4 papers
Components of strata of k-differentials and their orbit closures
Paul Apisa, Juliet Aygun
We obtain a complete classification of components of strata of holomorphic and meromorphic k-differentials. We show that, when genus is at least two and outside of explicit excepti…
Counting geodesics on prime-order -differentials
Juliet Aygun
We determine weak asymptotics of counting functions on generic surfaces in a component of a stratum of -differentials when is prime and genus is greater than . In order t…
Realizing pairs of multicurves as cylinders on translation surfaces
Juliet Aygun, Janet Barkdoll, Aaron Calderon +2
Any pair of intersecting cylinders on a translation surface is "coherent," in that the geometric and algebraic intersection numbers of their core curves are equal (up to sign). In…
A degree theorem for the simplicial closure of Auter space
Juliet Aygun, Jeremy Miller
The degree of a based graph is the number of essential nonbasepoint vertices after generic perturbation. Hatcher--Vogtmann's degree theorem states that the subcomplex of Auter spac…