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 …

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

This book is devoted to proving a theorem of Maryam Mirzakhani and explaining some of its
applications. In her dissertation, Mirzakhani established the asymptotic behavior, when L …

" This book is the companion to the CBMS lectures of Scott Wolpert at Central Connecticut
State University. The lectures span across areas of research progress on deformations of …

This paper presents a study of the asymptotic geometry of groups with contracting elements,
with emphasis on a subclass of statistically convex-cocompact (SCC) actions. The class of …

Let $ S_ {g, n} $ be a surface of genus $ g $ with $ n $ marked points. Let $ X $ be a
complete hyperbolic metric on $ S_ {g, n} $ with $ n $ cusps. Every isotopy class $[\gamma] …

arXiv:0811.2362v3 [math.DS] 19 Mar 2011 Page 1 arXiv:0811.2362v3 [math.DS] 19 Mar 2011
Counting closed geodesics in Moduli space Alex Eskin∗and Maryam Mirzakhani† October …

We consider the SL (2, ℝ) action on moduli spaces of quadratic differentials. If μ is an SL (2,
ℝ)-invariant probability measure, crucial information about the associated representation on …

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 …