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 …

Publisher Summary The theory of mathematical billiards can be partitioned into three areas:
convex billiards with smooth boundaries, billiards in polygons (and polyhedra), and …

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 …

We present an approach for counting the Teichmüller volumes of the moduli spaces of
Abelian differentials on a Riemann surface of genus g. We show that the volumes can be …

* This paper rests on the work of several mathematicians, H. Masur, J. Smillie, W. Veech and
A. Zorich among them, and it was strongly inspired by the work of A. Zorich and M …

We study the dynamics of the Teichmüller flow in the moduli space of Abelian differentials
(and more generally, its restriction to any connected component of a stratum). We show that …

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 …

ABSTRACT A holomorphic 1-form on a compact Riemann surface S naturally defines a flat
metric on S with cone-type singularities. We present the following surprising phenomenon …

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 …