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 …

Translation surfaces can be defined in an elementary way via polygons, and arise naturally
in the study of various basic dynamical systems. They can also be defined as di fferentials …

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 …

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

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 use the relation between the volumes of the strata of meromorphic quadratic differentials
with at most simple poles on the Riemann sphere and counting functions of the number of …

Patterson–Sullivan theory for groups with a strongly contracting element Page 1 Ergod. Th. &
Dynam. Sys., page 1 of 56 © The Author(s), 2024. Published by Cambridge University Press …

We introduce and systematically study the concept of a growth tight action. This generalizes
growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely …