4 papers
Large genus asymptotics for frequency of non-simple curves
Mingkun Liu, Kasra Rafi, Juan Souto +1
We give an expression for the frequency of non-simple curves in closed surfaces and exploit it to study relative frequencies of such curves in large genus. This extend to the case…
Lengths of saddle connections on random translation surfaces of large genus
Howard Masur, Kasra Rafi, Anja Randecker
We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus tending to infinity, the number o…
Benjamini-Schramm limits of high genus translation surfaces: research announcement
Lewis Bowen, Kasra Rafi, Hunter Vallejos
We prove that the sequence of Masur-Smillie-Veech (MSV) distributed random translation surfaces, with area equal to genus, Benjamini-Schramm converges as genus tends to infinity. T…
Classification of Stable Surfaces with respect to Automatic Continuity
Mladen Bestvina, George Domat, Kasra Rafi
We provide a complete classification of when the homeomorphism group of a stable surface, , has the automatic continuity property: Any homomorphism from Homeo to a separa…