This book explores infinite-type translation surfaces and is intended as an introductory text
for graduate and PhD students, as well as a reference for more advanced researchers …

The field of definition of an affine invariant submanifold ℳ is the smallest subfield of ℝ such
that ℳ can be defined in local period coordinates by linear equations with coefficients in this …

We show that every surface in the component H^\rm hyp (4) H hyp (4), that is the moduli
space of pairs (M, ω)(M, ω) where M is a genus three hyperelliptic Riemann surface and ω ω …

We analyze the rel leaves of the Arnoux–Yoccoz translation surfaces. We show that for any
genus g\geqslant 3 g⩾ 3, the leaf is dense in the connected component of the stratum H (g …

According to Thurston's classification, a diffeomorphism of a closed oriented surface is either
elliptic, reducible or a pseudo-Anosov diffeomorphism. The structure of pseudo-Anosov …

The moduli space of genus 3 translation surfaces with a single zero has two connected
components. We show that in the odd connected component Hodd (4) the only GL+(2, R) …

We consider a substitution associated with the Arnoux–Yoccoz interval exchange
transformation (IET) related to the tribonacci substitution. We construct the so-called stepped …

We study closures of GL 2+(R)-orbits in the total space Ω M g of the Hodge bundle over the
moduli space of curves under the assumption that they are algebraic manifolds. We show …

We show that each of Veech's original examples of translation surfaces with``optimal
dynamics''whose trace field is of degree greater than two has non-periodic directions of …

R.–Nous étudions le comportement des feuilletages mesurés harmoniques sur les
surfaces de Riemann compactes. Quand les périodes relatives varient, on peut observer …