687 citations · 860 across the 32 of their papers we have counts for
38 papers
Counting mapping classes by Nielsen-Thurston type
Spencer Dowdall, Howard Masur
This paper concerns the lattice counting problem for the mapping class group of a surface acting on Teichmüller space with the Teichmüller metric. In that problem the goal is t…
Counting pairs of saddle connections
J. S. Athreya, S. Fairchild, H. Masur
We show that for almost every translation surface the number of pairs of saddle connections with bounded magnitude of the cross product has asymptotic growth like where the…
Generic measures for translation surface flows
Howard Masur
We consider straight line flows on a translation surface that are minimal but not uniquely ergodic. We give bounds for the number of generic invariant probability measures.
Expected covering radius of a translation surface
Howard Masur, Kasra Rafi, Anja Randecker
A translation structure equips a Riemann surface with a singular flat metric. Not much is known about the shape of a random translation surface. We compute an upper bound on the ex…
Divergent on average directions of Teichmuller geodesic flow
Paul Apisa, Howard Masur
The set of directions from a quadratic differential that diverge on average under Teichmuller geodesic flow has Hausdorff dimension exactly equal to one-half.
The set of non-uniquely ergodic d-IETs has Hausdorff codimension 1/2
Jon Chaika, Howard Masur
We show that the set of not uniquely ergodic d-IETs has Hausdorff dimension d-3/2 (in the (d-1)-dimension space of d-IETs) for d>4. For d=4 this was shown by Athreya-Chaika and for…