Various problems of geometry, topology and dynamical systems on surfaces as well as
some questions concerning one-dimensional dynamical systems lead to the study of closed …

We prove results about orbit closures and equidistribution for the SL (2, ℝ) action on the
moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent …

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 …

Dynamics of <tex-math>$\text{SL}_{2}({\Bbb R})$</tex-math> over Moduli Space in Genus Two
Page 1 Annals of Mathematics, 165 (2007), 397-456 Dynamics of SL2(IR) over moduli space …

This text is an expanded version of the lecture notes of a minicourse (with the same title of
this text) delivered by the authors in the Bedlewo school" Modern Dynamics and its …

Let T be a 2-dimensional torus equipped with a flat Riemannian metric and a vector field
which is unitary and parallel for that metric. Then there exists a unique lattice Λ⊂ R2 such …

The moduli space of canonical divisors (with prescribed zeros and poles) on nonsingular
curves is not compact since the curve may degenerate. We define a proper moduli space of …

Abstract We express the Masur–Veech volume and the area Siegel–Veech constant of the
moduli space Q g, n of genus g meromorphic quadratic differentials with at most n simple …