118 citations · 293 across the 11 of their papers we have counts for
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Full rank affine invariant submanifolds
Maryam Mirzakhani, Alex Wright
We show that every GL(2, R) orbit closure of translation surfaces is either a connected component of a stratum, the hyperelliptic locus, or consists entirely of surfaces whose Jaco…
The boundary of an affine invariant submanifold
Maryam Mirzakhani, Alex Wright
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…
Isolation, equidistribution, and orbit closures for the SL(2,R) action on Moduli space
Alex Eskin, Maryam Mirzakhani, Amir Mohammadi
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 fl…
Invariant and stationary measures for the SL(2,R) action on Moduli space
Alex Eskin, Maryam Mirzakhani
We prove some ergodic-theoretic rigidity properties of the action of SL(2,R) on moduli space. In particular, we show that any ergodic measure invariant under the action of the uppe…
Counting closed geodesics in Moduli space
Alex Eskin, Maryam Mirzakhani
We compute the asymptotics, as R tends to infinity, of the number of closed geodesics in Moduli space of length at most R, or equivalently the number of pseudo-Anosov elements of t…
Lattice Point Asymptotics and Volume Growth on Teichmuller space
Jayadev Athreya, Alexander Bufetov, Alex Eskin +1
We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis to Teichmuller space. Let x be a point in Teichmuller space, and let B_R(x) be the ball of radius R centered at x (…