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 describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...

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

under

Adrien Douady Adrien Douady (; 25 September 1935 – 2 November 2006) was a French mathematician. Douady was a student of Henri Cartan at the École normale supérieure, and initially worked in homological algebra. His thesis concerned deformations of complex ...

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 statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

. At the

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

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

maître de conférences ''Maître'' (spelled ''Maitre'' according to post-1990 spelling rules) is a commonly used honorific for lawyers, judicial officers and notaries in France, Belgium, Switzerland and French-speaking parts of Canada. It is often written in its abbrev ...

'', 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 This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

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 set In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values wi ...

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