# Xavier Buff

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**Xavier Buff** (born 16 December 1971) is a French mathematician, specializing in [dynamical systems](/source/Dynamical_system).

Buff received in 1996 his Ph.D. ([promotion](/source/Doctorate)) from the [University of Paris-Sud](/source/University_of_Paris-Sud) under [Adrien Douady](/source/Adrien_Douady) with thesis *Points fixe de renormalisation*.[1] As a postdoc he was in the academic year 1997–1998 the H. C. Wang Assistant Professor at [Cornell University](/source/Cornell_University). At the [Paul Sabatier University](/source/Paul_Sabatier_University) (Université Toulouse III) he became in 1998 a *[maître de conférences](/source/Ma%C3%AEtre_de_conf%C3%A9rences)*, achieved in 2006 his [habilitation](/source/Habilitation) with habilitation thesis *Disques de Siegel et ensembles de Julia d'aire strictement positive*, and became in 2008 a full professor.[2]

In 2010 he was an [invited speaker at the International Congress of Mathematicians](/source/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](/source/Arnaud_Ch%C3%A9ritat). In 2006 Buff and Chéritat received the *Prix Leconte* of the French Academy of Sciences for their collaborative work on [Julia sets](/source/Julia_set) with positive mass; they proved the existence of quadratic polynomials that have positive Lebesgue measure.[3] In 2008 Buff, Chéritat, and Pascale Roesch received a Young Researchers grant[4] from [Agence Nationale de la Recherche](/source/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](http://annals.math.princeton.edu/2012/176-2/p01), Annals of Mathematics, vol. 176, 2012, pp. 673–746
- with A. Chéritat: [A new proof of a conjecture of Yoccoz](http://eudml.org/doc/219751), 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](https://www.jstor.org/stable/20159990), Annals of Mathematics, vol. 164, 2006, pp. 265–312
- with A. Chéritat: [Upper Bound for the Size of Quadratic Siegel Disks](http://www.math.univ-toulouse.fr/~buff/Preprints/QuadSize/QuadSize.pdf), Inventiones Mathematicae, vol. 156, 2004, pp. 1–24 [doi:10.1007/s00222-003-0331-6](https://doi.org/10.1007/s00222-003-0331-6)
- with C. Henriksen: [Julia sets in parameter spaces](http://www.math.univ-toulouse.fr/~buff/Preprints/JuliaCubic/Copies.pdf), Communications in Mathematical Physics, vol. 220, 2001, pp. 333–375 [doi:10.1007/PL00005568](https://doi.org/10.1007/PL00005568)
- with A. Chéritat: [Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive](http://www.math.univ-toulouse.fr/~buff/Preprints/CRASMesure/CRASMesure.pdf), C. R. Acad. Sci. Paris, vol. 341, 2005, pp. 669–674 [doi:10.1016/j.crma.2005.10.001](https://doi.org/10.1016/j.crma.2005.10.001)
- with [Leila Schneps](/source/Leila_Schneps), [Jérôme Fehrenbach](/source/J%C3%A9r%C3%B4me_Fehrenbach), Pierre Lochak, Pierre Vogel: Moduli Spaces of Curves, Mapping Class Groups and Field Theory, AMS and SMF 2003

## References

1. [Buff's homepage at Université Toulouse III](http://www.math.univ-toulouse.fr/~buff/)

1. [Jean-Christophe Yoccoz](/source/Jean-Christophe_Yoccoz): Ensembles de Julia de mesure positive et disques de Siegel des polynômes quadratiques, d’après X. Buff et A. Chéritat, Séminaire Bourbaki 966, 2006

1. Project number ANR-08-JCJC-0002-01, [At the Boundary of Chaos](http://www.math.univ-toulouse.fr/anr_abc/) [Archived](https://web.archive.org/web/20150716163026/http://www.math.univ-toulouse.fr/anr_abc/) 2015-07-16 at the Wayback Machine

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