (mathematics), function. Informally, the Fatou set of ...

s 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 grantProject number ANR-08-JCJC-0002-01
At the Boundary of Chaos
/ref> 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 *with C. Henriksen
Julia sets in parameter spaces
Communications in Mathematical Physics, vol. 220, 2001, pp. 333–375 *with A. Chéritat
Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive
C. R. Acad. Sci. Paris, vol. 341, 2005, pp. 669–674 *with

Leila Schneps Leila Schneps is an American mathematician and fiction writer at the Centre national de la recherche scientifique working in number theory. Schneps has written general audience math books and, under the pen name Catherine Shaw, has written mathe ...

, Jérôme Fehrenbach, Pierre Lochak, Pierre Vogel
Moduli Spaces of Curves, Mapping Class Groups and Field Theory
AMS and SMF 2003

References

{{DEFAULTSORT:Buff, Xavier 1971 births Living people 20th-century French mathematicians 21st-century French mathematicians University of Paris alumni Academic staff of the University of Toulouse Dynamical systems theorists