Publications

with M. Boshernitzan
" From a packing problem to quantiative recurrence in [0,1] and the Lagrange spectrum of interval exchanges"
Discrete Analysis 1749 (2017)
arXiv:1608.04591
This article provides optimal constants for two quantitative recurrence problems. First of all for recurrence of maps of the interval [0,1] that preserve the Lebesgue measure. On the other hand, we study the bottom of the Lagrange spectrum of interval exchange transformations. Both results are based on a unconventional packing problem in the plane with respect to the "pseudonorm" N(x,y) = sqrt(xy). 
with V. Berthé F. Dolce D. Perrin C. Reutenauer G. Rindone
"Return words of linear involutions and fundamental groups"
Erg. Th. and Dyn. Sys. 37 , n° 3 (2017) p. 693715
arXiv:1405.3529
We investigate the shifts associated with natural codings of linear involutions. We deduce, from the geometric representation of linear involutions as Poincaré maps of measured foliations, a suitable definition of return words which yields that the set of return words to a given word is a symmetric basis of the free group on the underlying alphabet A. The set of return words with respect to a subgroup of finite index G of the free group on A is also proved to be a symmetric basis of G 
with A. Avila
"Weakmixing directions in nonarithmetic Veech surfaces"
J. of AMS 29 (2016) p. 11671208
arXiv:1304.3318
In this paper we prove the genericity of weak mixing in nonarithmetic Veech surfaces (arithmetic is synonym for square tiled). We know since the work A. Avila and G. Forni (Ann. of Math. 165 (2007), see also arXiv:math/0406326) that weakmixing is prevalent in the space of translation surfaces. Nevertheless, there was no known example of surfaces for which the weakmixing is prevalent in almost every direction. Our result applies in particular to billiard in regular polygons studied by Veech (Inv. Math. 97 (1989)) and billiard in Lshaped tables introduced by C. McMullen (J. Amer. Math. Soc. 16 (2003)). 
with C. Mathéus
"Un contreexemple à la réciproque du critère de Forni pour la positivité des exposants de Lyapunov du cocycle de KontsevichZorich"
Math Res. Lett. 22 , n° 6 (2015) p. 16671678
arXiv:1103.1560
Forni proved that a certain geometric quantity gives a lower bound for the number of positive Lyapunov exponents of the KontsevichZorich cocycle (J. Mod. Dyn. 5, No. 2 (2011), see also arXiv:1009.4655). In this short note, we exhibit an example for which the geometric criterion is not satisfied but for which all Lyapunov exponents are positive. In order to prove positivity, we use a result of C. Matheus, M. Moeller and J.C. Yoccoz (arXiv:1305.2033) 
with C. Ulcigrai
"Diagonal changes in hyperelliptic components. A natural extension to FerencziZamboni induction"
Geom. Ded. 176 , n° 1 (2015) p. 117174
arXiv:1310.1052
In this article, we introduce an induction scheme for translation surfaces in hyperelliptic strata. It can be considered as a geometric counterpart to FerencziZamboni construction (J. Analyse Math. 112 (2010)) 
with V. Berthé
"Beyond substitutive dynamical systems: Sadic expansions"
RIMS Kôkyûroku Bessatsu B46 (2014) p. 81123
arXiv:1309.3960
Selfsimilar dynamical systems are example of highly structured dynamical systems. But there are much more systems of low complexity. One way to consider all of them is to slightly weaken the notion of selfsimilarity: we allow to see different patterns at different scales but all of them belong to a fixed family. The combinatorial counterpart of this construction are the socalled Sadic systems. 
with P. Hubert S. Lelièvre
"Diffusion for the periodic windtree model"
Ann. Sc. ENS 47 , n° 6 (2014) p. 10851110
arXiv:1107.1810
The windtree model is a billiard in the plane where scatterers are rectangles randomly displaced. We study a periodic version and prove that the diffusion rate is 2/3. More precisely the maximum distance reached by a particule before time T is around T^(2/3). It makes a large difference with random walks in the plane for which that quantity equals T^(1/2). 
"Divergent directions in some periodic windtree models"
J. of Mod. Dyn. 7 , n° 1 (2013) p. 129
arXiv:1107.2418
We prove that for many choice of rectangular obstacles, there exists divergent directions in the windtree model. 
"Cardinality of Rauzy classes"
Ann. Inst. Fourier 63 , n° 5 (2013) p. 16511715
arXiv:1106.0807
Rauzy classes are set of permutations that appear in a renormalization scheme of interval exchange transformations introduced by Rauzy and further studied by Veech. In this article we provide a formula for the cardinalities of Rauzy classes and make a conjecture about their asymptotics.
Prépublications

with E. Goujard P. Zograf A. Zorich
"Squaretiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata"
arXiv:1612.08374

with J.F. Bertazzon
"Étude d'une équation intégrale avec des méthodes combinatoires"
arXiv:1403.2235

with V. Berthé F. Docle D. Perrin C. Reteunauer G. Rindone
"Natural coding of linear involutions"
arXiv:1405.3529

with A. Zorich
"Cries and whispers in windtree forests"
arXiv:1502.06405

with A. Avila
"Some monoids of Pisot matrices"
arXiv:1506.03692
Articles de conférences

with D. Perrin V. Berthe C. De Felice J. Leroy C. Reutenauer G. Rindone
"Specular sets"
Words 2015
arXiv:1505.00707

with T. Hejda W. Steiner
"Balancedness of ArnouxRauzy and Brun words"
Words 2013
arXiv:1308.6694
Thèse
J'ai soutenu ma thèse sous la direction d'Arnaldo Nogueira le 16 Novembre 2011 présentation au format pdf. Mon mémoire est disponible en version longue (173 pages) et en version courte (57 pages).
Groupes de travail
Au printemps 2014, j'ai animé des séances d'introduction au logiciel Sage à l'université de Bordeaux. Pour plus d'informations voir la page wiki.
J'ai coorganisé avec Pascal Hubert et Erwan Lanneau un groupe de travail sur les travaux de BenoistQuint (la page contient quelques notes de cours et des références).