# Videos
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3. (talk by Howard Masur on joint work) Teichmuller Geodesics that Diverge on Average in Moduli Space (Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions March 2018) (abstract)

Given any quadratic differential the Hausdorff dimension of the divergent on average directions is 1/2.

2. Shouting Across the Void - Low Dimensional Orbit Closures in Hyperelliptic Components of Strata (Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions March 2018) (abstract)

Every orbit in a hyperelliptic component of a stratum of Abelian differentials is closed, dense, or contained in a locus of branched covers.

1. Marked Points, Hubbard and Earle-Kra, and Illumination (CMO BIRS Oaxaca 2016) (abstract)

Given a holomorphic family of Riemann surfaces is it possible to associate a holomorphically varying finite collection of points to each Riemann surface in the family? Hubbard showed that when the family is the entire moduli space of genus g Riemann surfaces this is possible only when g = 2 and the marked points are fixed points of the hyperelliptic involution. We will pose and resolve analogous questions for strata of translation surfaces with marked points. We will draw connections between GL(2,R)-invariant families of marked points on affine invariant submanifolds and holomorphically varying collections of points on closed totally geodesic families of Riemann surfaces. Finally we will discuss applications to billiard problems, specifically the finite blocking and illumination problems.