We prove some ergodic-theoretic rigidity properties of the action of on moduli space. In
particular, we show that any ergodic measure invariant under the action of the upper …

1.1. Moduli spaces of Abelian and quadratic differentials.—The moduli space Hg of pairs (C,
ω) where C is a smooth complex curve of genus g and ω is an Abelian differential (or, in the …

We describe the closure of the strata of Abelian differentials with prescribed type of zeros
and poles, in the projectivized Hodge bundle over the Deligne–Mumford moduli space of …

We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The
result is deduced from a generalization of a theorem of Möller. Namely, we prove that the …

We construct a compactification of the moduli spaces of abelian differentials on Riemann
surfaces with prescribed zeroes and poles. This compactification, called the moduli space of …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

We show that the Masur–Veech volumes and area Siegel–Veech constants can be obtained
using intersection theory on strata of Abelian differentials with prescribed orders of zeros. As …

The algebraic hull of the Kontsevich–Zorich cocycle Page 1 Annals of Mathematics 188 (2018),
281–313 https://doi.org/10.4007/annals.2018.188.1.5 The algebraic hull of the Kontsevich–Zorich …

We study the boundary of an affine invariant submanifold of a stratum of translation surfaces
in a partial compactification consisting of all finite area Abelian differentials over nodal …

We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge
structure. In particular, we establish a version of Deligne semisimplicity in this context. This …