Anja Randecker (Heidelberg University) : Large-genus asymptotics for translation surfaces

Translation structures on surfaces can be obtained in many different ways: as suspensions of interval exchange transformations, from holomorphic differentials, as cotangent vectors to Teichmuller space, or by unfolding polygonal billiards. We ask how such translation surfaces generically look like for large genus.
In the talk, I give an overview on the question of large-genus asymptotics. The focus will be on Siegel-Veech constants and a joint result with Howard Masur and Kasra Rafi on the distribution of the number of short saddle connections.